def get_stage_start(self, istage):
"""get the starting conditions (a CellCenterData2d object) for stage
istage"""
if istage == 0:
ytmp = self.start
else:
ytmp = patch.cell_center_data_clone(self.start)
for n in range(ytmp.nvar):
var = ytmp.get_var_by_index(n)
for s in range(istage):
var.v()[:, :] += self.dt*a[self.method][istage, s]*self.k[s].v(n=n)[:, :]
ytmp.t = self.t + c[self.method][istage]*self.dt
return ytmp
def get_stage_start(self, istage):
"""get the starting conditions (a CellCenterData2d object) for stage
istage"""
if istage == 0:
ytmp = self.start
else:
ytmp = patch.cell_center_data_clone(self.start)
for n in range(ytmp.nvar):
var = ytmp.get_var_by_index(n)
for s in range(istage):
var.v()[:, :] += self.dt * a[self.method][istage,
s] * self.k[s].v(
n=n)[:, :]
ytmp.t = self.t + c[self.method][istage] * self.dt
return ytmp
def evolve(self):
"""
Evolve the equations of compressible hydrodynamics through a
timestep dt.
"""
tm_evolve = self.tc.timer("evolve")
tm_evolve.begin()
myd = self.cc_data
# we need the solution at 3 time points and at the old and
# current iteration (except for m = 0 -- that doesn't change).
# This copy will initialize the the solution at all time nodes
# with the current (old) solution.
U_kold = []
U_kold.append(patch.cell_center_data_clone(self.cc_data))
U_kold.append(patch.cell_center_data_clone(self.cc_data))
U_kold.append(patch.cell_center_data_clone(self.cc_data))
U_knew = []
U_knew.append(U_kold[0])
U_knew.append(patch.cell_center_data_clone(self.cc_data))
U_knew.append(patch.cell_center_data_clone(self.cc_data))
# loop over iterations
for _ in range(1, 5):
# we need the advective term at all time nodes at the old
# iteration -- we'll compute this now
A_kold = []
for m in range(3):
_tmp = self.substep(U_kold[m])
A_kold.append(_tmp)
# loop over the time nodes and update
for m in range(2):
# update m to m+1 for knew
# compute A(U_m^{k+1})
A_knew = self.substep(U_knew[m])
# compute the integral over A at the old iteration
I = self.sdc_integral(m, m + 1, A_kold)
# and the final update
for n in range(self.ivars.nvar):
U_knew[m+1].data.v(n=n)[:, :] = U_knew[m].data.v(n=n) + \
0.5*self.dt * (A_knew.v(n=n) - A_kold[m].v(n=n)) + I.v(n=n)
# fill ghost cells
U_knew[m + 1].fill_BC_all()
# store the current iteration as the old iteration
for m in range(1, 3):
U_kold[m].data[:, :, :] = U_knew[m].data[:, :, :]
# store the new solution
self.cc_data.data[:, :, :] = U_knew[-1].data[:, :, :]
if self.particles is not None:
self.particles.update_particles(self.dt)
# increment the time
myd.t += self.dt
self.n += 1
tm_evolve.end()
def preevolve(self):
"""
preevolve is called before we being the timestepping loop. For
the incompressible solver, this does an initial projection on the
velocity field and then goes through the full evolution to get the
value of phi. The fluid state (u, v) is then reset to values
before this evolve.
"""
self.in_preevolve = True
myg = self.cc_data.grid
u = self.cc_data.get_var("x-velocity")
v = self.cc_data.get_var("y-velocity")
self.cc_data.fill_BC("x-velocity")
self.cc_data.fill_BC("y-velocity")
# 1. do the initial projection. This makes sure that our original
# velocity field satisties div U = 0
# next create the multigrid object. We want Neumann BCs on phi
# at solid walls and periodic on phi for periodic BCs
mg = MG.CellCenterMG2d(myg.nx,
myg.ny,
xl_BC_type="periodic",
xr_BC_type="periodic",
yl_BC_type="periodic",
yr_BC_type="periodic",
xmin=myg.xmin,
xmax=myg.xmax,
ymin=myg.ymin,
ymax=myg.ymax,
verbose=0)
# first compute divU
divU = mg.soln_grid.scratch_array()
divU.v()[:, :] = \
0.5*(u.ip(1) - u.ip(-1))/myg.dx + 0.5*(v.jp(1) - v.jp(-1))/myg.dy
# solve L phi = DU
# initialize our guess to the solution, set the RHS to divU and
# solve
mg.init_zeros()
mg.init_RHS(divU)
mg.solve(rtol=1.e-10)
# store the solution in our self.cc_data object -- include a single
# ghostcell
phi = self.cc_data.get_var("phi")
phi[:, :] = mg.get_solution(grid=myg)
# compute the cell-centered gradient of phi and update the
# velocities
gradp_x, gradp_y = mg.get_solution_gradient(grid=myg)
u[:, :] -= gradp_x
v[:, :] -= gradp_y
# fill the ghostcells
self.cc_data.fill_BC("x-velocity")
self.cc_data.fill_BC("y-velocity")
# 2. now get an approximation to gradp at n-1/2 by going through the
# evolution.
# store the current solution -- we'll restore it in a bit
orig_data = patch.cell_center_data_clone(self.cc_data)
# get the timestep
self.method_compute_timestep()
# evolve
self.evolve()
# update gradp_x and gradp_y in our main data object
new_gp_x = self.cc_data.get_var("gradp_x")
new_gp_y = self.cc_data.get_var("gradp_y")
orig_gp_x = orig_data.get_var("gradp_x")
orig_gp_y = orig_data.get_var("gradp_y")
orig_gp_x[:, :] = new_gp_x[:, :]
orig_gp_y[:, :] = new_gp_y[:, :]
self.cc_data = orig_data
if self.verbose > 0:
print("done with the pre-evolution")
self.in_preevolve = False
def evolve(self):
"""
Evolve the equations of compressible hydrodynamics through a
timestep dt.
"""
tm_evolve = self.tc.timer("evolve")
tm_evolve.begin()
myd = self.cc_data
# we need the solution at 3 time points and at the old and
# current iteration (except for m = 0 -- that doesn't change).
# This copy will initialize the the solution at all time nodes
# with the current (old) solution.
U_kold = []
U_kold.append(patch.cell_center_data_clone(self.cc_data))
U_kold.append(patch.cell_center_data_clone(self.cc_data))
U_kold.append(patch.cell_center_data_clone(self.cc_data))
U_knew = []
U_knew.append(U_kold[0])
U_knew.append(patch.cell_center_data_clone(self.cc_data))
U_knew.append(patch.cell_center_data_clone(self.cc_data))
# loop over iterations
for _ in range(1, 5):
# we need the advective term at all time nodes at the old
# iteration -- we'll compute this now
A_kold = []
for m in range(3):
_tmp = self.substep(U_kold[m])
A_kold.append(_tmp)
# loop over the time nodes and update
for m in range(2):
# update m to m+1 for knew
# compute A(U_m^{k+1})
A_knew = self.substep(U_knew[m])
# compute the integral over A at the old iteration
integral = self.sdc_integral(m, m+1, A_kold)
# and the final update
for n in range(self.ivars.nvar):
U_knew[m+1].data.v(n=n)[:, :] = U_knew[m].data.v(n=n) + \
0.5*self.dt * (A_knew.v(n=n) - A_kold[m].v(n=n)) + integral.v(n=n)
# fill ghost cells
U_knew[m+1].fill_BC_all()
# store the current iteration as the old iteration
for m in range(1, 3):
U_kold[m].data[:, :, :] = U_knew[m].data[:, :, :]
# store the new solution
self.cc_data.data[:, :, :] = U_knew[-1].data[:, :, :]
if self.particles is not None:
self.particles.update_particles(self.dt)
# increment the time
myd.t += self.dt
self.n += 1
tm_evolve.end()
def preevolve(self):
"""
preevolve is called before we being the timestepping loop. For
the low Mach solver, this does an initial projection on the
velocity field and then goes through the full evolution to get the
value of phi. The fluid state (rho, u, v) is then reset to values
before this evolve.
"""
myg = self.cc_data.grid
rho = self.cc_data.get_var("density")
u = self.cc_data.get_var("x-velocity")
v = self.cc_data.get_var("y-velocity")
self.cc_data.fill_BC("density")
self.cc_data.fill_BC("x-velocity")
self.cc_data.fill_BC("y-velocity")
# 1. do the initial projection. This makes sure that our original
# velocity field satisties div U = 0
# the coefficent for the elliptic equation is beta_0^2/rho
coeff = 1.0/rho[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2]
beta0 = self.base["beta0"]
coeff = coeff*beta0[np.newaxis,myg.jlo-1:myg.jhi+2]**2
# next create the multigrid object. We defined phi with
# the right BCs previously
mg = vcMG.VarCoeffCCMG2d(myg.nx, myg.ny,
xl_BC_type=self.cc_data.BCs["phi"].xlb,
xr_BC_type=self.cc_data.BCs["phi"].xrb,
yl_BC_type=self.cc_data.BCs["phi"].ylb,
yr_BC_type=self.cc_data.BCs["phi"].yrb,
xmin=myg.xmin, xmax=myg.xmax,
ymin=myg.ymin, ymax=myg.ymax,
coeffs=coeff,
coeffs_bc=self.cc_data.BCs["density"],
verbose=0)
# first compute div{beta_0 U}
div_beta_U = mg.soln_grid.scratch_array()
# u/v are cell-centered, divU is cell-centered
div_beta_U[mg.ilo:mg.ihi+1,mg.jlo:mg.jhi+1] = \
0.5*beta0[np.newaxis,mg.jlo:mg.jhi+1]* \
(u[myg.ilo+1:myg.ihi+2,myg.jlo:myg.jhi+1] -
u[myg.ilo-1:myg.ihi ,myg.jlo:myg.jhi+1])/myg.dx + \
0.5*(beta0[np.newaxis,myg.jlo+1:myg.jhi+2]* \
v[myg.ilo:myg.ihi+1,myg.jlo+1:myg.jhi+2] -
beta0[np.newaxis,myg.jlo-1:myg.jhi ]*
v[myg.ilo:myg.ihi+1,myg.jlo-1:myg.jhi ])/myg.dy
# solve D (beta_0^2/rho) G (phi/beta_0) = D( beta_0 U )
# set the RHS to divU and solve
mg.init_RHS(div_beta_U)
mg.solve(rtol=1.e-10)
# store the solution in our self.cc_data object -- include a single
# ghostcell
phi = self.cc_data.get_var("phi")
phi[:,:] = mg.get_solution(grid=myg)
# get the cell-centered gradient of phi and update the
# velocities
# FIXME: this update only needs to be done on the interior
# cells -- not ghost cells
gradp_x, gradp_y = mg.get_solution_gradient(grid=myg)
coeff = 1.0/rho[:,:]
coeff = coeff*beta0[np.newaxis,:]
u[:,:] -= coeff*gradp_x
v[:,:] -= coeff*gradp_y
# fill the ghostcells
self.cc_data.fill_BC("x-velocity")
self.cc_data.fill_BC("y-velocity")
# 2. now get an approximation to gradp at n-1/2 by going through the
# evolution.
# store the current solution -- we'll restore it in a bit
orig_data = patch.cell_center_data_clone(self.cc_data)
# get the timestep
dt = self.timestep()
# evolve
self.evolve(dt)
# update gradp_x and gradp_y in our main data object
new_gp_x = self.cc_data.get_var("gradp_x")
new_gp_y = self.cc_data.get_var("gradp_y")
orig_gp_x = orig_data.get_var("gradp_x")
orig_gp_y = orig_data.get_var("gradp_y")
orig_gp_x[:,:] = new_gp_x[:,:]
orig_gp_y[:,:] = new_gp_y[:,:]
self.cc_data = orig_data
if self.verbose > 0: print("done with the pre-evolution")
def preevolve(my_data):
"""
preevolve is called before we being the timestepping loop. For
the incompressible solver, this does an initial projection on the
velocity field and then goes through the full evolution to get the
value of phi. The fluid state (u, v) is then reset to values
before this evolve.
"""
myg = my_data.grid
u = my_data.get_var("x-velocity")
v = my_data.get_var("y-velocity")
my_data.fill_BC("x-velocity")
my_data.fill_BC("y-velocity")
# 1. do the initial projection. This makes sure that our original
# velocity field satisties div U = 0
# next create the multigrid object. We want Neumann BCs on phi
# at solid walls and periodic on phi for periodic BCs
MG = multigrid.CellCenterMG2d(myg.nx,
myg.ny,
xl_BC_type="periodic",
xr_BC_type="periodic",
yl_BC_type="periodic",
yr_BC_type="periodic",
xmin=myg.xmin,
xmax=myg.xmax,
ymin=myg.ymin,
ymax=myg.ymax,
verbose=0)
# first compute divU
divU = MG.soln_grid.scratch_array()
divU[MG.ilo:MG.ihi+1,MG.jlo:MG.jhi+1] = \
0.5*(u[myg.ilo+1:myg.ihi+2,myg.jlo:myg.jhi+1] -
u[myg.ilo-1:myg.ihi ,myg.jlo:myg.jhi+1])/myg.dx + \
0.5*(v[myg.ilo:myg.ihi+1,myg.jlo+1:myg.jhi+2] -
v[myg.ilo:myg.ihi+1,myg.jlo-1:myg.jhi ])/myg.dy
# solve L phi = DU
# initialize our guess to the solution
MG.init_zeros()
# setup the RHS of our Poisson equation
MG.init_RHS(divU)
# solve
MG.solve(rtol=1.e-10)
# store the solution in our my_data object -- include a single
# ghostcell
phi = my_data.get_var("phi")
solution = MG.get_solution()
phi[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2] = \
solution[MG.ilo-1:MG.ihi+2,MG.jlo-1:MG.jhi+2]
# compute the cell-centered gradient of phi and update the
# velocities
gradp_x = myg.scratch_array()
gradp_y = myg.scratch_array()
gradp_x[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] = \
0.5*(phi[myg.ilo+1:myg.ihi+2,myg.jlo:myg.jhi+1] -
phi[myg.ilo-1:myg.ihi ,myg.jlo:myg.jhi+1])/myg.dx
gradp_y[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] = \
0.5*(phi[myg.ilo:myg.ihi+1,myg.jlo+1:myg.jhi+2] -
phi[myg.ilo:myg.ihi+1,myg.jlo-1:myg.jhi ])/myg.dy
u[:, :] -= gradp_x
v[:, :] -= gradp_y
# fill the ghostcells
my_data.fill_BC("x-velocity")
my_data.fill_BC("y-velocity")
# 2. now get an approximation to gradp at n-1/2 by going through the
# evolution.
# store the current solution
copyData = patch.cell_center_data_clone(my_data)
# get the timestep
dt = timestep.timestep(copyData)
# evolve
evolve.evolve(copyData, dt)
# update gradp_x and gradp_y in our main data object
gp_x = my_data.get_var("gradp_x")
gp_y = my_data.get_var("gradp_y")
new_gp_x = copyData.get_var("gradp_x")
new_gp_y = copyData.get_var("gradp_y")
gp_x[:, :] = new_gp_x[:, :]
gp_y[:, :] = new_gp_y[:, :]
print "done with the pre-evolution"
def preevolve(self):
"""
preevolve is called before we being the timestepping loop. For
the incompressible solver, this does an initial projection on the
velocity field and then goes through the full evolution to get the
value of phi. The fluid state (u, v) is then reset to values
before this evolve.
"""
self.in_preevolve = True
myg = self.cc_data.grid
u = self.cc_data.get_var("x-velocity")
v = self.cc_data.get_var("y-velocity")
self.cc_data.fill_BC("x-velocity")
self.cc_data.fill_BC("y-velocity")
# 1. do the initial projection. This makes sure that our original
# velocity field satisties div U = 0
# next create the multigrid object. We want Neumann BCs on phi
# at solid walls and periodic on phi for periodic BCs
mg = MG.CellCenterMG2d(myg.nx, myg.ny,
xl_BC_type="periodic",
xr_BC_type="periodic",
yl_BC_type="periodic",
yr_BC_type="periodic",
xmin=myg.xmin, xmax=myg.xmax,
ymin=myg.ymin, ymax=myg.ymax,
verbose=0)
# first compute divU
divU = mg.soln_grid.scratch_array()
divU.v()[:, :] = \
0.5*(u.ip(1) - u.ip(-1))/myg.dx + 0.5*(v.jp(1) - v.jp(-1))/myg.dy
# solve L phi = DU
# initialize our guess to the solution, set the RHS to divU and
# solve
mg.init_zeros()
mg.init_RHS(divU)
mg.solve(rtol=1.e-10)
# store the solution in our self.cc_data object -- include a single
# ghostcell
phi = self.cc_data.get_var("phi")
phi[:, :] = mg.get_solution(grid=myg)
# compute the cell-centered gradient of phi and update the
# velocities
gradp_x, gradp_y = mg.get_solution_gradient(grid=myg)
u[:, :] -= gradp_x
v[:, :] -= gradp_y
# fill the ghostcells
self.cc_data.fill_BC("x-velocity")
self.cc_data.fill_BC("y-velocity")
# 2. now get an approximation to gradp at n-1/2 by going through the
# evolution.
# store the current solution -- we'll restore it in a bit
orig_data = patch.cell_center_data_clone(self.cc_data)
# get the timestep
self.method_compute_timestep()
# evolve
self.evolve()
# update gradp_x and gradp_y in our main data object
new_gp_x = self.cc_data.get_var("gradp_x")
new_gp_y = self.cc_data.get_var("gradp_y")
orig_gp_x = orig_data.get_var("gradp_x")
orig_gp_y = orig_data.get_var("gradp_y")
orig_gp_x[:, :] = new_gp_x[:, :]
orig_gp_y[:, :] = new_gp_y[:, :]
self.cc_data = orig_data
if self.verbose > 0:
print("done with the pre-evolution")
self.in_preevolve = False
def evolve(self):
"""
Evolve the linear advection equation through one timestep. We only
consider the "density" variable in the CellCenterData2d object that
is part of the Simulation.
"""
tm_evolve = self.tc.timer("evolve")
tm_evolve.begin()
myg = self.cc_data.grid
myd = self.cc_data
order = self.rp.get_param("advection.temporal_order")
if order == 2:
# time-integration -- RK2
myd_nhalf = patch.cell_center_data_clone(myd)
# initial slopes and n+1/2 state
k1 = self.substep(myd)
var = myd_nhalf.get_var("density")
var.v()[:,:] += 0.5*self.dt*k1.v()[:,:]
myd_nhalf.fill_BC_all()
# updated slopes, starting with the n+1/2 state
k2 = self.substep(myd_nhalf)
# final update
var = myd.get_var("density")
var.v()[:,:] += self.dt*k2.v()[:,:]
elif order == 4:
# time-integration -- RK4
# first slope (k1) is f(U^n)
k1 = self.substep(myd)
# second slope (k2) is f(U^n + 0.5*dt*k1)
myd1 = patch.cell_center_data_clone(myd)
var = myd1.get_var("density")
var.v()[:,:] += 0.5*self.dt*k1.v()[:,:]
myd1.fill_BC_all()
k2 = self.substep(myd1)
# third slope (k3) is f(U^n + 0.5*dt*k2)
myd2 = patch.cell_center_data_clone(myd)
var = myd2.get_var("density")
var.v()[:,:] += 0.5*self.dt*k2.v()[:,:]
myd2.fill_BC_all()
k3 = self.substep(myd2)
# last slope (k4) is f(U^n + dt*k3)
myd3 = patch.cell_center_data_clone(myd)
var = myd3.get_var("density")
var.v()[:,:] += self.dt*k3.v()[:,:]
myd3.fill_BC_all()
k4 = self.substep(myd3)
# final update
var = myd.get_var("density")
var.v()[:,:] += (self.dt/6.0)*(k1.v()[:,:] + 2.0*k2.v()[:,:] + 2.0*k3.v()[:,:] + k4.v()[:,:])
elif order == 103:
# time-integration -- SSP RK3 (from Shu & Osher 1989)
# compute u^1 = u^n + dt * L(u^n)
k0 = self.substep(myd)
u1 = patch.cell_center_data_clone(myd)
var1 = u1.get_var("density")
var1.v()[:,:] += self.dt*k0.v()[:,:]
u1.fill_BC_all()
# compute u^2 = (3/4) u^n + (1/4) u^1 + (1/4) dt * L(u^1)
k1 = self.substep(u1)
u2 = patch.cell_center_data_clone(myd)
varn = myd.get_var("density")
var1 = u1.get_var("density")
var2 = u2.get_var("density")
var2.v()[:,:] = 0.75*varn.v()[:,:] + 0.25*var1.v()[:,:] + 0.25*self.dt*k1.v()[:,:]
u2.fill_BC_all()
# compute u^new = (1/3) u^n + (2/3) u^2 + (2/3) dt L(u^2)
k2 = self.substep(u2)
var = myd.get_var("density")
var2 = u2.get_var("density")
var.v()[:,:] = (1.0/3.0)*var.v()[:,:] + (2.0/3.0)*var2.v()[:,:] + (2.0/3.0)*self.dt*k2.v()[:,:]
# increment the time
myd.t += self.dt
self.n += 1
tm_evolve.end()
def preevolve(self):
"""
preevolve is called before we being the timestepping loop. For
the low Mach solver, this does an initial projection on the
velocity field and then goes through the full evolution to get the
value of phi. The fluid state (rho, u, v) is then reset to values
before this evolve.
"""
self.in_preevolve = True
myg = self.cc_data.grid
rho = self.cc_data.get_var("density")
u = self.cc_data.get_var("x-velocity")
v = self.cc_data.get_var("y-velocity")
self.cc_data.fill_BC("density")
self.cc_data.fill_BC("x-velocity")
self.cc_data.fill_BC("y-velocity")
# 1. do the initial projection. This makes sure that our original
# velocity field satisties div U = 0
# the coefficent for the elliptic equation is beta_0^2/rho
coeff = 1/rho
beta0 = self.base["beta0"]
coeff.v()[:,:] = coeff.v()*beta0.v2d()**2
# next create the multigrid object. We defined phi with
# the right BCs previously
mg = vcMG.VarCoeffCCMG2d(myg.nx, myg.ny,
xl_BC_type=self.cc_data.BCs["phi"].xlb,
xr_BC_type=self.cc_data.BCs["phi"].xrb,
yl_BC_type=self.cc_data.BCs["phi"].ylb,
yr_BC_type=self.cc_data.BCs["phi"].yrb,
xmin=myg.xmin, xmax=myg.xmax,
ymin=myg.ymin, ymax=myg.ymax,
coeffs=coeff,
coeffs_bc=self.cc_data.BCs["density"],
verbose=0)
# first compute div{beta_0 U}
div_beta_U = mg.soln_grid.scratch_array()
# u/v are cell-centered, divU is cell-centered
div_beta_U.v()[:,:] = \
0.5*beta0.v2d()*(u.ip(1) - u.ip(-1))/myg.dx + \
0.5*(beta0.v2dp(1)*v.jp(1) - beta0.v2dp(-1)*v.jp(-1))/myg.dy
# solve D (beta_0^2/rho) G (phi/beta_0) = D( beta_0 U )
# set the RHS to divU and solve
mg.init_RHS(div_beta_U.d)
mg.solve(rtol=1.e-10)
# store the solution in our self.cc_data object -- include a single
# ghostcell
phi = self.cc_data.get_var("phi")
phi.d[:,:] = mg.get_solution(grid=myg).d
# get the cell-centered gradient of phi and update the
# velocities
# FIXME: this update only needs to be done on the interior
# cells -- not ghost cells
gradp_x, gradp_y = mg.get_solution_gradient(grid=myg)
coeff = 1.0/rho
coeff.v()[:,:] = coeff.v()*beta0.v2d()
u.v()[:,:] -= coeff.v()*gradp_x.v()
v.v()[:,:] -= coeff.v()*gradp_y.v()
# fill the ghostcells
self.cc_data.fill_BC("x-velocity")
self.cc_data.fill_BC("y-velocity")
# 2. now get an approximation to gradp at n-1/2 by going through the
# evolution.
# store the current solution -- we'll restore it in a bit
orig_data = patch.cell_center_data_clone(self.cc_data)
# get the timestep
self.compute_timestep()
# evolve
self.evolve()
# update gradp_x and gradp_y in our main data object
new_gp_x = self.cc_data.get_var("gradp_x")
new_gp_y = self.cc_data.get_var("gradp_y")
orig_gp_x = orig_data.get_var("gradp_x")
orig_gp_y = orig_data.get_var("gradp_y")
orig_gp_x.d[:,:] = new_gp_x.d[:,:]
orig_gp_y.d[:,:] = new_gp_y.d[:,:]
self.cc_data = orig_data
if self.verbose > 0: print("done with the pre-evolution")
self.in_preevolve = False
def preevolve(self):
"""
preevolve is called before we being the timestepping loop. For
the incompressible solver, this does an initial projection on the
velocity field and then goes through the full evolution to get the
value of phi. The fluid state (u, v) is then reset to values
before this evolve.
"""
myg = self.cc_data.grid
u = self.cc_data.get_var("x-velocity")
v = self.cc_data.get_var("y-velocity")
self.cc_data.fill_BC("x-velocity")
self.cc_data.fill_BC("y-velocity")
# 1. do the initial projection. This makes sure that our original
# velocity field satisties div U = 0
# next create the multigrid object. We defined phi with
# the right BCs previously
mg = MG.CellCenterMG2d(myg.nx,
myg.ny,
xl_BC_type=self.cc_data.BCs["phi"].xlb,
xr_BC_type=self.cc_data.BCs["phi"].xrb,
yl_BC_type=self.cc_data.BCs["phi"].ylb,
yr_BC_type=self.cc_data.BCs["phi"].yrb,
xmin=myg.xmin,
xmax=myg.xmax,
ymin=myg.ymin,
ymax=myg.ymax,
verbose=0)
# first compute divU
divU = mg.soln_grid.scratch_array()
divU[mg.ilo:mg.ihi+1,mg.jlo:mg.jhi+1] = \
0.5*(u[myg.ilo+1:myg.ihi+2,myg.jlo:myg.jhi+1] -
u[myg.ilo-1:myg.ihi ,myg.jlo:myg.jhi+1])/myg.dx + \
0.5*(v[myg.ilo:myg.ihi+1,myg.jlo+1:myg.jhi+2] -
v[myg.ilo:myg.ihi+1,myg.jlo-1:myg.jhi ])/myg.dy
# solve L phi = DU
# initialize our guess to the solution, set the RHS to divU and
# solve
mg.init_zeros()
mg.init_RHS(divU)
mg.solve(rtol=1.e-10)
# store the solution in our self.cc_data object -- include a single
# ghostcell
phi = self.cc_data.get_var("phi")
solution = mg.get_solution()
phi[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2] = \
solution[mg.ilo-1:mg.ihi+2,mg.jlo-1:mg.jhi+2]
# compute the cell-centered gradient of phi and update the
# velocities
gradp_x = myg.scratch_array()
gradp_y = myg.scratch_array()
gradp_x[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] = \
0.5*(phi[myg.ilo+1:myg.ihi+2,myg.jlo:myg.jhi+1] -
phi[myg.ilo-1:myg.ihi ,myg.jlo:myg.jhi+1])/myg.dx
gradp_y[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] = \
0.5*(phi[myg.ilo:myg.ihi+1,myg.jlo+1:myg.jhi+2] -
phi[myg.ilo:myg.ihi+1,myg.jlo-1:myg.jhi ])/myg.dy
u[:, :] -= gradp_x
v[:, :] -= gradp_y
# fill the ghostcells
self.cc_data.fill_BC("x-velocity")
self.cc_data.fill_BC("y-velocity")
# 2. now get an approximation to gradp at n-1/2 by going through the
# evolution.
# store the current solution -- we'll restore it in a bit
orig_data = patch.cell_center_data_clone(self.cc_data)
# get the timestep
dt = self.timestep()
# evolve
self.evolve(dt)
# update gradp_x and gradp_y in our main data object
new_gp_x = self.cc_data.get_var("gradp_x")
new_gp_y = self.cc_data.get_var("gradp_y")
orig_gp_x = orig_data.get_var("gradp_x")
orig_gp_y = orig_data.get_var("gradp_y")
orig_gp_x[:, :] = new_gp_x[:, :]
orig_gp_y[:, :] = new_gp_y[:, :]
self.cc_data = orig_data
print("done with the pre-evolution")
def preevolve(my_data):
"""
preevolve is called before we being the timestepping loop. For
the incompressible solver, this does an initial projection on the
velocity field and then goes through the full evolution to get the
value of phi. The fluid state (u, v) is then reset to values
before this evolve.
"""
myg = my_data.grid
u = my_data.get_var("x-velocity")
v = my_data.get_var("y-velocity")
my_data.fill_BC("x-velocity")
my_data.fill_BC("y-velocity")
# 1. do the initial projection. This makes sure that our original
# velocity field satisties div U = 0
# next create the multigrid object. We want Neumann BCs on phi
# at solid walls and periodic on phi for periodic BCs
MG = multigrid.CellCenterMG2d(myg.nx, myg.ny,
xl_BC_type="periodic", xr_BC_type="periodic",
yl_BC_type="periodic", yr_BC_type="periodic",
xmin=myg.xmin, xmax=myg.xmax,
ymin=myg.ymin, ymax=myg.ymax,
verbose=0)
# first compute divU
divU = MG.soln_grid.scratch_array()
divU[MG.ilo:MG.ihi+1,MG.jlo:MG.jhi+1] = \
0.5*(u[myg.ilo+1:myg.ihi+2,myg.jlo:myg.jhi+1] -
u[myg.ilo-1:myg.ihi ,myg.jlo:myg.jhi+1])/myg.dx + \
0.5*(v[myg.ilo:myg.ihi+1,myg.jlo+1:myg.jhi+2] -
v[myg.ilo:myg.ihi+1,myg.jlo-1:myg.jhi ])/myg.dy
# solve L phi = DU
# initialize our guess to the solution
MG.init_zeros()
# setup the RHS of our Poisson equation
MG.init_RHS(divU)
# solve
MG.solve(rtol=1.e-10)
# store the solution in our my_data object -- include a single
# ghostcell
phi = my_data.get_var("phi")
solution = MG.get_solution()
phi[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2] = \
solution[MG.ilo-1:MG.ihi+2,MG.jlo-1:MG.jhi+2]
# compute the cell-centered gradient of phi and update the
# velocities
gradp_x = myg.scratch_array()
gradp_y = myg.scratch_array()
gradp_x[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] = \
0.5*(phi[myg.ilo+1:myg.ihi+2,myg.jlo:myg.jhi+1] -
phi[myg.ilo-1:myg.ihi ,myg.jlo:myg.jhi+1])/myg.dx
gradp_y[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] = \
0.5*(phi[myg.ilo:myg.ihi+1,myg.jlo+1:myg.jhi+2] -
phi[myg.ilo:myg.ihi+1,myg.jlo-1:myg.jhi ])/myg.dy
u[:,:] -= gradp_x
v[:,:] -= gradp_y
# fill the ghostcells
my_data.fill_BC("x-velocity")
my_data.fill_BC("y-velocity")
# 2. now get an approximation to gradp at n-1/2 by going through the
# evolution.
# store the current solution
copyData = patch.cell_center_data_clone(my_data)
# get the timestep
dt = timestep.timestep(copyData)
# evolve
evolve.evolve(copyData, dt)
# update gradp_x and gradp_y in our main data object
gp_x = my_data.get_var("gradp_x")
gp_y = my_data.get_var("gradp_y")
new_gp_x = copyData.get_var("gradp_x")
new_gp_y = copyData.get_var("gradp_y")
gp_x[:,:] = new_gp_x[:,:]
gp_y[:,:] = new_gp_y[:,:]
print "done with the pre-evolution"
def evolve(self):
"""
Evolve the equations of compressible hydrodynamics through a
timestep dt.
"""
tm_evolve = self.tc.timer("evolve")
tm_evolve.begin()
myg = self.cc_data.grid
myd = self.cc_data
order = self.rp.get_param("compressible.temporal_order")
if order == 2:
# time-integration -- RK2
myd_nhalf = patch.cell_center_data_clone(myd)
# initial slopes and n+1/2 state
k1 = self.substep(myd)
for n in range(self.vars.nvar):
var = myd_nhalf.get_var_by_index(n)
var.v()[:, :] += 0.5 * self.dt * k1.v(n=n)[:, :]
myd_nhalf.fill_BC_all()
# updated slopes, starting with the n+1/2 state
k2 = self.substep(myd_nhalf)
# final update
for n in range(self.vars.nvar):
var = myd.get_var_by_index(n)
var.v()[:, :] += self.dt * k2.v(n=n)[:, :]
elif order == 4:
# time-integration -- RK4
# first slope (k1) is f(U^n)
k1 = self.substep(myd)
# second slope (k2) is f(U^n + 0.5*dt*k1)
myd1 = patch.cell_center_data_clone(myd)
for n in range(self.vars.nvar):
var = myd1.get_var_by_index(n)
var.v()[:, :] += 0.5 * self.dt * k1.v(n=n)[:, :]
myd1.fill_BC_all()
k2 = self.substep(myd1)
# third slope (k3) is f(U^n + 0.5*dt*k2)
myd2 = patch.cell_center_data_clone(myd)
for n in range(self.vars.nvar):
var = myd2.get_var_by_index(n)
var.v()[:, :] += 0.5 * self.dt * k2.v(n=n)[:, :]
myd2.fill_BC_all()
k3 = self.substep(myd2)
# last slope (k4) is f(U^n + dt*k3)
myd3 = patch.cell_center_data_clone(myd)
for n in range(self.vars.nvar):
var = myd3.get_var_by_index(n)
var.v()[:, :] += self.dt * k3.v(n=n)[:, :]
myd3.fill_BC_all()
k4 = self.substep(myd3)
# final update
for n in range(self.vars.nvar):
var = myd.get_var_by_index(n)
var.v()[:, :] += (
self.dt / 6.0) * (k1.v(n=n)[:, :] + 2.0 * k2.v(n=n)[:, :] +
2.0 * k3.v(n=n)[:, :] + k4.v(n=n)[:, :])
# increment the time
myd.t += self.dt
self.n += 1
tm_evolve.end()
def preevolve(self):
"""
preevolve is called before we being the timestepping loop. For
the incompressible solver, this does an initial projection on the
velocity field and then goes through the full evolution to get the
value of phi. The fluid state (u, v) is then reset to values
before this evolve.
"""
myg = self.cc_data.grid
u = self.cc_data.get_var("x-velocity")
v = self.cc_data.get_var("y-velocity")
self.cc_data.fill_BC("x-velocity")
self.cc_data.fill_BC("y-velocity")
# 1. do the initial projection. This makes sure that our original
# velocity field satisties div U = 0
# next create the multigrid object. We defined phi with
# the right BCs previously
mg = MG.CellCenterMG2d(myg.nx, myg.ny,
xl_BC_type=self.cc_data.BCs["phi"].xlb,
xr_BC_type=self.cc_data.BCs["phi"].xrb,
yl_BC_type=self.cc_data.BCs["phi"].ylb,
yr_BC_type=self.cc_data.BCs["phi"].yrb,
xmin=myg.xmin, xmax=myg.xmax,
ymin=myg.ymin, ymax=myg.ymax,
verbose=0)
# first compute divU
divU = mg.soln_grid.scratch_array()
divU[mg.ilo:mg.ihi+1,mg.jlo:mg.jhi+1] = \
0.5*(u[myg.ilo+1:myg.ihi+2,myg.jlo:myg.jhi+1] -
u[myg.ilo-1:myg.ihi ,myg.jlo:myg.jhi+1])/myg.dx + \
0.5*(v[myg.ilo:myg.ihi+1,myg.jlo+1:myg.jhi+2] -
v[myg.ilo:myg.ihi+1,myg.jlo-1:myg.jhi ])/myg.dy
# solve L phi = DU
# initialize our guess to the solution, set the RHS to divU and
# solve
mg.init_zeros()
mg.init_RHS(divU)
mg.solve(rtol=1.e-10)
# store the solution in our self.cc_data object -- include a single
# ghostcell
phi = self.cc_data.get_var("phi")
solution = mg.get_solution()
phi[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2] = \
solution[mg.ilo-1:mg.ihi+2,mg.jlo-1:mg.jhi+2]
# compute the cell-centered gradient of phi and update the
# velocities
gradp_x = myg.scratch_array()
gradp_y = myg.scratch_array()
gradp_x[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] = \
0.5*(phi[myg.ilo+1:myg.ihi+2,myg.jlo:myg.jhi+1] -
phi[myg.ilo-1:myg.ihi ,myg.jlo:myg.jhi+1])/myg.dx
gradp_y[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] = \
0.5*(phi[myg.ilo:myg.ihi+1,myg.jlo+1:myg.jhi+2] -
phi[myg.ilo:myg.ihi+1,myg.jlo-1:myg.jhi ])/myg.dy
u[:,:] -= gradp_x
v[:,:] -= gradp_y
# fill the ghostcells
self.cc_data.fill_BC("x-velocity")
self.cc_data.fill_BC("y-velocity")
# 2. now get an approximation to gradp at n-1/2 by going through the
# evolution.
# store the current solution -- we'll restore it in a bit
orig_data = patch.cell_center_data_clone(self.cc_data)
# get the timestep
dt = self.timestep()
# evolve
self.evolve(dt)
# update gradp_x and gradp_y in our main data object
new_gp_x = self.cc_data.get_var("gradp_x")
new_gp_y = self.cc_data.get_var("gradp_y")
orig_gp_x = orig_data.get_var("gradp_x")
orig_gp_y = orig_data.get_var("gradp_y")
orig_gp_x[:,:] = new_gp_x[:,:]
orig_gp_y[:,:] = new_gp_y[:,:]
self.cc_data = orig_data
print("done with the pre-evolution")