def PlaneWave(CoordSystem="Cartesian",
default_time=0,
default_k0=1,
default_k1=1,
default_k2=1):
# Step 1: Set parameters defined in other modules
DIM = par.parval_from_str("grid::DIM")
# Step 2: Set up Cartesian coordinates in terms of the native CoordSystem we have chosen.
# E.g., if CoordSystem="Cartesian", then xxCart = [xx[0],xx[1],xx[2]]
# or if CoordSystem="Spherical", then xxCart = [xx[0]*sp.sin(xx[1])*sp.cos(xx[2]),
# xx[0]*sp.sin(xx[1])*sp.sin(xx[2]),
# xx[0]*sp.cos(xx[1])]
par.set_parval_from_str("reference_metric::CoordSystem", CoordSystem)
rfm.reference_metric()
xxCart = rfm.xxCart
# Step 3: Declare free parameters intrinsic to these initial data
time = par.Cparameters("REAL", thismodule, "time", default_time)
kk = par.Cparameters("REAL", thismodule, ["kk0", "kk1", "kk2"],
[default_k0, default_k1, default_k2])
# Step 4: Normalize the k vector
kk_norm_factor = sp.sqrt(kk[0]**2 + kk[1]**2 + kk[2]**2)
# Step 5: Compute k_norm.x
dot_product = sp.sympify(0)
for i in range(DIM):
dot_product += kk[i] * xxCart[i]
dot_product /= kk_norm_factor
# Step 6: Set initial data for uu and vv, where vv_ID = \partial_t uu_ID.
global uu_ID, vv_ID
uu_ID = sp.sin(dot_product - wavespeed * time) + 2
vv_ID = sp.diff(uu_ID, time)
def SphericalGaussian(CoordSystem="Cartesian",
default_time=0,
default_sigma=3):
# Step 1: Set parameters for the wave
DIM = par.parval_from_str("grid::DIM")
# Step 2: Set up Cartesian coordinates in terms of the native CoordSystem we have chosen.
# E.g., if CoordSystem="Cartesian", then xxCart = [xx[0],xx[1],xx[2]]
# or if CoordSystem="Spherical", then xxCart = [xx[0]*sp.sin(xx[1])*sp.cos(xx[2]),
# xx[0]*sp.sin(xx[1])*sp.sin(xx[2]),
# xx[0]*sp.cos(xx[1])]
par.set_parval_from_str("reference_metric::CoordSystem", CoordSystem)
rfm.reference_metric() # Must call this function to specify rfm.xxCart
xxCart = rfm.xxCart
# Step 3: Declare free parameters intrinsic to these initial data
time = par.Cparameters("REAL", thismodule, "time", default_time)
sigma = par.Cparameters("REAL", thismodule, "sigma", default_sigma)
# Step 4: Compute r
r = sp.sympify(0)
for i in range(DIM):
r += xxCart[i]**2
r = sp.sqrt(r)
# Step 5: Set initial data for uu and vv, where vv_ID = \partial_t uu_ID.
global uu_ID, vv_ID
# uu_ID = (r - wavespeed*time)/r * sp.exp(- (r - wavespeed*time)**2 / (2*sigma**2) )
uu_ID = (+(r - wavespeed * time) / r * sp.exp(-(r - wavespeed * time)**2 /
(2 * sigma**2)) +
(r + wavespeed * time) / r * sp.exp(-(r + wavespeed * time)**2 /
(2 * sigma**2)))
vv_ID = sp.diff(uu_ID, time)
def u4U_in_terms_of_ValenciavU__rescale_ValenciavU_by_applying_speed_limit(
alpha, betaU, gammaDD, ValenciavU):
# Inputs: Metric lapse alpha, shift betaU, 3-metric gammaDD, Valencia 3-velocity ValenciavU
# Outputs (as globals): u4U_ito_ValenciavU, rescaledValenciavU
# R = gamma_{ij} v^i v^j
R = sp.sympify(0)
for i in range(3):
for j in range(3):
R += gammaDD[i][j] * ValenciavU[i] * ValenciavU[j]
thismodule = __name__
# The default value isn't terribly important here, since we can overwrite in the main C code
GAMMA_SPEED_LIMIT = par.Cparameters("REAL", thismodule,
"GAMMA_SPEED_LIMIT",
10.0) # Default value based on
# IllinoisGRMHD.
# GiRaFFE default = 2000.0
Rmax = 1 - 1 / (GAMMA_SPEED_LIMIT * GAMMA_SPEED_LIMIT)
# Now, we set Rstar = min(Rmax,R):
# If R < Rmax, then Rstar = 0.5*(Rmax+R-Rmax+R) = R
# If R >= Rmax, then Rstar = 0.5*(Rmax+R+Rmax-R) = Rmax
Rstar = sp.Rational(1, 2) * (Rmax + R - nrpyAbs(Rmax - R))
# We add TINYDOUBLE to R below to avoid a 0/0, which occurs when
# ValenciavU == 0 for all Valencia 3-velocity components.
# "Those tiny *doubles* make me warm all over
# with a feeling that I'm gonna love you till the end of time."
# - Adapted from Connie Francis' "Tiny Bubbles"
TINYDOUBLE = par.Cparameters("#define", thismodule, "TINYDOUBLE", 1e-100)
# The rescaled (speed-limited) Valencia 3-velocity
# is given by, v_{(n)}^i = sqrt{Rstar/R} v^i
global rescaledValenciavU
rescaledValenciavU = ixp.zerorank1()
for i in range(3):
# If R == 0, then Rstar == 0, so sqrt( Rstar/(R+TINYDOUBLE) )=sqrt(0/1e-100) = 0
# If your velocities are of order 1e-100 and this is physically
# meaningful, there must be something wrong with your unit conversion.
rescaledValenciavU[i] = ValenciavU[i] * sp.sqrt(Rstar /
(R + TINYDOUBLE))
# Finally compute u^mu in terms of Valenciav^i
# u^0 = 1/(alpha-sqrt(1-R^*))
global u4U_ito_ValenciavU
u4U_ito_ValenciavU = ixp.zerorank1(DIM=4)
u4U_ito_ValenciavU[0] = 1 / (alpha * sp.sqrt(1 - Rstar))
# u^i = u^0 ( alpha v^i_{(n)} - beta^i ), where v^i_{(n)} is the Valencia 3-velocity
for i in range(3):
u4U_ito_ValenciavU[i + 1] = u4U_ito_ValenciavU[0] * (
alpha * rescaledValenciavU[i] - betaU[i])
def BrillLindquist(ComputeADMGlobalsOnly=False):
global Cartxyz, gammaCartDD, KCartDD, alphaCart, betaCartU, BCartU
# Step 2: Setting up Brill-Lindquist initial data
thismodule = "Brill-Lindquist"
BH1_posn_x, BH1_posn_y, BH1_posn_z = par.Cparameters(
"REAL", thismodule, ["BH1_posn_x", "BH1_posn_y", "BH1_posn_z"])
BH1_mass = par.Cparameters("REAL", thismodule, ["BH1_mass"])
BH2_posn_x, BH2_posn_y, BH2_posn_z = par.Cparameters(
"REAL", thismodule, ["BH2_posn_x", "BH2_posn_y", "BH2_posn_z"])
BH2_mass = par.Cparameters("REAL", thismodule, ["BH2_mass"])
# Step 2.a: Set spatial dimension (must be 3 for BSSN)
DIM = 3
par.set_parval_from_str("grid::DIM", DIM)
global Cartxyz, gammaCartDD, KCartDD, alphaCart, betaCartU, BCartU
Cartxyz = ixp.declarerank1("Cartxyz")
# Step 2.b: Set psi, the conformal factor:
psi = sp.sympify(1)
psi += BH1_mass / (2 * sp.sqrt((Cartxyz[0] - BH1_posn_x)**2 +
(Cartxyz[1] - BH1_posn_y)**2 +
(Cartxyz[2] - BH1_posn_z)**2))
psi += BH2_mass / (2 * sp.sqrt((Cartxyz[0] - BH2_posn_x)**2 +
(Cartxyz[1] - BH2_posn_y)**2 +
(Cartxyz[2] - BH2_posn_z)**2))
# Step 2.c: Set all needed ADM variables in Cartesian coordinates
gammaCartDD = ixp.zerorank2()
KCartDD = ixp.zerorank2() # K_{ij} = 0 for these initial data
for i in range(DIM):
gammaCartDD[i][i] = psi**4
alphaCart = 1 / psi**2
betaCartU = ixp.zerorank1(
) # We generally choose \beta^i = 0 for these initial data
BCartU = ixp.zerorank1(
) # We generally choose B^i = 0 for these initial data
if ComputeADMGlobalsOnly == True:
return
cf,hDD,lambdaU,aDD,trK,alpha,vetU,betU = \
AtoB.Convert_Spherical_or_Cartesian_ADM_to_BSSN_curvilinear("Cartesian",Cartxyz,
gammaCartDD,KCartDD,alphaCart,betaCartU,BCartU)
global returnfunction
returnfunction = bIDf.BSSN_ID_function_string(cf, hDD, lambdaU, aDD, trK,
alpha, vetU, betU)
def MaxwellCartesian_ID():
DIM = par.parval_from_str("grid::DIM")
x, y, z = gri.register_gridfunctions("AUX", ["x", "y", "z"])
gammaDD = ixp.register_gridfunctions_for_single_rank2("AUX","gammaDD", "sym01") # The AUX or EVOL designation is *not*
# used in diagnostic modules.
# Step 1: Declare free parameters intrinsic to these initial data
amp,lam = par.Cparameters("REAL",__name__,["amp","lam"], [1.0,1.0]) # __name__ = "MaxwellCartesian_ID", this module's name
# Step 2: Set the initial data
system = par.parval_from_str("System_to_use")
if system == "System_I" or system == "System_II":
global AidD,EidD,psi_ID
AidD = ixp.zerorank1()
EidD = ixp.zerorank1()
EidU = ixp.zerorank1()
# Set the coordinate transformations:
radial = sp.sqrt(x*x + y*y + z*z)
polar = sp.atan2(sp.sqrt(x*x + y*y),z)
EU_phi = 8*amp*radial*sp.sin(polar)*lam*lam*sp.exp(-lam*radial*radial)
EidU[0] = -(y * EU_phi)/sp.sqrt(x*x + y*y)
EidU[1] = (x * EU_phi)/sp.sqrt(x*x + y*y)
# The z component (2)is zero.
for i in range(DIM):
for j in range(DIM):
EidD[i] += gammaDD[i][j] * EidU[j]
psi_ID = sp.sympify(0)
if system == "System_II":
global Gamma_ID
Gamma_ID = sp.sympify(0)
else:
print("Invalid choice of system: System_to_use must be either System_I or System_II")
def BSSN_source_terms_for_BSSN_constraints(custom_T4UU=None):
global sourceterm_H, sourceterm_MU
# Step 4.a: Call BSSN_source_terms_ito_T4UU to get SDD, SD, S, & rho
if custom_T4UU == "unrescaled BSSN source terms already given":
SDD = ixp.declarerank2("SDD", "sym01")
SD = ixp.declarerank1("SD")
S = sp.symbols("S", real=True)
rho = sp.symbols("rho", real=True)
else:
SDD, SD, S, rho = stress_energy_source_terms_ito_T4UU_and_ADM_or_BSSN_metricvars(
"BSSN", custom_T4UU)
PI = par.Cparameters("REAL", thismodule, ["PI"],
"3.14159265358979323846264338327950288")
# Step 4.b: Add source term to the Hamiltonian constraint H
sourceterm_H = -16 * PI * rho
# Step 4.c: Add source term to the momentum constraint M^i
# Step 4.c.i: Compute gammaUU in terms of BSSN quantities
import BSSN.ADM_in_terms_of_BSSN as AitoB
AitoB.ADM_in_terms_of_BSSN() # Provides gammaUU
# Step 4.c.ii: Raise S_i
SU = ixp.zerorank1()
for i in range(3):
for j in range(3):
SU[i] += AitoB.gammaUU[i][j] * SD[j]
# Step 4.c.iii: Add source term to momentum constraint & rescale:
sourceterm_MU = ixp.zerorank1()
for i in range(3):
sourceterm_MU[i] = -8 * PI * SU[i] / rfm.ReU[i]
def TOV_ADM_T4UUmunu(ComputeADMT4UUmunuGlobalsOnly=False):
global Sph_r_th_ph, r, th, ph, gammaSphDD, KSphDD, alphaSph, betaSphU, BSphU, T4UU
# All gridfunctions will be written in terms of spherical coordinates (r, th, ph):
r, th, ph = sp.symbols('r th ph', real=True)
thismodule = "TOV"
DIM = 3
par.set_parval_from_str("grid::DIM", DIM)
# Input parameters read in from the TOV data file:
rbar, expnu, exp4phi, P, rho = par.Cparameters(
"REAL", thismodule, ["rbar", "expnu", "exp4phi", "P", "rho"],
[1e300, 1e300, 1e300, 1e300, 1e300]) # Must be read from TOV data
# file; set to crazy values to ensure this
# Step 4.2: Construct ADM quantities:
# *** The physical spatial metric in spherical basis ***
# In isotropic coordinates,
# gamma_{ij} = e^{4 phi} eta_{ij},
# where eta is the flat-space 3-metric in spherical coordinates
gammaSphDD = ixp.zerorank2()
gammaSphDD[0][0] = exp4phi
gammaSphDD[1][1] = exp4phi * rbar**2
gammaSphDD[2][2] = exp4phi * rbar**2 * sp.sin(th)**2
# *** The extrinsic curvature in spherical basis ***
# K_{ij} = 0 for the TOV solution
KSphDD = ixp.zerorank2()
# *** The lapse and shift in spherical basis ***
# alpha = exp^{nu/2} for the TOV solution
# \beta^i = 0 for the TOV solution
alphaSph = sp.sqrt(expnu)
betaSphU = ixp.zerorank1()
BSphU = ixp.zerorank1()
# Step 4.3: Construct T^{mu nu}:
T4UU = ixp.zerorank2(DIM=4)
# T^tt = e^(-nu) * rho
T4UU[0][0] = rho / expnu
# T^{ii} = P / gamma_{ii}
for i in range(3):
T4UU[i + 1][i + 1] = P / gammaSphDD[i][i]
if ComputeADMT4UUmunuGlobalsOnly == True:
return
Sph_r_th_ph = [r, th, ph]
cf, hDD, lambdaU, aDD, trK, alpha, vetU, betU = \
AtoB.Convert_Spherical_or_Cartesian_ADM_to_BSSN_curvilinear("Spherical", Sph_r_th_ph,
gammaSphDD, KSphDD, alphaSph, betaSphU, BSphU)
sDD, sD, S, rho = \
AtoB.Convert_Spherical_or_Cartesian_T4UUmunu_to_BSSN_curvilinear("Spherical", Sph_r_th_ph, T4UU)
global returnfunction
returnfunction = bIDf.BSSN_ID_function_string(cf, hDD, lambdaU, aDD, trK,
alpha, vetU, betU)
def compute_u0_noif(gammaDD, alpha, ValenciavU):
# Inputs: Metric gammaDD, lapse alpha, Valencia 3-velocity ValenciavU
# Outputs: u^0, speed-limited ValenciavU
# R = gamma_{ij} v^i v^j
R = par.Cparameters("#define", thismodule, "TINYDOUBLE", 1e-100)
# We initialize R to TINYDOUBLE instead of 0 to avoid a 0/0 below,
# in the case that ValenciavU == 0 for all Valencia 3-velocities.
# "Those tiny *doubles* make me warm all over
# with a feeling that I'm gonna love you till the end of time."
# - Adapted from Connie Francis' "Tiny Bubbles"
for i in range(DIM):
for j in range(DIM):
R += gammaDD[i][j] * ValenciavU[i] * ValenciavU[j]
# The default value isn't terribly important here, since we'll overwrite in the main C code
GAMMA_SPEED_LIMIT = par.Cparameters("REAL", thismodule,
"GAMMA_SPEED_LIMIT",
10.0) # Default value based on
# IllinoisGRMHD.
# GiRaFFE default = 2000.0
# Rmax = 1 - 1/Gamma_{\max}^2
Rmax = 1 - 1 / (GAMMA_SPEED_LIMIT * GAMMA_SPEED_LIMIT)
# Now, we set Rmax = min(Rmax,R):
# If Rmax>R, then Rmax = 0.5*(Rmax+R-Rmax+R) = R
# If R>Rmax, then Rmax = 0.5*(Rmax+R+Rmax-R) = Rmax
# If R==TINYDOUBLE, then Rmax = 0.5*(Rmax-Rmax) = 0, since, e.g., 10 +/- 1e-100 = 10 exactly in double precision
Rmax = sp.Rational(1, 2) * (Rmax + R - sp.Abs(Rmax - R))
# With our rescaled Rmax, v^i = sqrt{Rmax/R} v^i
global rescaledValenciavU, rescaledu0
rescaledValenciavU = ixp.zerorank1()
for i in range(DIM):
# If R == TINYDOUBLE, then Rmax=0,R=1e-100, and we get Rmax/R=0.
# If your velocities are of order 1e-100 and this is physically
# meaningful, there must be something wrong with your unit conversion.
rescaledValenciavU[i] = ValenciavU[i] * sp.sqrt(Rmax / R)
# We stick with the "rescaled" version since we redefine Rmax as detailed above
# u^0 = 1/(alpha-sqrt(1-R_{\max}))
rescaledu0 = 1 / (alpha * sp.sqrt(1 - Rmax))
def BSSN_source_terms_for_BSSN_RHSs(custom_T4UU=None):
global sourceterm_trK_rhs, sourceterm_a_rhsDD, sourceterm_lambda_rhsU, sourceterm_Lambdabar_rhsU
# Step 3.a: Call BSSN_source_terms_ito_T4UU to get SDD, SD, S, & rho
if custom_T4UU == "unrescaled BSSN source terms already given":
SDD = ixp.declarerank2("SDD", "sym01")
SD = ixp.declarerank1("SD")
S = sp.symbols("S", real=True)
rho = sp.symbols("rho", real=True)
else:
SDD, SD, S, rho = stress_energy_source_terms_ito_T4UU_and_ADM_or_BSSN_metricvars(
"BSSN", custom_T4UU)
PI = par.Cparameters("REAL", thismodule, ["PI"],
"3.14159265358979323846264338327950288")
alpha = sp.symbols("alpha", real=True)
# Step 3.b: trK_rhs
sourceterm_trK_rhs = 4 * PI * alpha * (rho + S)
# Step 3.c: Abar_rhsDD:
# Step 3.c.i: Compute trace-free part of S_{ij}:
import BSSN.BSSN_quantities as Bq
Bq.BSSN_basic_tensors() # Sets gammabarDD
gammabarUU, dummydet = ixp.symm_matrix_inverter3x3(
Bq.gammabarDD) # Set gammabarUU
tracefree_SDD = ixp.zerorank2()
for i in range(3):
for j in range(3):
tracefree_SDD[i][j] = SDD[i][j]
for i in range(3):
for j in range(3):
for k in range(3):
for m in range(3):
tracefree_SDD[i][j] += -sp.Rational(1, 3) * Bq.gammabarDD[
i][j] * gammabarUU[k][m] * SDD[k][m]
# Step 3.c.ii: Define exp_m4phi = e^{-4 phi}
Bq.phi_and_derivs()
# Step 3.c.iii: Evaluate stress-energy part of AbarDD's RHS
sourceterm_a_rhsDD = ixp.zerorank2()
for i in range(3):
for j in range(3):
Abar_rhsDDij = -8 * PI * alpha * Bq.exp_m4phi * tracefree_SDD[i][j]
sourceterm_a_rhsDD[i][j] = Abar_rhsDDij / rfm.ReDD[i][j]
# Step 3.d: Stress-energy part of Lambdabar_rhsU = stressenergy_Lambdabar_rhsU
sourceterm_Lambdabar_rhsU = ixp.zerorank1()
for i in range(3):
for j in range(3):
sourceterm_Lambdabar_rhsU[
i] += -16 * PI * alpha * gammabarUU[i][j] * SD[j]
sourceterm_lambda_rhsU = ixp.zerorank1()
for i in range(3):
sourceterm_lambda_rhsU[i] = sourceterm_Lambdabar_rhsU[i] / rfm.ReU[i]
def generate_C_code_for_Stilde_flux(out_dir,inputs_provided = False, alpha_face=None, gamma_faceDD=None, beta_faceU=None,
Valenciav_rU=None, B_rU=None, Valenciav_lU=None, B_lU=None, sqrt4pi=None,
outCparams = "outCverbose=False,CSE_sorting=none"):
if not inputs_provided:
# We will pass values of the gridfunction on the cell faces into the function. This requires us
# to declare them as C parameters in NRPy+. We will denote this with the _face infix/suffix.
alpha_face = gri.register_gridfunctions("AUXEVOL","alpha_face")
gamma_faceDD = ixp.register_gridfunctions_for_single_rank2("AUXEVOL","gamma_faceDD","sym01")
beta_faceU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL","beta_faceU")
# We'll need some more gridfunctions, now, to represent the reconstructions of BU and ValenciavU
# on the right and left faces
Valenciav_rU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL","Valenciav_rU",DIM=3)
B_rU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL","B_rU",DIM=3)
Valenciav_lU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL","Valenciav_lU",DIM=3)
B_lU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL","B_lU",DIM=3)
sqrt4pi = par.Cparameters("REAL",thismodule,"sqrt4pi","sqrt(4.0*M_PI)")
for flux_dirn in range(3):
calculate_Stilde_flux(flux_dirn,alpha_face,gamma_faceDD,beta_faceU,\
Valenciav_rU,B_rU,Valenciav_lU,B_lU,sqrt4pi)
Stilde_flux_to_print = [\
Stilde_fluxD[0],\
Stilde_fluxD[1],\
Stilde_fluxD[2],\
]
Stilde_flux_names = [\
"Stilde_fluxD0",\
"Stilde_fluxD1",\
"Stilde_fluxD2",\
]
desc = "Compute the flux of all 3 components of tilde{S}_i on the right face in the " + str(flux_dirn) + "."
name = "calculate_Stilde_flux_D" + str(flux_dirn) + "_right"
outCfunction(
outfile = os.path.join(out_dir,name+".h"), desc=desc, name=name,
params ="const paramstruct *params,const REAL *auxevol_gfs,REAL *rhs_gfs",
body = Memory_Read \
+outputC(Stilde_flux_to_print,Stilde_flux_names,"returnstring",params=outCparams).replace("IDX4","IDX4S")\
+Memory_Write.replace(invdx[0],invdx[flux_dirn]),
loopopts ="InteriorPoints",
rel_path_for_Cparams=os.path.join("../"))
desc = "Compute the flux of all 3 components of tilde{S}_i on the left face in the " + str(flux_dirn) + "."
name = "calculate_Stilde_flux_D" + str(flux_dirn) + "_left"
outCfunction(
outfile = os.path.join(out_dir,name+".h"), desc=desc, name=name,
params ="const paramstruct *params,const REAL *auxevol_gfs,REAL *rhs_gfs",
body = Memory_Read.replace(indices[flux_dirn],indicesp1[flux_dirn]) \
+outputC(Stilde_flux_to_print,Stilde_flux_names,"returnstring",params=outCparams).replace("IDX4","IDX4S")\
+Memory_Write.replace(invdx[0],invdx[flux_dirn]).replace(assignment,assignmentp1),
loopopts ="InteriorPoints",
rel_path_for_Cparams=os.path.join("../"))
def InitialData_PlaneWave():
# Step 1: Set parameters defined in other modules
wavespeed = swrhs.wavespeed
DIM = par.parval_from_str("grid::DIM")
xx = gri.xx
# Step 2: Declare free parameters intrinsic to these initial data
time = par.Cparameters("REAL", thismodule, "time")
kk = par.Cparameters("REAL", thismodule, ["kk0", "kk1", "kk2"])
# Step 3: Normalize the k vector
kk_norm = sp.sqrt(kk[0]**2 + kk[1]**2 + kk[2]**2)
# Step 4: Compute k.x
dot_product = sp.sympify(0)
for i in range(DIM):
dot_product += xx[i] * kk[i]
dot_product /= kk_norm
# Step 5: Set initial data for uu and vv, where vv_ID = \partial_t uu_ID.
global uu_ID, vv_ID
uu_ID = sp.sin(dot_product - wavespeed * time) + 2
vv_ID = sp.diff(uu_ID, time)
def GiRaFFEfood_NRPy_1D_tests(ID_type="DegenAlfvenWave", stagger_enable=False):
global AD, ValenciaVU
AD = ixp.zerorank1()
if ID_type == "DegenAlfvenWave":
mu_DAW = par.Cparameters("REAL", thismodule, ["mu_DAW"],
-0.5) # The wave speed
AD = Axyz_func(Ax_DAW,
Ay_DAW,
Az_DAW,
stagger_enable,
gammamu=sp.sympify(1) /
sp.sqrt(sp.sympify(1) - mu_AW**2))
ValenciaVU = ValenciavU_DAW(mu_DAW=mu_DAW, gammamu=gammamu)
elif ID_type == "FastWave":
AD = Axyz_func(Ax_FW, Ay_FW, Az_FW, stagger_enable)
ValenciaVU = ValenciavU_FW()
def add_to_Cfunction_dict__AD_gauge_term_psi6Phi_fin_diff(includes=None):
xi_damping = par.Cparameters("REAL",thismodule,"xi_damping",0.1)
GRFFE.compute_psi6Phi_rhs_damping_term(alpha,psi6Phi,xi_damping)
AevolParen_dD = ixp.declarerank1("AevolParen_dD",DIM=3)
PhievolParenU_dD = ixp.declarerank2("PhievolParenU_dD","nosym",DIM=3)
A_rhsD = ixp.zerorank1()
psi6Phi_rhs = GRFFE.psi6Phi_damping
for i in range(3):
A_rhsD[i] += -AevolParen_dD[i]
psi6Phi_rhs += -PhievolParenU_dD[i][i]
# Add Kreiss-Oliger dissipation to the GRFFE RHSs:
# psi6Phi_dKOD = ixp.declarerank1("psi6Phi_dKOD")
# AD_dKOD = ixp.declarerank2("AD_dKOD","nosym")
# for i in range(3):
# psi6Phi_rhs += diss_strength*psi6Phi_dKOD[i]*rfm.ReU[i] # ReU[i] = 1/scalefactor_orthog_funcform[i]
# for j in range(3):
# A_rhsD[j] += diss_strength*AD_dKOD[j][i]*rfm.ReU[i] # ReU[i] = 1/scalefactor_orthog_funcform[i]
RHSs_to_print = [
lhrh(lhs=gri.gfaccess("rhs_gfs","AD0"),rhs=A_rhsD[0]),
lhrh(lhs=gri.gfaccess("rhs_gfs","AD1"),rhs=A_rhsD[1]),
lhrh(lhs=gri.gfaccess("rhs_gfs","AD2"),rhs=A_rhsD[2]),
lhrh(lhs=gri.gfaccess("rhs_gfs","psi6Phi"),rhs=psi6Phi_rhs),
]
desc = "Calculate AD gauge term and psi6Phi RHSs"
name = "calculate_AD_gauge_psi6Phi_RHSs"
params ="const paramstruct *params,const REAL *in_gfs,const REAL *auxevol_gfs,REAL *rhs_gfs"
body = fin.FD_outputC("returnstring",RHSs_to_print,params=outCparams)
loopopts ="InteriorPoints"
add_to_Cfunction_dict(
includes=includes,
desc=desc,
name=name, params=params,
body=body, loopopts=loopopts)
outC_function_dict[name] = outC_function_dict[name].replace("= NGHOSTS","= NGHOSTS_A2B").replace("NGHOSTS+Nxx0","Nxx_plus_2NGHOSTS0-NGHOSTS_A2B").replace("NGHOSTS+Nxx1","Nxx_plus_2NGHOSTS1-NGHOSTS_A2B").replace("NGHOSTS+Nxx2","Nxx_plus_2NGHOSTS2-NGHOSTS_A2B")
def calculate_Stilde_flux(flux_dirn,inputs_provided=True,alpha_face=None,gamma_faceDD=None,beta_faceU=None,\
Valenciav_rU=None,B_rU=None,Valenciav_lU=None,B_lU=None,sqrt4pi=None):
if not inputs_provided:
# We will pass values of the gridfunction on the cell faces into the function. This requires us
# to declare them as C parameters in NRPy+. We will denote this with the _face infix/suffix.
alpha_face = gri.register_gridfunctions("AUXEVOL", "alpha_face")
gamma_faceDD = ixp.register_gridfunctions_for_single_rank2(
"AUXEVOL", "gamma_faceDD", "sym01")
beta_faceU = ixp.register_gridfunctions_for_single_rank1(
"AUXEVOL", "beta_faceU")
# We'll need some more gridfunctions, now, to represent the reconstructions of BU and ValenciavU
# on the right and left faces
Valenciav_rU = ixp.register_gridfunctions_for_single_rank1(
"AUXEVOL", "Valenciav_rU", DIM=3)
B_rU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL",
"B_rU",
DIM=3)
Valenciav_lU = ixp.register_gridfunctions_for_single_rank1(
"AUXEVOL", "Valenciav_lU", DIM=3)
B_lU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL",
"B_lU",
DIM=3)
sqrt4pi = par.Cparameters("REAL", thismodule, "sqrt4pi",
"sqrt(4.0*M_PI)")
find_cmax_cmin(flux_dirn, gamma_faceDD, beta_faceU, alpha_face)
global Stilde_fluxD
Stilde_fluxD = ixp.zerorank3()
for mom_comp in range(3):
calculate_GRFFE_Tmunu_and_contractions(flux_dirn, mom_comp, gamma_faceDD,beta_faceU,alpha_face,\
Valenciav_rU,B_rU,sqrt4pi)
Fr = F
Ur = U
calculate_GRFFE_Tmunu_and_contractions(flux_dirn, mom_comp, gamma_faceDD,beta_faceU,alpha_face,\
Valenciav_lU,B_lU,sqrt4pi)
Fl = F
Ul = U
Stilde_fluxD[mom_comp] = HLLE_solver(cmax, cmin, Fr, Fl, Ur, Ul)
# License: BSD 2-Clause
# COMPLETE DOCUMENTATION (JUPYTER NOTEBOOKS):
# START PAGE (start here!): ../NRPy+_Tutorial.ipynb
# THIS MODULE: ../Tutorial-VacuumMaxwell_Flat_Cartesian_ID.ipynb
# Step P1: Import needed NRPy+ core modules:
import NRPy_param_funcs as par # NRPy+: Parameter interface
# The name of this module ("CommonParams") is given by __name__:
thismodule = __name__
# Parameters common to/needed by all VacuumMaxwell Python modules
# Step P2: Define the C parameters amp, lam, time, and wavespeed.
# These variables proper SymPy variables, so they can be
# used in SymPy expressions. In the C code, it acts
# just like a usual parameter, whose value is
# specified in the parameter file.
# amplitude
amp = par.Cparameters("REAL", thismodule, "amp", default_vals=1.0)
# lambda
lam = par.Cparameters("REAL", thismodule, "lam", default_vals=1.0)
time = par.Cparameters("REAL", thismodule, "time", default_vals=0.0)
wavespeed = par.Cparameters("REAL", thismodule, "wavespeed", default_vals=1.0)
def GiRaFFE_NRPy_Main_Driver_generate_all(out_dir):
cmd.mkdir(out_dir)
gammaDD = ixp.register_gridfunctions_for_single_rank2("AUXEVOL",
"gammaDD",
"sym01",
DIM=3)
betaU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL",
"betaU",
DIM=3)
alpha = gri.register_gridfunctions("AUXEVOL", "alpha")
AD = ixp.register_gridfunctions_for_single_rank1("EVOL", "AD")
BU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL", "BU")
ValenciavU = ixp.register_gridfunctions_for_single_rank1(
"AUXEVOL", "ValenciavU")
psi6Phi = gri.register_gridfunctions("EVOL", "psi6Phi")
StildeD = ixp.register_gridfunctions_for_single_rank1("EVOL", "StildeD")
ixp.register_gridfunctions_for_single_rank1("AUXEVOL",
"PhievolParenU",
DIM=3)
gri.register_gridfunctions("AUXEVOL", "AevolParen")
# Declare this symbol:
sqrt4pi = par.Cparameters("REAL", thismodule, "sqrt4pi", "sqrt(4.0*M_PI)")
GRHD.compute_sqrtgammaDET(gammaDD)
GRFFE.compute_AD_source_term_operand_for_FD(GRHD.sqrtgammaDET, betaU,
alpha, psi6Phi, AD)
GRFFE.compute_psi6Phi_rhs_flux_term_operand(gammaDD, GRHD.sqrtgammaDET,
betaU, alpha, AD, psi6Phi)
parens_to_print = [\
lhrh(lhs=gri.gfaccess("auxevol_gfs","AevolParen"),rhs=GRFFE.AevolParen),\
lhrh(lhs=gri.gfaccess("auxevol_gfs","PhievolParenU0"),rhs=GRFFE.PhievolParenU[0]),\
lhrh(lhs=gri.gfaccess("auxevol_gfs","PhievolParenU1"),rhs=GRFFE.PhievolParenU[1]),\
lhrh(lhs=gri.gfaccess("auxevol_gfs","PhievolParenU2"),rhs=GRFFE.PhievolParenU[2]),\
]
subdir = "RHSs"
cmd.mkdir(os.path.join(out_dir, subdir))
desc = "Calculate quantities to be finite-differenced for the GRFFE RHSs"
name = "calculate_AD_gauge_term_psi6Phi_flux_term_for_RHSs"
outCfunction(
outfile=os.path.join(out_dir, subdir, name + ".h"),
desc=desc,
name=name,
params=
"const paramstruct *restrict params,const REAL *restrict in_gfs,REAL *restrict auxevol_gfs",
body=fin.FD_outputC("returnstring", parens_to_print,
params=outCparams).replace("IDX4", "IDX4S"),
loopopts="AllPoints",
rel_path_for_Cparams=os.path.join("../"))
xi_damping = par.Cparameters("REAL", thismodule, "xi_damping", 0.1)
GRFFE.compute_psi6Phi_rhs_damping_term(alpha, psi6Phi, xi_damping)
AevolParen_dD = ixp.declarerank1("AevolParen_dD", DIM=3)
PhievolParenU_dD = ixp.declarerank2("PhievolParenU_dD", "nosym", DIM=3)
A_rhsD = ixp.zerorank1()
psi6Phi_rhs = GRFFE.psi6Phi_damping
for i in range(3):
A_rhsD[i] += -AevolParen_dD[i]
psi6Phi_rhs += -PhievolParenU_dD[i][i]
# Add Kreiss-Oliger dissipation to the GRFFE RHSs:
# psi6Phi_dKOD = ixp.declarerank1("psi6Phi_dKOD")
# AD_dKOD = ixp.declarerank2("AD_dKOD","nosym")
# for i in range(3):
# psi6Phi_rhs += diss_strength*psi6Phi_dKOD[i]*rfm.ReU[i] # ReU[i] = 1/scalefactor_orthog_funcform[i]
# for j in range(3):
# A_rhsD[j] += diss_strength*AD_dKOD[j][i]*rfm.ReU[i] # ReU[i] = 1/scalefactor_orthog_funcform[i]
RHSs_to_print = [\
lhrh(lhs=gri.gfaccess("rhs_gfs","AD0"),rhs=A_rhsD[0]),\
lhrh(lhs=gri.gfaccess("rhs_gfs","AD1"),rhs=A_rhsD[1]),\
lhrh(lhs=gri.gfaccess("rhs_gfs","AD2"),rhs=A_rhsD[2]),\
lhrh(lhs=gri.gfaccess("rhs_gfs","psi6Phi"),rhs=psi6Phi_rhs),\
]
desc = "Calculate AD gauge term and psi6Phi RHSs"
name = "calculate_AD_gauge_psi6Phi_RHSs"
source_Ccode = outCfunction(
outfile="returnstring",
desc=desc,
name=name,
params=
"const paramstruct *params,const REAL *in_gfs,const REAL *auxevol_gfs,REAL *rhs_gfs",
body=fin.FD_outputC("returnstring", RHSs_to_print,
params=outCparams).replace("IDX4", "IDX4S"),
loopopts="InteriorPoints",
rel_path_for_Cparams=os.path.join("../")).replace(
"= NGHOSTS", "= NGHOSTS_A2B").replace(
"NGHOSTS+Nxx0", "Nxx_plus_2NGHOSTS0-NGHOSTS_A2B").replace(
"NGHOSTS+Nxx1", "Nxx_plus_2NGHOSTS1-NGHOSTS_A2B").replace(
"NGHOSTS+Nxx2", "Nxx_plus_2NGHOSTS2-NGHOSTS_A2B")
# Note the above .replace() functions. These serve to expand the loop range into the ghostzones, since
# the second-order FD needs fewer than some other algorithms we use do.
with open(os.path.join(out_dir, subdir, name + ".h"), "w") as file:
file.write(source_Ccode)
source.write_out_functions_for_StildeD_source_term(
os.path.join(out_dir, subdir), outCparams, gammaDD, betaU, alpha,
ValenciavU, BU, sqrt4pi)
subdir = "FCVAL"
cmd.mkdir(os.path.join(out_dir, subdir))
FCVAL.GiRaFFE_NRPy_FCVAL(os.path.join(out_dir, subdir))
subdir = "PPM"
cmd.mkdir(os.path.join(out_dir, subdir))
PPM.GiRaFFE_NRPy_PPM(os.path.join(out_dir, subdir))
# We will pass values of the gridfunction on the cell faces into the function. This requires us
# to declare them as C parameters in NRPy+. We will denote this with the _face infix/suffix.
alpha_face = gri.register_gridfunctions("AUXEVOL", "alpha_face")
gamma_faceDD = ixp.register_gridfunctions_for_single_rank2(
"AUXEVOL", "gamma_faceDD", "sym01")
beta_faceU = ixp.register_gridfunctions_for_single_rank1(
"AUXEVOL", "beta_faceU")
# We'll need some more gridfunctions, now, to represent the reconstructions of BU and ValenciavU
# on the right and left faces
Valenciav_rU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL",
"Valenciav_rU",
DIM=3)
B_rU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL",
"B_rU",
DIM=3)
Valenciav_lU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL",
"Valenciav_lU",
DIM=3)
B_lU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL",
"B_lU",
DIM=3)
subdir = "RHSs"
Af.GiRaFFE_NRPy_Afield_flux(os.path.join(out_dir, subdir))
Sf.generate_C_code_for_Stilde_flux(os.path.join(out_dir,
subdir), True, alpha_face,
gamma_faceDD, beta_faceU, Valenciav_rU,
B_rU, Valenciav_lU, B_lU, sqrt4pi)
subdir = "boundary_conditions"
cmd.mkdir(os.path.join(out_dir, subdir))
BC.GiRaFFE_NRPy_BCs(os.path.join(out_dir, subdir))
subdir = "A2B"
cmd.mkdir(os.path.join(out_dir, subdir))
A2B.GiRaFFE_NRPy_A2B(os.path.join(out_dir, subdir), gammaDD, AD, BU)
C2P_P2C.GiRaFFE_NRPy_C2P(StildeD, BU, gammaDD, betaU, alpha)
values_to_print = [\
lhrh(lhs=gri.gfaccess("in_gfs","StildeD0"),rhs=C2P_P2C.outStildeD[0]),\
lhrh(lhs=gri.gfaccess("in_gfs","StildeD1"),rhs=C2P_P2C.outStildeD[1]),\
lhrh(lhs=gri.gfaccess("in_gfs","StildeD2"),rhs=C2P_P2C.outStildeD[2]),\
lhrh(lhs=gri.gfaccess("auxevol_gfs","ValenciavU0"),rhs=C2P_P2C.ValenciavU[0]),\
lhrh(lhs=gri.gfaccess("auxevol_gfs","ValenciavU1"),rhs=C2P_P2C.ValenciavU[1]),\
lhrh(lhs=gri.gfaccess("auxevol_gfs","ValenciavU2"),rhs=C2P_P2C.ValenciavU[2])\
]
subdir = "C2P"
cmd.mkdir(os.path.join(out_dir, subdir))
desc = "Apply fixes to \tilde{S}_i and recompute the velocity to match with current sheet prescription."
name = "GiRaFFE_NRPy_cons_to_prims"
outCfunction(
outfile=os.path.join(out_dir, subdir, name + ".h"),
desc=desc,
name=name,
params=
"const paramstruct *params,REAL *xx[3],REAL *auxevol_gfs,REAL *in_gfs",
body=fin.FD_outputC("returnstring", values_to_print,
params=outCparams).replace("IDX4", "IDX4S"),
loopopts="AllPoints,Read_xxs",
rel_path_for_Cparams=os.path.join("../"))
C2P_P2C.GiRaFFE_NRPy_P2C(gammaDD, betaU, alpha, ValenciavU, BU, sqrt4pi)
values_to_print = [\
lhrh(lhs=gri.gfaccess("in_gfs","StildeD0"),rhs=C2P_P2C.StildeD[0]),\
lhrh(lhs=gri.gfaccess("in_gfs","StildeD1"),rhs=C2P_P2C.StildeD[1]),\
lhrh(lhs=gri.gfaccess("in_gfs","StildeD2"),rhs=C2P_P2C.StildeD[2]),\
]
desc = "Recompute StildeD after current sheet fix to Valencia 3-velocity to ensure consistency between conservative & primitive variables."
name = "GiRaFFE_NRPy_prims_to_cons"
outCfunction(
outfile=os.path.join(out_dir, subdir, name + ".h"),
desc=desc,
name=name,
params="const paramstruct *params,REAL *auxevol_gfs,REAL *in_gfs",
body=fin.FD_outputC("returnstring", values_to_print,
params=outCparams).replace("IDX4", "IDX4S"),
loopopts="AllPoints",
rel_path_for_Cparams=os.path.join("../"))
# Write out the main driver itself:
with open(os.path.join(out_dir, "GiRaFFE_NRPy_Main_Driver.h"),
"w") as file:
file.write(r"""// Structure to track ghostzones for PPM:
typedef struct __gf_and_gz_struct__ {
REAL *gf;
int gz_lo[4],gz_hi[4];
} gf_and_gz_struct;
// Some additional constants needed for PPM:
const int VX=0,VY=1,VZ=2,BX=3,BY=4,BZ=5;
const int NUM_RECONSTRUCT_GFS = 6;
// Include ALL functions needed for evolution
#include "RHSs/calculate_AD_gauge_term_psi6Phi_flux_term_for_RHSs.h"
#include "RHSs/calculate_AD_gauge_psi6Phi_RHSs.h"
#include "PPM/reconstruct_set_of_prims_PPM_GRFFE_NRPy.c"
#include "FCVAL/interpolate_metric_gfs_to_cell_faces.h"
#include "RHSs/calculate_StildeD0_source_term.h"
#include "RHSs/calculate_StildeD1_source_term.h"
#include "RHSs/calculate_StildeD2_source_term.h"
#include "../calculate_E_field_flat_all_in_one.h"
#include "RHSs/calculate_Stilde_flux_D0.h"
#include "RHSs/calculate_Stilde_flux_D1.h"
#include "RHSs/calculate_Stilde_flux_D2.h"
#include "boundary_conditions/GiRaFFE_boundary_conditions.h"
#include "A2B/driver_AtoB.h"
#include "C2P/GiRaFFE_NRPy_cons_to_prims.h"
#include "C2P/GiRaFFE_NRPy_prims_to_cons.h"
void override_BU_with_old_GiRaFFE(const paramstruct *restrict params,REAL *restrict auxevol_gfs,const int n) {
#include "set_Cparameters.h"
char filename[100];
sprintf(filename,"BU0_override-%08d.bin",n);
FILE *out2D = fopen(filename, "rb");
fread(auxevol_gfs+BU0GF*Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1*Nxx_plus_2NGHOSTS2,
sizeof(double),Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1*Nxx_plus_2NGHOSTS2,out2D);
fclose(out2D);
sprintf(filename,"BU1_override-%08d.bin",n);
out2D = fopen(filename, "rb");
fread(auxevol_gfs+BU1GF*Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1*Nxx_plus_2NGHOSTS2,
sizeof(double),Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1*Nxx_plus_2NGHOSTS2,out2D);
fclose(out2D);
sprintf(filename,"BU2_override-%08d.bin",n);
out2D = fopen(filename, "rb");
fread(auxevol_gfs+BU2GF*Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1*Nxx_plus_2NGHOSTS2,
sizeof(double),Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1*Nxx_plus_2NGHOSTS2,out2D);
fclose(out2D);
}
void GiRaFFE_NRPy_RHSs(const paramstruct *restrict params,REAL *restrict auxevol_gfs,const REAL *restrict in_gfs,REAL *restrict rhs_gfs) {
#include "set_Cparameters.h"
// First thing's first: initialize the RHSs to zero!
#pragma omp parallel for
for(int ii=0;ii<Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1*Nxx_plus_2NGHOSTS2*NUM_EVOL_GFS;ii++) {
rhs_gfs[ii] = 0.0;
}
// Next calculate the easier source terms that don't require flux directions
// This will also reset the RHSs for each gf at each new timestep.
calculate_AD_gauge_term_psi6Phi_flux_term_for_RHSs(params,in_gfs,auxevol_gfs);
calculate_AD_gauge_psi6Phi_RHSs(params,in_gfs,auxevol_gfs,rhs_gfs);
// Now, we set up a bunch of structs of pointers to properly guide the PPM algorithm.
// They also count the number of ghostzones available.
gf_and_gz_struct in_prims[NUM_RECONSTRUCT_GFS], out_prims_r[NUM_RECONSTRUCT_GFS], out_prims_l[NUM_RECONSTRUCT_GFS];
int which_prims_to_reconstruct[NUM_RECONSTRUCT_GFS],num_prims_to_reconstruct;
const int Nxxp2NG012 = Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1*Nxx_plus_2NGHOSTS2;
REAL *temporary = auxevol_gfs + Nxxp2NG012*AEVOLPARENGF; //We're not using this anymore
// This sets pointers to the portion of auxevol_gfs containing the relevant gridfunction.
int ww=0;
in_prims[ww].gf = auxevol_gfs + Nxxp2NG012*VALENCIAVU0GF;
out_prims_r[ww].gf = auxevol_gfs + Nxxp2NG012*VALENCIAV_RU0GF;
out_prims_l[ww].gf = auxevol_gfs + Nxxp2NG012*VALENCIAV_LU0GF;
ww++;
in_prims[ww].gf = auxevol_gfs + Nxxp2NG012*VALENCIAVU1GF;
out_prims_r[ww].gf = auxevol_gfs + Nxxp2NG012*VALENCIAV_RU1GF;
out_prims_l[ww].gf = auxevol_gfs + Nxxp2NG012*VALENCIAV_LU1GF;
ww++;
in_prims[ww].gf = auxevol_gfs + Nxxp2NG012*VALENCIAVU2GF;
out_prims_r[ww].gf = auxevol_gfs + Nxxp2NG012*VALENCIAV_RU2GF;
out_prims_l[ww].gf = auxevol_gfs + Nxxp2NG012*VALENCIAV_LU2GF;
ww++;
in_prims[ww].gf = auxevol_gfs + Nxxp2NG012*BU0GF;
out_prims_r[ww].gf = auxevol_gfs + Nxxp2NG012*B_RU0GF;
out_prims_l[ww].gf = auxevol_gfs + Nxxp2NG012*B_LU0GF;
ww++;
in_prims[ww].gf = auxevol_gfs + Nxxp2NG012*BU1GF;
out_prims_r[ww].gf = auxevol_gfs + Nxxp2NG012*B_RU1GF;
out_prims_l[ww].gf = auxevol_gfs + Nxxp2NG012*B_LU1GF;
ww++;
in_prims[ww].gf = auxevol_gfs + Nxxp2NG012*BU2GF;
out_prims_r[ww].gf = auxevol_gfs + Nxxp2NG012*B_RU2GF;
out_prims_l[ww].gf = auxevol_gfs + Nxxp2NG012*B_LU2GF;
ww++;
// Prims are defined AT ALL GRIDPOINTS, so we set the # of ghostzones to zero:
for(int i=0;i<NUM_RECONSTRUCT_GFS;i++) for(int j=1;j<=3;j++) { in_prims[i].gz_lo[j]=0; in_prims[i].gz_hi[j]=0; }
// Left/right variables are not yet defined, yet we set the # of gz's to zero by default:
for(int i=0;i<NUM_RECONSTRUCT_GFS;i++) for(int j=1;j<=3;j++) { out_prims_r[i].gz_lo[j]=0; out_prims_r[i].gz_hi[j]=0; }
for(int i=0;i<NUM_RECONSTRUCT_GFS;i++) for(int j=1;j<=3;j++) { out_prims_l[i].gz_lo[j]=0; out_prims_l[i].gz_hi[j]=0; }
ww=0;
which_prims_to_reconstruct[ww]=VX; ww++;
which_prims_to_reconstruct[ww]=VY; ww++;
which_prims_to_reconstruct[ww]=VZ; ww++;
which_prims_to_reconstruct[ww]=BX; ww++;
which_prims_to_reconstruct[ww]=BY; ww++;
which_prims_to_reconstruct[ww]=BZ; ww++;
num_prims_to_reconstruct=ww;
// In each direction, perform the PPM reconstruction procedure.
// Then, add the fluxes to the RHS as appropriate.
for(int flux_dirn=0;flux_dirn<3;flux_dirn++) {
// In each direction, interpolate the metric gfs (gamma,beta,alpha) to cell faces.
interpolate_metric_gfs_to_cell_faces(params,auxevol_gfs,flux_dirn+1);
// Then, reconstruct the primitive variables on the cell faces.
// This function is housed in the file: "reconstruct_set_of_prims_PPM_GRFFE_NRPy.c"
reconstruct_set_of_prims_PPM_GRFFE_NRPy(params, auxevol_gfs, flux_dirn+1, num_prims_to_reconstruct,
which_prims_to_reconstruct, in_prims, out_prims_r, out_prims_l, temporary);
// For example, if flux_dirn==0, then at gamma_faceDD00(i,j,k) represents gamma_{xx}
// at (i-1/2,j,k), Valenciav_lU0(i,j,k) is the x-component of the velocity at (i-1/2-epsilon,j,k),
// and Valenciav_rU0(i,j,k) is the x-component of the velocity at (i-1/2+epsilon,j,k).
if(flux_dirn==0) {
// Next, we calculate the source term for StildeD. Again, this also resets the rhs_gfs array at
// each new timestep.
calculate_StildeD0_source_term(params,auxevol_gfs,rhs_gfs);
// Now, compute the electric field on each face of a cell and add it to the RHSs as appropriate
//calculate_E_field_D0_right(params,auxevol_gfs,rhs_gfs);
//calculate_E_field_D0_left(params,auxevol_gfs,rhs_gfs);
// Finally, we calculate the flux of StildeD and add the appropriate finite-differences
// to the RHSs.
calculate_Stilde_flux_D0(params,auxevol_gfs,rhs_gfs);
}
else if(flux_dirn==1) {
calculate_StildeD1_source_term(params,auxevol_gfs,rhs_gfs);
//calculate_E_field_D1_right(params,auxevol_gfs,rhs_gfs);
//calculate_E_field_D1_left(params,auxevol_gfs,rhs_gfs);
calculate_Stilde_flux_D1(params,auxevol_gfs,rhs_gfs);
}
else {
calculate_StildeD2_source_term(params,auxevol_gfs,rhs_gfs);
//calculate_E_field_D2_right(params,auxevol_gfs,rhs_gfs);
//calculate_E_field_D2_left(params,auxevol_gfs,rhs_gfs);
calculate_Stilde_flux_D2(params,auxevol_gfs,rhs_gfs);
}
for(int count=0;count<=1;count++) {
// This function is written to be general, using notation that matches the forward permutation added to AD2,
// i.e., [F_HLL^x(B^y)]_z corresponding to flux_dirn=0, count=1.
// The SIGN parameter is necessary because
// -E_z(x_i,y_j,z_k) = 0.25 ( [F_HLL^x(B^y)]_z(i+1/2,j,k)+[F_HLL^x(B^y)]_z(i-1/2,j,k)
// -[F_HLL^y(B^x)]_z(i,j+1/2,k)-[F_HLL^y(B^x)]_z(i,j-1/2,k) )
// Note the negative signs on the reversed permutation terms!
// By cyclically permuting with flux_dirn, we
// get contributions to the other components, and by incrementing count, we get the backward permutations:
// Let's suppose flux_dirn = 0. Then we will need to update Ay (count=0) and Az (count=1):
// flux_dirn=count=0 -> AD0GF+(flux_dirn+1+count)%3 = AD0GF + (0+1+0)%3=AD1GF <- Updating Ay!
// (flux_dirn)%3 = (0)%3 = 0 Vx
// (flux_dirn-count+2)%3 = (0-0+2)%3 = 2 Vz . Inputs Vx, Vz -> SIGN = -1 ; 2.0*((REAL)count)-1.0=-1 check!
// flux_dirn=0,count=1 -> AD0GF+(flux_dirn+1+count)%3 = AD0GF + (0+1+1)%3=AD2GF <- Updating Az!
// (flux_dirn)%3 = (0)%3 = 0 Vx
// (flux_dirn-count+2)%3 = (0-1+2)%3 = 1 Vy . Inputs Vx, Vy -> SIGN = +1 ; 2.0*((REAL)count)-1.0=2-1=+1 check!
// Let's suppose flux_dirn = 1. Then we will need to update Az (count=0) and Ax (count=1):
// flux_dirn=1,count=0 -> AD0GF+(flux_dirn+1+count)%3 = AD0GF + (1+1+0)%3=AD2GF <- Updating Az!
// (flux_dirn)%3 = (1)%3 = 1 Vy
// (flux_dirn-count+2)%3 = (1-0+2)%3 = 0 Vx . Inputs Vy, Vx -> SIGN = -1 ; 2.0*((REAL)count)-1.0=-1 check!
// flux_dirn=count=1 -> AD0GF+(flux_dirn+1+count)%3 = AD0GF + (1+1+1)%3=AD0GF <- Updating Ax!
// (flux_dirn)%3 = (1)%3 = 1 Vy
// (flux_dirn-count+2)%3 = (1-1+2)%3 = 2 Vz . Inputs Vy, Vz -> SIGN = +1 ; 2.0*((REAL)count)-1.0=2-1=+1 check!
// Let's suppose flux_dirn = 2. Then we will need to update Ax (count=0) and Ay (count=1):
// flux_dirn=2,count=0 -> AD0GF+(flux_dirn+1+count)%3 = AD0GF + (2+1+0)%3=AD0GF <- Updating Ax!
// (flux_dirn)%3 = (2)%3 = 2 Vz
// (flux_dirn-count+2)%3 = (2-0+2)%3 = 1 Vy . Inputs Vz, Vy -> SIGN = -1 ; 2.0*((REAL)count)-1.0=-1 check!
// flux_dirn=2,count=1 -> AD0GF+(flux_dirn+1+count)%3 = AD0GF + (2+1+1)%3=AD1GF <- Updating Ay!
// (flux_dirn)%3 = (2)%3 = 2 Vz
// (flux_dirn-count+2)%3 = (2-1+2)%3 = 0 Vx . Inputs Vz, Vx -> SIGN = +1 ; 2.0*((REAL)count)-1.0=2-1=+1 check!
calculate_E_field_flat_all_in_one(params,
&auxevol_gfs[IDX4ptS(VALENCIAV_RU0GF+(flux_dirn)%3, 0)],&auxevol_gfs[IDX4ptS(VALENCIAV_RU0GF+(flux_dirn-count+2)%3, 0)],
&auxevol_gfs[IDX4ptS(VALENCIAV_LU0GF+(flux_dirn)%3, 0)],&auxevol_gfs[IDX4ptS(VALENCIAV_LU0GF+(flux_dirn-count+2)%3, 0)],
&auxevol_gfs[IDX4ptS(B_RU0GF +(flux_dirn)%3, 0)],&auxevol_gfs[IDX4ptS(B_RU0GF +(flux_dirn-count+2)%3, 0)],
&auxevol_gfs[IDX4ptS(B_LU0GF +(flux_dirn)%3, 0)],&auxevol_gfs[IDX4ptS(B_LU0GF +(flux_dirn-count+2)%3, 0)],
&auxevol_gfs[IDX4ptS(B_RU0GF +(flux_dirn-count+2)%3, 0)],
&auxevol_gfs[IDX4ptS(B_LU0GF +(flux_dirn-count+2)%3, 0)],
&rhs_gfs[IDX4ptS(AD0GF+(flux_dirn+1+count)%3,0)], 2.0*((REAL)count)-1.0, flux_dirn);
}
}
}
void GiRaFFE_NRPy_post_step(const paramstruct *restrict params,REAL *xx[3],REAL *restrict auxevol_gfs,REAL *restrict evol_gfs,const int n) {
// First, apply BCs to AD and psi6Phi. Then calculate BU from AD
apply_bcs_potential(params,evol_gfs);
driver_A_to_B(params,evol_gfs,auxevol_gfs);
//override_BU_with_old_GiRaFFE(params,auxevol_gfs,n);
// Apply fixes to StildeD, then recompute the velocity at the new timestep.
// Apply the current sheet prescription to the velocities
GiRaFFE_NRPy_cons_to_prims(params,xx,auxevol_gfs,evol_gfs);
// Then, recompute StildeD to be consistent with the new velocities
//GiRaFFE_NRPy_prims_to_cons(params,auxevol_gfs,evol_gfs);
// Finally, apply outflow boundary conditions to the velocities.
apply_bcs_velocity(params,auxevol_gfs);
}
""")
import GiRaFFE_NRPy.GiRaFFE_NRPy_C2P_P2C as C2P_P2C
import GiRaFFE_NRPy.GiRaFFE_NRPy_Source_Terms as source
thismodule = "GiRaFFE_NRPy_Main_Driver"
CoordSystem = "Cartesian"
outCparams = "outCverbose=False,CSE_sorting=none"
par.set_parval_from_str("reference_metric::CoordSystem", CoordSystem)
rfm.reference_metric(
) # Create ReU, ReDD needed for rescaling B-L initial data, generating BSSN RHSs, etc.
# Default Kreiss-Oliger dissipation strength
default_KO_strength = 0.1
diss_strength = par.Cparameters("REAL", thismodule, "diss_strength",
default_KO_strength)
def GiRaFFE_NRPy_Main_Driver_generate_all(out_dir):
cmd.mkdir(out_dir)
gammaDD = ixp.register_gridfunctions_for_single_rank2("AUXEVOL",
"gammaDD",
"sym01",
DIM=3)
betaU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL",
"betaU",
DIM=3)
alpha = gri.register_gridfunctions("AUXEVOL", "alpha")
AD = ixp.register_gridfunctions_for_single_rank1("EVOL", "AD")
BU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL", "BU")
def BSSN_RHSs__generate_symbolic_expressions():
######################################
# START: GENERATE SYMBOLIC EXPRESSIONS
print("Generating symbolic expressions for BSSN RHSs...")
start = time.time()
# Enable rfm_precompute infrastructure, which results in
# BSSN RHSs that are free of transcendental functions,
# even in curvilinear coordinates, so long as
# ConformalFactor is set to "W" (default).
par.set_parval_from_str("reference_metric::enable_rfm_precompute","True")
par.set_parval_from_str("reference_metric::rfm_precompute_Ccode_outdir",os.path.join(outdir,"rfm_files/"))
# Evaluate BSSN + BSSN gauge RHSs with rfm_precompute enabled:
import BSSN.BSSN_quantities as Bq
par.set_parval_from_str("BSSN.BSSN_quantities::LeaveRicciSymbolic","True")
rhs.BSSN_RHSs()
if T4UU != None:
import BSSN.BSSN_stress_energy_source_terms as Bsest
Bsest.BSSN_source_terms_for_BSSN_RHSs(T4UU)
rhs.trK_rhs += Bsest.sourceterm_trK_rhs
for i in range(3):
# Needed for Gamma-driving shift RHSs:
rhs.Lambdabar_rhsU[i] += Bsest.sourceterm_Lambdabar_rhsU[i]
# Needed for BSSN RHSs:
rhs.lambda_rhsU[i] += Bsest.sourceterm_lambda_rhsU[i]
for j in range(3):
rhs.a_rhsDD[i][j] += Bsest.sourceterm_a_rhsDD[i][j]
gaugerhs.BSSN_gauge_RHSs()
# Add Kreiss-Oliger dissipation to the BSSN RHSs:
thismodule = "KO_Dissipation"
diss_strength = par.Cparameters("REAL", thismodule, "diss_strength", default_KO_strength)
alpha_dKOD = ixp.declarerank1("alpha_dKOD")
cf_dKOD = ixp.declarerank1("cf_dKOD")
trK_dKOD = ixp.declarerank1("trK_dKOD")
betU_dKOD = ixp.declarerank2("betU_dKOD","nosym")
vetU_dKOD = ixp.declarerank2("vetU_dKOD","nosym")
lambdaU_dKOD = ixp.declarerank2("lambdaU_dKOD","nosym")
aDD_dKOD = ixp.declarerank3("aDD_dKOD","sym01")
hDD_dKOD = ixp.declarerank3("hDD_dKOD","sym01")
for k in range(3):
gaugerhs.alpha_rhs += diss_strength*alpha_dKOD[k]*rfm.ReU[k] # ReU[k] = 1/scalefactor_orthog_funcform[k]
rhs.cf_rhs += diss_strength* cf_dKOD[k]*rfm.ReU[k] # ReU[k] = 1/scalefactor_orthog_funcform[k]
rhs.trK_rhs += diss_strength* trK_dKOD[k]*rfm.ReU[k] # ReU[k] = 1/scalefactor_orthog_funcform[k]
for i in range(3):
if "2ndOrder" in ShiftCondition:
gaugerhs.bet_rhsU[i] += diss_strength* betU_dKOD[i][k]*rfm.ReU[k] # ReU[k] = 1/scalefactor_orthog_funcform[k]
gaugerhs.vet_rhsU[i] += diss_strength* vetU_dKOD[i][k]*rfm.ReU[k] # ReU[k] = 1/scalefactor_orthog_funcform[k]
rhs.lambda_rhsU[i] += diss_strength*lambdaU_dKOD[i][k]*rfm.ReU[k] # ReU[k] = 1/scalefactor_orthog_funcform[k]
for j in range(3):
rhs.a_rhsDD[i][j] += diss_strength*aDD_dKOD[i][j][k]*rfm.ReU[k] # ReU[k] = 1/scalefactor_orthog_funcform[k]
rhs.h_rhsDD[i][j] += diss_strength*hDD_dKOD[i][j][k]*rfm.ReU[k] # ReU[k] = 1/scalefactor_orthog_funcform[k]
# We use betaU as our upwinding control vector:
Bq.BSSN_basic_tensors()
betaU = Bq.betaU
# Now that we are finished with all the rfm hatted
# quantities in generic precomputed functional
# form, let's restore them to their closed-
# form expressions.
par.set_parval_from_str("reference_metric::enable_rfm_precompute","False") # Reset to False to disable rfm_precompute.
rfm.ref_metric__hatted_quantities()
par.set_parval_from_str("BSSN.BSSN_quantities::LeaveRicciSymbolic","False")
end = time.time()
print("(BENCH) Finished BSSN RHS symbolic expressions in "+str(end-start)+" seconds.")
# END: GENERATE SYMBOLIC EXPRESSIONS
######################################
BSSN_RHSs_SymbExpressions = [lhrh(lhs=gri.gfaccess("rhs_gfs","aDD00"), rhs=rhs.a_rhsDD[0][0]),
lhrh(lhs=gri.gfaccess("rhs_gfs","aDD01"), rhs=rhs.a_rhsDD[0][1]),
lhrh(lhs=gri.gfaccess("rhs_gfs","aDD02"), rhs=rhs.a_rhsDD[0][2]),
lhrh(lhs=gri.gfaccess("rhs_gfs","aDD11"), rhs=rhs.a_rhsDD[1][1]),
lhrh(lhs=gri.gfaccess("rhs_gfs","aDD12"), rhs=rhs.a_rhsDD[1][2]),
lhrh(lhs=gri.gfaccess("rhs_gfs","aDD22"), rhs=rhs.a_rhsDD[2][2]),
lhrh(lhs=gri.gfaccess("rhs_gfs","alpha"), rhs=gaugerhs.alpha_rhs),
lhrh(lhs=gri.gfaccess("rhs_gfs","betU0"), rhs=gaugerhs.bet_rhsU[0]),
lhrh(lhs=gri.gfaccess("rhs_gfs","betU1"), rhs=gaugerhs.bet_rhsU[1]),
lhrh(lhs=gri.gfaccess("rhs_gfs","betU2"), rhs=gaugerhs.bet_rhsU[2]),
lhrh(lhs=gri.gfaccess("rhs_gfs","cf"), rhs=rhs.cf_rhs),
lhrh(lhs=gri.gfaccess("rhs_gfs","hDD00"), rhs=rhs.h_rhsDD[0][0]),
lhrh(lhs=gri.gfaccess("rhs_gfs","hDD01") ,rhs=rhs.h_rhsDD[0][1]),
lhrh(lhs=gri.gfaccess("rhs_gfs","hDD02"), rhs=rhs.h_rhsDD[0][2]),
lhrh(lhs=gri.gfaccess("rhs_gfs","hDD11"), rhs=rhs.h_rhsDD[1][1]),
lhrh(lhs=gri.gfaccess("rhs_gfs","hDD12"), rhs=rhs.h_rhsDD[1][2]),
lhrh(lhs=gri.gfaccess("rhs_gfs","hDD22"), rhs=rhs.h_rhsDD[2][2]),
lhrh(lhs=gri.gfaccess("rhs_gfs","lambdaU0"),rhs=rhs.lambda_rhsU[0]),
lhrh(lhs=gri.gfaccess("rhs_gfs","lambdaU1"),rhs=rhs.lambda_rhsU[1]),
lhrh(lhs=gri.gfaccess("rhs_gfs","lambdaU2"),rhs=rhs.lambda_rhsU[2]),
lhrh(lhs=gri.gfaccess("rhs_gfs","trK"), rhs=rhs.trK_rhs),
lhrh(lhs=gri.gfaccess("rhs_gfs","vetU0"), rhs=gaugerhs.vet_rhsU[0]),
lhrh(lhs=gri.gfaccess("rhs_gfs","vetU1"), rhs=gaugerhs.vet_rhsU[1]),
lhrh(lhs=gri.gfaccess("rhs_gfs","vetU2"), rhs=gaugerhs.vet_rhsU[2]) ]
return [betaU,BSSN_RHSs_SymbExpressions]
#
# **Additional variables needed for spacetime evolution**:
#
# * Desired coordinate system
# * Desired initial lapse $\alpha$ and shift $\beta^i$. We will choose our gauge conditions as $\alpha=1$ and $\beta^i=B^i=0$. $\alpha = \psi^{-2}$ will yield much better behavior, but the conformal factor $\psi$ depends on the desired *destination* coordinate system (which may not be spherical coordinates).
# Step 1: Initialize core Python/NRPy+ modules
import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends
import NRPy_param_funcs as par # NRPy+: Parameter interface
import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support
import BSSN.ADM_Exact_Spherical_or_Cartesian_to_BSSNCurvilinear as AtoB
thismodule = __name__
# Input parameters:
M = par.Cparameters("REAL", thismodule, ["M"], [1.0])
# ComputeADMGlobalsOnly == True will only set up the ADM global quantities.
# == False will perform the full ADM SphorCart->BSSN Curvi conversion
def StaticTrumpet(ComputeADMGlobalsOnly = False):
global Sph_r_th_ph,r,th,ph, gammaSphDD, KSphDD, alphaSph, betaSphU, BSphU
# All gridfunctions will be written in terms of spherical coordinates (r, th, ph):
r,th,ph = sp.symbols('r th ph', real=True)
# Step 0: Set spatial dimension (must be 3 for BSSN)
DIM = 3
par.set_parval_from_str("grid::DIM",DIM)
# Step 1: Set psi, the conformal factor:
def generate_C_code_for_Stilde_flux(
out_dir,
inputs_provided=False,
alpha_face=None,
gamma_faceDD=None,
beta_faceU=None,
Valenciav_rU=None,
B_rU=None,
Valenciav_lU=None,
B_lU=None,
sqrt4pi=None,
outCparams="outCverbose=False,CSE_sorting=none",
write_cmax_cmin=False):
if not inputs_provided:
# We will pass values of the gridfunction on the cell faces into the function. This requires us
# to declare them as C parameters in NRPy+. We will denote this with the _face infix/suffix.
alpha_face = gri.register_gridfunctions("AUXEVOL", "alpha_face")
gamma_faceDD = ixp.register_gridfunctions_for_single_rank2(
"AUXEVOL", "gamma_faceDD", "sym01")
beta_faceU = ixp.register_gridfunctions_for_single_rank1(
"AUXEVOL", "beta_faceU")
# We'll need some more gridfunctions, now, to represent the reconstructions of BU and ValenciavU
# on the right and left faces
Valenciav_rU = ixp.register_gridfunctions_for_single_rank1(
"AUXEVOL", "Valenciav_rU", DIM=3)
B_rU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL",
"B_rU",
DIM=3)
Valenciav_lU = ixp.register_gridfunctions_for_single_rank1(
"AUXEVOL", "Valenciav_lU", DIM=3)
B_lU = ixp.register_gridfunctions_for_single_rank1("AUXEVOL",
"B_lU",
DIM=3)
sqrt4pi = par.Cparameters("REAL", thismodule, "sqrt4pi",
"sqrt(4.0*M_PI)")
# We'll also need to store the results of the HLLE step between functions.
ixp.register_gridfunctions_for_single_rank1("AUXEVOL",
"Stilde_flux_HLLED")
input_params_for_Stilde_flux = "const paramstruct *params,REAL *auxevol_gfs,REAL *rhs_gfs"
if write_cmax_cmin:
name_suffixes = ["_x", "_y", "_z"]
for flux_dirn in range(3):
calculate_Stilde_flux(flux_dirn,alpha_face,gamma_faceDD,beta_faceU,\
Valenciav_rU,B_rU,Valenciav_lU,B_lU,sqrt4pi)
Stilde_flux_to_print = [
lhrh(lhs=gri.gfaccess("out_gfs", "Stilde_flux_HLLED0"),
rhs=Stilde_fluxD[0]),
lhrh(lhs=gri.gfaccess("out_gfs", "Stilde_flux_HLLED1"),
rhs=Stilde_fluxD[1]),
lhrh(lhs=gri.gfaccess("out_gfs", "Stilde_flux_HLLED2"),
rhs=Stilde_fluxD[2])
]
if write_cmax_cmin:
Stilde_flux_to_print = Stilde_flux_to_print \
+[
lhrh(lhs=gri.gfaccess("out_gfs","cmax"+name_suffixes[flux_dirn]),rhs=chsp.cmax),
lhrh(lhs=gri.gfaccess("out_gfs","cmin"+name_suffixes[flux_dirn]),rhs=chsp.cmin)
]
desc = "Compute the flux term of all 3 components of tilde{S}_i on the left face in the " + str(
flux_dirn) + "direction for all components."
name = "calculate_Stilde_flux_D" + str(flux_dirn)
Ccode_function = outCfunction(
outfile="returnstring",
desc=desc,
name=name,
params=input_params_for_Stilde_flux,
body=fin.FD_outputC("returnstring",
Stilde_flux_to_print,
params=outCparams),
loopopts="InteriorPoints",
rel_path_to_Cparams=os.path.join("../")).replace(
"NGHOSTS+Nxx0", "NGHOSTS+Nxx0+1").replace(
"NGHOSTS+Nxx1",
"NGHOSTS+Nxx1+1").replace("NGHOSTS+Nxx2", "NGHOSTS+Nxx2+1")
with open(os.path.join(out_dir, name + ".h"), "w") as file:
file.write(Ccode_function)
pre_body = """// Notice in the loop below that we go from 3 to cctk_lsh-3 for i, j, AND k, even though
// we are only computing the flux in one direction. This is because in the end,
// we only need the rhs's from 3 to cctk_lsh-3 for i, j, and k.
const REAL invdxi[4] = {1e100,invdx0,invdx1,invdx2};
const REAL invdx = invdxi[flux_dirn];"""
FD_body = """const int index = IDX3S(i0,i1,i2);
const int indexp1 = IDX3S(i0+kronecker_delta[flux_dirn][0],i1+kronecker_delta[flux_dirn][1],i2+kronecker_delta[flux_dirn][2]);
rhs_gfs[IDX4ptS(STILDED0GF,index)] += (auxevol_gfs[IDX4ptS(STILDE_FLUX_HLLED0GF,index)] - auxevol_gfs[IDX4ptS(STILDE_FLUX_HLLED0GF,indexp1)] ) * invdx;
rhs_gfs[IDX4ptS(STILDED1GF,index)] += (auxevol_gfs[IDX4ptS(STILDE_FLUX_HLLED1GF,index)] - auxevol_gfs[IDX4ptS(STILDE_FLUX_HLLED1GF,indexp1)] ) * invdx;
rhs_gfs[IDX4ptS(STILDED2GF,index)] += (auxevol_gfs[IDX4ptS(STILDE_FLUX_HLLED2GF,index)] - auxevol_gfs[IDX4ptS(STILDE_FLUX_HLLED2GF,indexp1)] ) * invdx;"""
desc = "Compute the difference in the flux of StildeD on the opposite faces in flux_dirn for all components."
name = "calculate_Stilde_rhsD"
outCfunction(
outfile=os.path.join(out_dir, name + ".h"),
desc=desc,
name=name,
params=
"const int flux_dirn,const paramstruct *params,const REAL *auxevol_gfs,REAL *rhs_gfs",
preloop=pre_body,
body=FD_body,
loopopts="InteriorPoints",
rel_path_to_Cparams=os.path.join("../"))
from outputC import nrpyAbs # NRPy+: Core C code output module
import NRPy_param_funcs as par # NRPy+: parameter interface
import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends
thismodule = __name__
TINYDOUBLE = par.Cparameters("REAL", thismodule, "TINYDOUBLE", 1e-100)
def min_noif(a, b):
# Returns the minimum of a and b
if a == sp.sympify(0):
return sp.Rational(1, 2) * (b - nrpyAbs(b))
if b == sp.sympify(0):
return sp.Rational(1, 2) * (a - nrpyAbs(a))
return sp.Rational(1, 2) * (a + b - nrpyAbs(a - b))
def max_noif(a, b):
# Returns the maximum of a and b
if a == sp.sympify(0):
return sp.Rational(1, 2) * (b + nrpyAbs(b))
if b == sp.sympify(0):
return sp.Rational(1, 2) * (a + nrpyAbs(a))
return sp.Rational(1, 2) * (a + b + nrpyAbs(a - b))
def coord_leq_bound(x, xstar):
# Returns 1.0 if x <= xstar, 0.0 otherwise.
# Requires appropriately defined TINYDOUBLE
return min_noif(x - xstar - TINYDOUBLE, 0.0) / (x - xstar - TINYDOUBLE)
# grid.py: functions & parameters related to numerical grids:
# functions: Automatic loop output, output C code needed for gridfunction memory I/O, gridfunction registration
# Initialize globals related to the grid
glb_gridfcs_list = []
glb_gridfc = namedtuple('gridfunction', 'gftype name')
thismodule = __name__
par.initialize_param(
par.glb_param("char", thismodule, "GridFuncMemAccess", "SENRlike"))
par.initialize_param(par.glb_param("char", thismodule, "MemAllocStyle", "210"))
par.initialize_param(par.glb_param("INT", thismodule, "DIM", 3))
par.initialize_param(
par.glb_param("INT", thismodule, "Nx[DIM]", "SetAtCRuntime"))
xx = par.Cparameters("REALARRAY", thismodule, ["xx0", "xx1", "xx2", "xx3"])
def variable_type(var):
var_is_gf = False
for gf in range(len(glb_gridfcs_list)):
if str(var) == glb_gridfcs_list[gf].name:
var_is_gf = True
var_is_parameter = False
for paramname in range(len(par.glb_params_list)):
if str(var) == par.glb_params_list[paramname].parname:
var_is_parameter = True
if var_is_parameter and var_is_gf:
print("Error: variable " + str(var) +
" is registered both as a gridfunction and as a Cparameter.")
exit(1)
# <a id='step2'></a>
# ### Set the vector $A_k$
# The vector potential is given as
# \begin{align}
# A_x &= 0 \\
# A_y &= \left \{ \begin{array}{lll}\gamma_\mu x - 0.015 & \mbox{if} & x \leq -0.1/\gamma_\mu \\
# 1.15 \gamma_\mu x - 0.03g(x) & \mbox{if} & -0.1/\gamma_\mu \leq x \leq 0.1/\gamma_\mu \\
# 1.3 \gamma_\mu x - 0.015 & \mbox{if} & x \geq 0.1/\gamma_\mu \end{array} \right. , \\
# A_z &= y - \gamma_\mu (1-\mu)x .
# \end{align}
# First, however, we must set $$\gamma_\mu = (1-\mu^2)^{-1/2}$$ and $$g(x) = \cos (5\pi \gamma_\mu x)/\pi$$.
# $$\label{step2}$$
mu_AW = par.Cparameters("REAL",thismodule,["mu_AW"], -0.5) # The wave speed
M_PI = par.Cparameters("#define",thismodule,["M_PI"], "")
def GiRaFFEfood_HO_1D_tests():
gammamu = 1/sp.sqrt(1-mu_AW**2)
# We'll use reference_metric.py to define x and y
x = rfm.xxCart[0]
y = rfm.xxCart[1]
g_AW = sp.cos(5*M_PI*gammamu*x)/M_PI
# Now, we can define the vector potential. We will create three copies of this variable, because the potential is uniquely defined in three zones. Data for $x \leq -0.1/\gamma_\mu$ shall be referred to as "left", data for $-0.1/\gamma_\mu \leq x \leq 0.1/\gamma_\mu$ as "center", and data for $x \geq 0.1/\gamma_\mu$ as "right".
#
# Starting on the left,
# * The black hole mass, M
# * The black hole spin parameter, a
# Step P0: Load needed modules
import sympy as sp
import NRPy_param_funcs as par
from outputC import *
import indexedexp as ixp
import reference_metric as rfm
import BSSN.ADM_Exact_Spherical_or_Cartesian_to_BSSNCurvilinear as AtoB
import BSSN.BSSN_ID_function_string as bIDf
thismodule = __name__
# Input parameters:
M, a, r0 = par.Cparameters("REAL", thismodule, ["M", "a", "r0"],
[1.0, 0.9, 1.0])
# ComputeADMGlobalsOnly == True will only set up the ADM global quantities.
# == False will perform the full ADM SphorCart->BSSN Curvi conversion
def ShiftedKerrSchild(ComputeADMGlobalsOnly=False):
global Sph_r_th_ph, r, th, ph, rho2, gammaSphDD, KSphDD, alphaSph, betaSphU, BSphU
# All gridfunctions will be written in terms of spherical coordinates (r, th, ph):
r, th, ph = sp.symbols('r th ph', real=True)
DIM = 3
par.set_parval_from_str("grid::DIM", DIM)
# Auxiliary variables:
rho2 = sp.symbols('rho2', real=True)
import loop
import reference_metric as rfm
par.set_parval_from_str("reference_metric::CoordSystem", "Cartesian")
rfm.reference_metric()
# Step 1a: Set commonly used parameters.
thismodule = "GiRaFFEfood_NRPy_Aligned_Rotator"
# Set the spatial dimension parameter to 3.
par.set_parval_from_str("grid::DIM", 3)
DIM = par.parval_from_str("grid::DIM")
B_p_aligned_rotator, R_NS_aligned_rotator = par.Cparameters(
"REAL",
thismodule,
# B_p_aligned_rotator = the intensity of the magnetic field and
# R_NS_aligned_rotator= "Neutron star" radius
["B_p_aligned_rotator", "R_NS_aligned_rotator"],
[1e-5, 1.0])
# The angular velocity of the "neutron star"
Omega_aligned_rotator = par.Cparameters("REAL", thismodule,
"Omega_aligned_rotator", 1e3)
# <a id='step2'></a>
#
# ### Step 2: Set the vectors A in Spherical coordinates
# $$\label{step2}$$
#
# \[Back to [top](#top)\]
#
def BSSN_constraints(add_T4UUmunu_source_terms=False):
# Step 1.a: Set spatial dimension (must be 3 for BSSN, as BSSN is
# a 3+1-dimensional decomposition of the general
# relativistic field equations)
DIM = 3
# Step 1.b: Given the chosen coordinate system, set up
# corresponding reference metric and needed
# reference metric quantities
# The following function call sets up the reference metric
# and related quantities, including rescaling matrices ReDD,
# ReU, and hatted quantities.
rfm.reference_metric()
# Step 2: Hamiltonian constraint.
# First declare all needed variables
Bq.declare_BSSN_gridfunctions_if_not_declared_already() # Sets trK
Bq.BSSN_basic_tensors() # Sets AbarDD
Bq.gammabar__inverse_and_derivs() # Sets gammabarUU
Bq.AbarUU_AbarUD_trAbar_AbarDD_dD() # Sets AbarUU and AbarDD_dD
Bq.RicciBar__gammabarDD_dHatD__DGammaUDD__DGammaU() # Sets RbarDD
Bq.phi_and_derivs() # Sets phi_dBarD & phi_dBarDD
###############################
###############################
# HAMILTONIAN CONSTRAINT
###############################
###############################
# Term 1: 2/3 K^2
global H
H = sp.Rational(2, 3) * Bq.trK**2
# Term 2: -A_{ij} A^{ij}
for i in range(DIM):
for j in range(DIM):
H += -Bq.AbarDD[i][j] * Bq.AbarUU[i][j]
# Term 3a: trace(Rbar)
Rbartrace = sp.sympify(0)
for i in range(DIM):
for j in range(DIM):
Rbartrace += Bq.gammabarUU[i][j] * Bq.RbarDD[i][j]
# Term 3b: -8 \bar{\gamma}^{ij} \bar{D}_i \phi \bar{D}_j \phi = -8*phi_dBar_times_phi_dBar
# Term 3c: -8 \bar{\gamma}^{ij} \bar{D}_i \bar{D}_j \phi = -8*phi_dBarDD_contraction
phi_dBar_times_phi_dBar = sp.sympify(0) # Term 3b
phi_dBarDD_contraction = sp.sympify(0) # Term 3c
for i in range(DIM):
for j in range(DIM):
phi_dBar_times_phi_dBar += Bq.gammabarUU[i][j] * Bq.phi_dBarD[
i] * Bq.phi_dBarD[j]
phi_dBarDD_contraction += Bq.gammabarUU[i][j] * Bq.phi_dBarDD[i][j]
# Add Term 3:
H += Bq.exp_m4phi * (Rbartrace - 8 *
(phi_dBar_times_phi_dBar + phi_dBarDD_contraction))
if add_T4UUmunu_source_terms:
M_PI = par.Cparameters("#define", thismodule, "M_PI",
"") # M_PI is pi as defined in C
BTmunu.define_BSSN_T4UUmunu_rescaled_source_terms()
rho = BTmunu.rho
H += -16 * M_PI * rho
# FIXME: ADD T4UUmunu SOURCE TERMS TO MOMENTUM CONSTRAINT!
# Step 3: M^i, the momentum constraint
###############################
###############################
# MOMENTUM CONSTRAINT
###############################
###############################
# SEE Tutorial-BSSN_constraints.ipynb for full documentation.
global MU
MU = ixp.zerorank1()
# Term 2: 6 A^{ij} \partial_j \phi:
for i in range(DIM):
for j in range(DIM):
MU[i] += 6 * Bq.AbarUU[i][j] * Bq.phi_dD[j]
# Term 3: -2/3 \bar{\gamma}^{ij} K_{,j}
trK_dD = ixp.declarerank1(
"trK_dD") # Not defined in BSSN_RHSs; only trK_dupD is defined there.
for i in range(DIM):
for j in range(DIM):
MU[i] += -sp.Rational(2, 3) * Bq.gammabarUU[i][j] * trK_dD[j]
# First define aDD_dD:
aDD_dD = ixp.declarerank3("aDD_dD", "sym01")
# Then evaluate the conformal covariant derivative \bar{D}_j \bar{A}_{lm}
AbarDD_dBarD = ixp.zerorank3()
for i in range(DIM):
for j in range(DIM):
for k in range(DIM):
AbarDD_dBarD[i][j][k] = Bq.AbarDD_dD[i][j][k]
for l in range(DIM):
AbarDD_dBarD[i][j][
k] += -Bq.GammabarUDD[l][k][i] * Bq.AbarDD[l][j]
AbarDD_dBarD[i][j][
k] += -Bq.GammabarUDD[l][k][j] * Bq.AbarDD[i][l]
# Term 1: Contract twice with the metric to make \bar{D}_{j} \bar{A}^{ij}
for i in range(DIM):
for j in range(DIM):
for k in range(DIM):
for l in range(DIM):
MU[i] += Bq.gammabarUU[i][k] * Bq.gammabarUU[j][
l] * AbarDD_dBarD[k][l][j]
# Finally, we multiply by e^{-4 phi} and rescale the momentum constraint:
for i in range(DIM):
MU[i] *= Bq.exp_m4phi / rfm.ReU[i]
def ShiftedKerrSchild(ComputeADMGlobalsOnly = False):
global Sph_r_th_ph,r,th,ph, rho2, gammaSphDD, KSphDD, alphaSph, betaSphU, BSphU
# All gridfunctions will be written in terms of spherical coordinates (r, th, ph):
r,th,ph = sp.symbols('r th ph', real=True)
thismodule = "ShiftedKerrSchild"
DIM = 3
par.set_parval_from_str("grid::DIM",DIM)
# Input parameters:
M, a, r0 = par.Cparameters("REAL", thismodule, ["M", "a", "r0"])
# Auxiliary variables:
rho2 = sp.symbols('rho2', real=True)
# r_{KS} = r + r0
rKS = r+r0
# rho^2 = rKS^2 + a^2*cos^2(theta)
rho2 = rKS*rKS + a*a*sp.cos(th)**2
# alpha = 1/sqrt{1 + M*rKS/rho^2}
alphaSph = 1/(sp.sqrt(1 + 2*M*rKS/rho2))
# Initialize the shift vector, \beta^i, to zero.
betaSphU = ixp.zerorank1()
# beta^r = alpha^2*2Mr/rho^2
betaSphU[0] = alphaSph*alphaSph*2*M*rKS/rho2
# Time derivative of shift vector beta^i, B^i, is zero.
BSphU = ixp.zerorank1()
# Initialize \gamma_{ij} to zero.
gammaSphDD = ixp.zerorank2()
# gammaDD{rKS rKS} = 1 +2M*rKS/rho^2
gammaSphDD[0][0] = 1 + 2*M*rKS/rho2
# gammaDD{rKS phi} = -a*gammaDD{r r}*sin^2(theta)
gammaSphDD[0][2] = gammaSphDD[2][0] = -a*gammaSphDD[0][0]*sp.sin(th)**2
# gammaDD{theta theta} = rho^2
gammaSphDD[1][1] = rho2
# gammaDD{phi phi} = (rKS^2 + a^2 + 2Mr/rho^2*a^2*sin^2(theta))*sin^2(theta)
gammaSphDD[2][2] = (rKS*rKS + a*a + 2*M*rKS*a*a*sp.sin(th)**2/rho2)*sp.sin(th)**2
# *** Define Useful Quantities A, B, D ***
# A = (a^2*cos^2(2theta) + a^2 + 2r^2)
A = (a*a*sp.cos(2*th) + a*a + 2*rKS*rKS)
# B = A + 4M*rKS
B = A + 4*M*rKS
# D = \sqrt(2M*rKS/(a^2cos^2(theta) + rKS^2) + 1)
D = sp.sqrt(2*M*rKS/(a*a*sp.cos(th)**2 + rKS*rKS) + 1)
# *** The extrinsic curvature in spherical polar coordinates ***
# Establish the 3x3 zero-matrix
KSphDD = ixp.zerorank2()
# *** Fill in the nonzero components ***
# *** This will create an upper-triangular matrix ***
# K_{r r} = D(A+2Mr)/(A^2*B)[4M(a^2*cos(2theta) + a^2 - 2r^2)]
KSphDD[0][0] = D*(A+2*M*rKS)/(A*A*B)*(4*M*(a*a*sp.cos(2*th)+a*a-2*rKS*rKS))
# K_{r theta} = D/(AB)[8a^2*Mr*sin(theta)cos(theta)]
KSphDD[0][1] = KSphDD[1][0] = D/(A*B)*(8*a*a*M*rKS*sp.sin(th)*sp.cos(th))
# K_{r phi} = D/A^2[-2aMsin^2(theta)(a^2cos(2theta)+a^2-2r^2)]
KSphDD[0][2] = KSphDD[2][0] = D/(A*A)*(-2*a*M*sp.sin(th)**2*(a*a*sp.cos(2*th)+a*a-2*rKS*rKS))
# K_{theta theta} = D/B[4Mr^2]
KSphDD[1][1] = D/B*(4*M*rKS*rKS)
# K_{theta phi} = D/(AB)*(-8*a^3*Mr*sin^3(theta)cos(theta))
KSphDD[1][2] = KSphDD[2][1] = D/(A*B)*(-8*a**3*M*rKS*sp.sin(th)**3*sp.cos(th))
# K_{phi phi} = D/(A^2*B)[2Mr*sin^2(theta)(a^4(M+3r)
# +4a^2r^2(2r-M)+4a^2r*cos(2theta)(a^2+r(M+2r))+8r^5)]
KSphDD[2][2] = D/(A*A*B)*(2*M*rKS*sp.sin(th)**2*(a**4*(rKS-M)*sp.cos(4*th)\
+ a**4*(M+3*rKS)+4*a*a*rKS*rKS*(2*rKS-M)\
+ 4*a*a*rKS*sp.cos(2*th)*(a*a + rKS*(M + 2*rKS)) + 8*rKS**5))
if ComputeADMGlobalsOnly == True:
return
# Validated against original SENR:
#print(sp.mathematica_code(gammaSphDD[1][1]))
Sph_r_th_ph = [r,th,ph]
cf,hDD,lambdaU,aDD,trK,alpha,vetU,betU = \
AtoB.Convert_Spherical_or_Cartesian_ADM_to_BSSN_curvilinear("Spherical", Sph_r_th_ph,
gammaSphDD,KSphDD,alphaSph,betaSphU,BSphU)
global returnfunction
returnfunction = bIDf.BSSN_ID_function_string(cf,hDD,lambdaU,aDD,trK,alpha,vetU,betU)
# * Desired initial lapse $\alpha$ and shift $\beta^i$. We will choose our gauge conditions as $\alpha=1$ and $\beta^i=B^i=0$. $\alpha = \psi^{-2}$ will yield much better behavior, but the conformal factor $\psi$ depends on the desired *destination* coordinate system (which may not be spherical coordinates).
# Step P0: Load needed modules
import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends
import NRPy_param_funcs as par # NRPy+: Parameter interface
import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support
import sys # Standard Python module for multiplatform OS-level functions
from pickling import pickle_NRPy_env # NRPy+: Pickle/unpickle NRPy+ environment, for parallel codegen
import BSSN.ADM_Exact_Spherical_or_Cartesian_to_BSSNCurvilinear as AtoB
thismodule = __name__
# The UIUC initial data represent a Kerr black hole with mass M
# and dimensionless spin chi in UIUC quasi-isotropic coordinates,
# see https://arxiv.org/abs/1001.4077
# Input parameters:
M, chi = par.Cparameters("REAL", thismodule, ["M", "chi"], [1.0, 0.99])
# ComputeADMGlobalsOnly == True will only set up the ADM global quantities.
# == False will perform the full ADM SphorCart->BSSN Curvi conversion
def UIUCBlackHole(ComputeADMGlobalsOnly=False,
include_NRPy_basic_defines_and_pickle=False):
global Sph_r_th_ph, r, th, ph, gammaSphDD, KSphDD, alphaSph, betaSphU, BSphU
# All gridfunctions will be written in terms of spherical coordinates (r, th, ph):
r, th, ph = sp.symbols('r th ph', real=True)
# Step 0: Set spatial dimension (must be 3 for BSSN)
DIM = 3
par.set_parval_from_str("grid::DIM", DIM)
# * Desired initial lapse $\alpha$ and shift $\beta^i$
#
# **Transformation to curvilinear coordinates**:
# * Once the above variables have been set in Cartesian coordinates, we will apply the appropriate coordinate transformations and tensor rescalings ([described in the BSSN NRPy+ tutorial module](Tutorial-BSSNCurvilinear.ipynb))
# Step 1: Initialize core Python/NRPy+ modules
import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends
import NRPy_param_funcs as par # NRPy+: Parameter interface
import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support
from pickling import pickle_NRPy_env # NRPy+: Pickle/unpickle NRPy+ environment, for parallel codegen
import BSSN.ADM_Exact_Spherical_or_Cartesian_to_BSSNCurvilinear as AtoB
thismodule = __name__
BH1_posn_x, BH1_posn_y, BH1_posn_z = par.Cparameters("REAL", thismodule,
["BH1_posn_x", "BH1_posn_y", "BH1_posn_z"],
[0.0, 0.0, +0.5])
BH1_mass = par.Cparameters("REAL", thismodule, ["BH1_mass"], 1.0)
BH2_posn_x, BH2_posn_y, BH2_posn_z = par.Cparameters("REAL", thismodule,
["BH2_posn_x", "BH2_posn_y", "BH2_posn_z"],
[0.0, 0.0, -0.5])
BH2_mass = par.Cparameters("REAL", thismodule, ["BH2_mass"], 1.0)
# ComputeADMGlobalsOnly == True will only set up the ADM global quantities.
# == False will perform the full ADM SphorCart->BSSN Curvi conversion
def BrillLindquist(ComputeADMGlobalsOnly = False, include_NRPy_basic_defines_and_pickle=False):
# Step 2: Setting up Brill-Lindquist initial data
# Step 2.a: Set spatial dimension (must be 3 for BSSN)
DIM = 3
import reference_metric as rfm
par.set_parval_from_str("reference_metric::CoordSystem", "Cartesian")
rfm.reference_metric()
# Step 1a: Set commonly used parameters.
thismodule = "GiRaFFEfood_HO"
# Set the spatial dimension parameter to 3.
par.set_parval_from_str("grid::DIM", 3)
DIM = par.parval_from_str("grid::DIM")
# Create a parameter to control the initial data choice. For now, this will only have Exact Wald as an option.
par.initialize_param(
par.glb_param("char", thismodule, "IDchoice", "Exact_Wald"))
# Step 1b: Set needed Cparameters
M = par.Cparameters("REAL", thismodule, ["M"],
1.0) # The mass of the black hole
M_PI = par.Cparameters("#define", thismodule, ["M_PI"], "") # pi, 3.141592...
KerrSchild_radial_shift = par.Cparameters("REAL", thismodule,
"KerrSchild_radial_shift",
0.4) # Default value for ExactWald
def GiRaFFEfood_HO_Exact_Wald():
# <a id='step2'></a>
#
# ### Step 2: Set the vectors A and E in Spherical coordinates
# $$\label{step2}$$
#
# \[Back to [top](#top)\]
#
