def heatcond(src, dst, key, par, gd, l1, l2, m1, m2, n1, n2, nghost):
if key == "hcond":
n1shift,n2shift,m1shift,m2shift,l1shift,l2shift=der_limits(
n1,n2,m1,m2,l1,l2,nghost)
if "tt" in dst["data"].keys():
tt = dst["data/tt"][n1shift,n2shift,m1shift,m2shift,l1shift,l2shift]
else:
calc_derived_data(src["data"], dst["data"], "tt", par,
gd, l1, l2, m1, m2, n1, n2, nghost)
tt = dst["data/tt"][n1shift,n2shift,m1shift,m2shift,l1shift,l2shift]
lntt = np.log(dst["data/tt"][n1shift,n2shift,m1shift,m2shift,l1shift,l2shift])
gradlnT = grad(lntt,grid.dx,grid.dy,grid.dz,x=grid.x[l1shift:l2shift],y=grid.y[m1shift:m2shift],coordinate_system=param.coord_system)
del2T = del2(tt,grid.dx,grid.dy,grid.dz,x=grid.x[l1shift:l2shift],y=grid.y[m1shift:m2shift],coordinate_system=param.coord_system)
if "rho" in src["data"].keys():
lnrho = np.log(src["rho"][n1shift,n2shift,m1shift,m2shift,l1shift,l2shift])
gradlnrho = grad(lnrho,grid.dx,grid.dy,grid.dz,x=grid.x[l1shift:l2shift],y=grid.y[m1shift:m2shift],coordinate_system=param.coord_system)
lrho = True
elif "lnrho" in src["data"].keys():
lnrho = src["lnrho"][n1shift,n2shift,m1shift,m2shift,l1shift,l2shift]
gradlnrho = grad(lnrho,grid.dx,grid.dy,grid.dz,x=grid.x[l1shift:l2shift],y=grid.y[m1shift:m2shift],coordinate_system=param.coord_system)
lrho = True
else:
lrho = False
var = par.cp*par.chi*del2T/tt
if lrho:
var += par.cp*par.chi*dot(gradlnrho,gradlnT)
n1r,m1r,l1r = under_limits(n1,m1,l1,n1shift,m1shift,l1shift,nghost)
return var[n1r:n2-n1+n1r,m1r:m2-m1+m1r,l1r:l2-l1+l1r]
def resistive(src, dst, key, par, gd, l1, l2, m1, m2, n1, n2, nghost):
if key == "etadel2a":
n1shift,n2shift,m1shift,m2shift,l1shift,l2shift=der_limits(
n1,n2,m1,m2,l1,l2,nghost)
if "ax" in src["data"].keys():
aa = np.array([
src["data/ax"][n1shift:n2shift,m1shift:m2shift,l1shift:l2shift],
src["data/ay"][n1shift:n2shift,m1shift:m2shift,l1shift:l2shift],
src["data/az"][n1shift:n2shift,m1shift:m2shift,l1shift:l2shift]
])
if par.eta == 0.:
print("no resistivity used setting etadel2a=0 in resistive")
var = np.zeros_like(aa)
else:
var = par.eta*del2(aa, gd.dx, gd.dy, gd.dz,x=gd.x[l1shift:l2shift],y=gd.y[m1shift:m2shift],coordinate_system=par.coord_system)
else:
print("no vector potential for resistive calculation")
for key in src["data"].keys():
if len(src["data"][key].shape) == 3:
var = np.zeros([3,src["data"][key].shape[0],
src["data"][key].shape[1],
src["data"][key].shape[2] ])
break
n1r,m1r,l1r = under_limits(n1,m1,l1,n1shift,m1shift,l1shift,nghost)
return var[:,n1r:n2-n1+n1r,m1r:m2-m1+m1r,l1r:l2-l1+l1r]
def rostrain(src, dst, key, par, gd, l1, l2, m1, m2, n1, n2, nghost):
if key == "fvisc":
n1shift,n2shift,m1shift,m2shift,l1shift,l2shift=der_limits(
n1,n2,m1,m2,l1,l2,nghost)
if par.nu > 0:
uu = np.array([
src["data/ux"][n1shift:n2shift,m1shift:m2shift,l1shift:l2shift],
src["data/uy"][n1shift:n2shift,m1shift:m2shift,l1shift:l2shift],
src["data/uz"][n1shift:n2shift,m1shift:m2shift,l1shift:l2shift]
])
#viscous forces
th2 = 2./3
th1 = 1./3
fvisc = np.zeros_like(uu)
del2u = np.zeros_like(uu)
for j in range(0,3):
del2u[j] = del2(uu[j],gd.dx,gd.dy,gd.dz,x=gd.x[l1shift:l2shift],y=gd.y[m1shift:m2shift],coordinate_system=par.coord_system)
fvisc += param.nu*del2u
del(del2u)
divu = div(uu,grid.dx,grid.dy,grid.dz,x=grid.x[l1shift:l2shift],y=grid.y[m1shift:m2shift],coordinate_system=param.coord_system)
graddivu = grad(divu,grid.dx,grid.dy,grid.dz,x=grid.x[l1shift:l2shift],y=grid.y[m1shift:m2shift],coordinate_system=param.coord_system)
fvisc += th1*par.nu*graddivu
del(graddivu)
if "rho" in src["data"].keys():
lnrho = np.log(src["data/rho"][n1shift:n2shift,m1shift:m2shift,l1shift:l2shift])
lrho = True
elif "lnrho" in src["data"].keys():
lnrho = src["data/lnrho"][n1shift:n2shift,m1shift:m2shift,l1shift:l2shift]
lrho = True
else:
lrho = False
if lrho:
tmp0 = grad(uu[0],grid.dx,grid.dy,grid.dz,x=grid.x[l1shift:l2shift],y=grid.y[m1shift:m2shift],coordinate_system=param.coord_system)
tmp1 = grad(uu[1],grid.dx,grid.dy,grid.dz,x=grid.x[l1shift:l2shift],y=grid.y[m1shift:m2shift],coordinate_system=param.coord_system)
tmp2 = grad(uu[2],grid.dx,grid.dy,grid.dz,x=grid.x[l1shift:l2shift],y=grid.y[m1shift:m2shift],coordinate_system=param.coord_system)
gradlnrho = grad(lnrho,grid.dx,grid.dy,grid.dz,x=grid.x[l1shift:l2shift],y=grid.y[m1shift:m2shift],coordinate_system=param.coord_system)
Sglnrho = np.zeros_like(uu)
Sglnrho[0] = dot(tmp0,gradlnrho) +\
(tmp0[0]+tmp1[0]+tmp2[0]-th2*divu)*gradlnrho[0]
Sglnrho[1] = dot(tmp1,gradlnrho) +\
(tmp0[1]+tmp1[1]+tmp2[1]-th2*divu)*gradlnrho[1]
Sglnrho[2] = dot(tmp2,gradlnrho) +\
(tmp0[2]+tmp1[2]+tmp2[2]-th2*divu)*gradlnrho[2]
fvisc += par.nu*Sglnrho
del(gradlnrho,Sglnrho)
del(divu)
n1r,m1r,l1r = under_limits(n1,m1,l1,n1shift,m1shift,l1shift,nghost)
return fvisc[:,n1r:n2-n1+n1r,m1r:m2-m1+m1r,l1r:l2-l1+l1r]
def fluid_reynolds(uu,
param,
grid,
lnrho=list(),
shock=list(),
nghost=3,
lmix=True,
quiet=True):
"""
Computes the fluid Reynolds number from the advective and effective
viscous expressions in the momentum equation.
call signature:
fluid_reynolds(uu, ivisc, grid, rho=None, shock=None, nghost=3)
Keyword arguments:
*uu*:
The velocity field [3,mz,my,mx] from the simulation data
*param*:
The Param simulation object with viscosity data information
*grid*:
The Grid simulation object
*lnrho*:
The log density field if it is non-uniform
*shock*:
The shock variable if shock viscosity is applied
*nghost*:
The number of ghost zones appropriate to the order of accuracy
*lmix*:
Option not to include hyper values when Laplacian values present
"""
#viscous forces
th2 = 2. / 3
th1 = 1. / 3
fvisc = np.zeros_like(uu)
#molecular viscosity contribution
ldel2, lshock, lhyper3 = False, False, False
for ivisc in param.ivisc:
if not 'shock' in ivisc and not 'hyper' in ivisc\
and not '\n' in ivisc:
ldel2 = True
if 'shock' in ivisc:
lshock = True
if 'hyper3' in ivisc:
lhyper3 = True
if ldel2:
if lhyper3:
lhyper3 = lhyper3 == lmix
del2u = np.zeros_like(uu)
for j in range(0, 3):
del2u[j] = del2(uu[j],
grid.dx,
grid.dy,
grid.dz,
x=grid.x,
y=grid.y,
coordinate_system=param.coord_system)
del2u[j, :nghost, nghost:-nghost,
nghost:-nghost] = del2u[j, -2 * nghost:-nghost,
nghost:-nghost, nghost:-nghost]
del2u[j, -nghost:, nghost:-nghost,
nghost:-nghost] = del2u[j, nghost:2 * nghost, nghost:-nghost,
nghost:-nghost]
del2u[j, nghost:-nghost, :nghost,
nghost:-nghost] = del2u[j, nghost:-nghost,
-2 * nghost:-nghost, nghost:-nghost]
del2u[j, nghost:-nghost, -nghost:,
nghost:-nghost] = del2u[j, nghost:-nghost, nghost:2 * nghost,
nghost:-nghost]
del2u[j, nghost:-nghost,
nghost:-nghost, :nghost] = del2u[j, nghost:-nghost,
nghost:-nghost,
-2 * nghost:-nghost]
del2u[j, nghost:-nghost, nghost:-nghost,
-nghost:] = del2u[j, nghost:-nghost, nghost:-nghost,
nghost:2 * nghost]
for ivisc in param.ivisc:
ivisc = str.strip(ivisc, '\n')
if 'nu-const' not in ivisc and 'shock' not in ivisc\
and 'hyper' not in ivisc and len(ivisc) > 0:
print(
'fluid_reynolds WARNING: ' + ivisc + ' not implemented\n' +
'terms may be missing from the standard rate of strain tensor'
)
fvisc = fvisc + param.nu * del2u
del (del2u)
tmp0 = grad(uu[0],
grid.dx,
grid.dy,
grid.dz,
x=grid.x,
y=grid.y,
coordinate_system=param.coord_system)
for j in range(0, 3):
tmp0[j, :nghost, nghost:-nghost,
nghost:-nghost] = tmp0[j, -2 * nghost:-nghost, nghost:-nghost,
nghost:-nghost]
tmp0[j, -nghost:, nghost:-nghost,
nghost:-nghost] = tmp0[j, nghost:2 * nghost, nghost:-nghost,
nghost:-nghost]
tmp0[j, nghost:-nghost, :nghost,
nghost:-nghost] = tmp0[j, nghost:-nghost, -2 * nghost:-nghost,
nghost:-nghost]
tmp0[j, nghost:-nghost, -nghost:,
nghost:-nghost] = tmp0[j, nghost:-nghost, nghost:2 * nghost,
nghost:-nghost]
tmp0[j, nghost:-nghost,
nghost:-nghost, :nghost] = tmp0[j, nghost:-nghost, nghost:-nghost,
-2 * nghost:-nghost]
tmp0[j, nghost:-nghost, nghost:-nghost,
-nghost:] = tmp0[j, nghost:-nghost, nghost:-nghost,
nghost:2 * nghost]
tmp1 = grad(uu[1],
grid.dx,
grid.dy,
grid.dz,
x=grid.x,
y=grid.y,
coordinate_system=param.coord_system)
for j in range(0, 3):
tmp1[j, :nghost, nghost:-nghost,
nghost:-nghost] = tmp1[j, -2 * nghost:-nghost, nghost:-nghost,
nghost:-nghost]
tmp1[j, -nghost:, nghost:-nghost,
nghost:-nghost] = tmp1[j, nghost:2 * nghost, nghost:-nghost,
nghost:-nghost]
tmp1[j, nghost:-nghost, :nghost,
nghost:-nghost] = tmp1[j, nghost:-nghost, -2 * nghost:-nghost,
nghost:-nghost]
tmp1[j, nghost:-nghost, -nghost:,
nghost:-nghost] = tmp1[j, nghost:-nghost, nghost:2 * nghost,
nghost:-nghost]
tmp1[j, nghost:-nghost,
nghost:-nghost, :nghost] = tmp1[j, nghost:-nghost, nghost:-nghost,
-2 * nghost:-nghost]
tmp1[j, nghost:-nghost, nghost:-nghost,
-nghost:] = tmp1[j, nghost:-nghost, nghost:-nghost,
nghost:2 * nghost]
tmp2 = grad(uu[2],
grid.dx,
grid.dy,
grid.dz,
x=grid.x,
y=grid.y,
coordinate_system=param.coord_system)
for j in range(0, 3):
tmp2[j, :nghost, nghost:-nghost,
nghost:-nghost] = tmp2[j, -2 * nghost:-nghost, nghost:-nghost,
nghost:-nghost]
tmp2[j, -nghost:, nghost:-nghost,
nghost:-nghost] = tmp2[j, nghost:2 * nghost, nghost:-nghost,
nghost:-nghost]
tmp2[j, nghost:-nghost, :nghost,
nghost:-nghost] = tmp2[j, nghost:-nghost, -2 * nghost:-nghost,
nghost:-nghost]
tmp2[j, nghost:-nghost, -nghost:,
nghost:-nghost] = tmp2[j, nghost:-nghost, nghost:2 * nghost,
nghost:-nghost]
tmp2[j, nghost:-nghost,
nghost:-nghost, :nghost] = tmp2[j, nghost:-nghost, nghost:-nghost,
-2 * nghost:-nghost]
tmp2[j, nghost:-nghost, nghost:-nghost,
-nghost:] = tmp2[j, nghost:-nghost, nghost:-nghost,
nghost:2 * nghost]
#effect of compressibility
if len(lnrho) > 0:
divu = div(uu,
grid.dx,
grid.dy,
grid.dz,
x=grid.x,
y=grid.y,
coordinate_system=param.coord_system)
divu[:nghost, nghost:-nghost,
nghost:-nghost] = divu[-2 * nghost:-nghost, nghost:-nghost,
nghost:-nghost]
divu[-nghost:, nghost:-nghost,
nghost:-nghost] = divu[nghost:2 * nghost, nghost:-nghost,
nghost:-nghost]
divu[nghost:-nghost, :nghost,
nghost:-nghost] = divu[nghost:-nghost, -2 * nghost:-nghost,
nghost:-nghost]
divu[nghost:-nghost, -nghost:,
nghost:-nghost] = divu[nghost:-nghost, nghost:2 * nghost,
nghost:-nghost]
divu[nghost:-nghost,
nghost:-nghost, :nghost] = divu[nghost:-nghost, nghost:-nghost,
-2 * nghost:-nghost]
divu[nghost:-nghost, nghost:-nghost,
-nghost:] = divu[nghost:-nghost, nghost:-nghost,
nghost:2 * nghost]
gradlnrho = grad(lnrho,
grid.dx,
grid.dy,
grid.dz,
x=grid.x,
y=grid.y,
coordinate_system=param.coord_system)
for j in range(0, 3):
gradlnrho[j, :nghost, nghost:-nghost,
nghost:-nghost] = gradlnrho[j, -2 * nghost:-nghost,
nghost:-nghost,
nghost:-nghost]
gradlnrho[j, -nghost:, nghost:-nghost,
nghost:-nghost] = gradlnrho[j, nghost:2 * nghost,
nghost:-nghost,
nghost:-nghost]
gradlnrho[j, nghost:-nghost, :nghost,
nghost:-nghost] = gradlnrho[j, nghost:-nghost,
-2 * nghost:-nghost,
nghost:-nghost]
gradlnrho[j, nghost:-nghost, -nghost:,
nghost:-nghost] = gradlnrho[j, nghost:-nghost,
nghost:2 * nghost,
nghost:-nghost]
gradlnrho[j, nghost:-nghost,
nghost:-nghost, :nghost] = gradlnrho[j, nghost:-nghost,
nghost:-nghost,
-2 * nghost:-nghost]
gradlnrho[j, nghost:-nghost, nghost:-nghost,
-nghost:] = gradlnrho[j, nghost:-nghost, nghost:-nghost,
nghost:2 * nghost]
Sglnrho = np.zeros_like(uu)
Sglnrho[0] = dot(tmp0,gradlnrho) +\
(tmp0[0]+tmp1[0]+tmp2[0]-th2*divu)*gradlnrho[0]
Sglnrho[1] = dot(tmp1,gradlnrho) +\
(tmp0[1]+tmp1[1]+tmp2[1]-th2*divu)*gradlnrho[1]
Sglnrho[2] = dot(tmp2,gradlnrho) +\
(tmp0[2]+tmp1[2]+tmp2[2]-th2*divu)*gradlnrho[2]
graddivu = grad(divu,
grid.dx,
grid.dy,
grid.dz,
x=grid.x,
y=grid.y,
coordinate_system=param.coord_system)
for j in range(0, 3):
graddivu[j, :nghost, nghost:-nghost,
nghost:-nghost] = graddivu[j, -2 * nghost:-nghost,
nghost:-nghost, nghost:-nghost]
graddivu[j, -nghost:, nghost:-nghost,
nghost:-nghost] = graddivu[j, nghost:2 * nghost,
nghost:-nghost, nghost:-nghost]
graddivu[j, nghost:-nghost, :nghost,
nghost:-nghost] = graddivu[j, nghost:-nghost,
-2 * nghost:-nghost,
nghost:-nghost]
graddivu[j, nghost:-nghost, -nghost:,
nghost:-nghost] = graddivu[j, nghost:-nghost,
nghost:2 * nghost,
nghost:-nghost]
graddivu[j, nghost:-nghost,
nghost:-nghost, :nghost] = graddivu[j, nghost:-nghost,
nghost:-nghost,
-2 * nghost:-nghost]
graddivu[j, nghost:-nghost, nghost:-nghost,
-nghost:] = graddivu[j, nghost:-nghost, nghost:-nghost,
nghost:2 * nghost]
fvisc = fvisc + param.nu * (th1 * graddivu + Sglnrho)
del (Sglnrho)
elif param.ldensity:
print('fluid_reynolds WARNING: no lnrho provided\n' +
'rate of strain tensor likely incomplete')
#shock contribution
if lshock:
if len(shock) == 0:
print('fluid_reynolds WARNING: no shock provided\n' +
'rate of strain tensor likely incomplete')
else:
shock[:nghost, nghost:-nghost,
nghost:-nghost] = shock[-2 * nghost:-nghost, nghost:-nghost,
nghost:-nghost]
shock[-nghost:, nghost:-nghost,
nghost:-nghost] = shock[nghost:2 * nghost, nghost:-nghost,
nghost:-nghost]
shock[nghost:-nghost, :nghost,
nghost:-nghost] = shock[nghost:-nghost, -2 * nghost:-nghost,
nghost:-nghost]
shock[nghost:-nghost, -nghost:,
nghost:-nghost] = shock[nghost:-nghost, nghost:2 * nghost,
nghost:-nghost]
shock[nghost:-nghost,
nghost:-nghost, :nghost] = shock[nghost:-nghost,
nghost:-nghost,
-2 * nghost:-nghost]
shock[nghost:-nghost, nghost:-nghost,
-nghost:] = shock[nghost:-nghost, nghost:-nghost,
nghost:2 * nghost]
divugradlnrho = np.zeros_like(uu)
gradshock = grad(shock,
grid.dx,
grid.dy,
grid.dz,
x=grid.x,
y=grid.y,
coordinate_system=param.coord_system)
for j in range(0, 3):
gradshock[j, :nghost, nghost:-nghost,
nghost:-nghost] = gradshock[j, -2 * nghost:-nghost,
nghost:-nghost,
nghost:-nghost]
gradshock[j, -nghost:, nghost:-nghost,
nghost:-nghost] = gradshock[j, nghost:2 * nghost,
nghost:-nghost,
nghost:-nghost]
gradshock[j, nghost:-nghost, :nghost,
nghost:-nghost] = gradshock[j, nghost:-nghost,
-2 * nghost:-nghost,
nghost:-nghost]
gradshock[j, nghost:-nghost, -nghost:,
nghost:-nghost] = gradshock[j, nghost:-nghost,
nghost:2 * nghost,
nghost:-nghost]
gradshock[j, nghost:-nghost,
nghost:-nghost, :nghost] = gradshock[j,
nghost:-nghost,
nghost:-nghost,
-2 *
nghost:-nghost]
gradshock[j, nghost:-nghost, nghost:-nghost,
-nghost:] = gradshock[j, nghost:-nghost,
nghost:-nghost,
nghost:2 * nghost]
for j in range(0, 3):
divugradlnrho[j] = param.nu_shock*divu*gradshock[j] +\
param.nu_shock*shock*(divu*gradlnrho[j] + graddivu[j])
del (divu, gradshock, gradlnrho, graddivu)
fvisc = fvisc + divugradlnrho
del (divugradlnrho)
if lhyper3:
#deluij5 = np.zeros_like([uu,uu,uu])
#uij5glnrho to be included
del6u = np.zeros_like(uu)
for j in range(0, 3):
del6u[j] = del6(uu[j], grid.dx, grid.dy, grid.dz)
del6u[j, :nghost, nghost:-nghost,
nghost:-nghost] = del6u[j, -2 * nghost:-nghost,
nghost:-nghost, nghost:-nghost]
del6u[j, -nghost:, nghost:-nghost,
nghost:-nghost] = del6u[j, nghost:2 * nghost, nghost:-nghost,
nghost:-nghost]
del6u[j, nghost:-nghost, :nghost,
nghost:-nghost] = del6u[j, nghost:-nghost,
-2 * nghost:-nghost, nghost:-nghost]
del6u[j, nghost:-nghost, -nghost:,
nghost:-nghost] = del6u[j, nghost:-nghost, nghost:2 * nghost,
nghost:-nghost]
del6u[j, nghost:-nghost,
nghost:-nghost, :nghost] = del6u[j, nghost:-nghost,
nghost:-nghost,
-2 * nghost:-nghost]
del6u[j, nghost:-nghost, nghost:-nghost,
-nghost:] = del6u[j, nghost:-nghost, nghost:-nghost,
nghost:2 * nghost]
#del6 for non-cartesian tba
#del6u[j] = del6(uu[j],grid.dx,grid.dy,grid.dz,x=grid.x,y=grid.y,
# coordinate_system=param.coord_system)
fvisc = fvisc + param.nu_hyper3 * del6u
del (del6u)
fvisc2 = np.sqrt(dot2(fvisc))
#advective forces
advec = np.zeros_like(uu)
advec[0] = dot(uu, tmp0)
advec[1] = dot(uu, tmp1)
advec[0] = dot(uu, tmp2)
del (tmp0, tmp1, tmp2)
advec2 = np.sqrt(dot2(advec))
del (advec)
#avoid division by zero
if fvisc2.max() > 0:
fvisc2[np.where(fvisc2 == 0)] = fvisc2[np.where(fvisc2 > 0)].min()
Re = advec2 / fvisc2
#set minimum floor to exclude zero-valued Re
Re[np.where(Re == 0)] = Re[np.where(Re > 0)].min()
else:
Re = advec2
print('Re undefined')
return Re