vel=vel,
scalars=['rho'],
transformation='cylindrical',
coordinate_names=('x', 'phi', 'y'))
f_t, e_t = mms.evaluate('div(vel*rho*cp*temp) - div(k * grad(temp))',
temp,
variable='temp',
vel=vel,
scalars=['rho', 'cp', 'k'],
transformation='cylindrical',
coordinate_names=('x', 'phi', 'y'))
rho = sympy.Symbol('rho')
e_rhou = e_u * rho
e_rhov = e_v * rho
mms.print_hit(e_u, 'exact_u')
mms.print_hit(e_rhou, 'exact_rhou', rho='${rho}')
mms.print_hit(f_u, 'forcing_u', mu='${mu}', rho='${rho}')
mms.print_hit(e_v, 'exact_v')
mms.print_hit(e_rhov, 'exact_rhov', rho='${rho}')
mms.print_hit(f_v, 'forcing_v', mu='${mu}', rho='${rho}')
mms.print_hit(e_p, 'exact_p')
mms.print_hit(f_p, 'forcing_p', rho='${rho}')
mms.print_hit(e_t, 'exact_t')
mms.print_hit(f_t, 'forcing_t', k='${k}', rho='${rho}', cp='${cp}')
#!/usr/bin/env python3
import mms
f, e = mms.evaluate('div(vel*u) - div(diff*grad(u)) + u', 'sin(x)*cos(y)', variable='u',
vel='a*(e_i + 2*e_j)', scalars=['a', 'diff'])
mms.print_hit(e, 'exact')
mms.print_hit(f, 'forcing', a='${a}', diff='${diff}')
v,
variable='v',
vel=vel,
p=p,
scalars=['mu', 'rho'],
transformation='cylindrical',
coordinate_names=('x', 'phi', 'y'))
f_p, e_p = mms.evaluate('div(vel*rho)',
p,
variable='p',
vel=vel,
scalars=['rho'],
transformation='cylindrical',
coordinate_names=('x', 'phi', 'y'))
rho = sympy.Symbol('rho')
e_rhou = e_u * rho
e_rhov = e_v * rho
mms.print_hit(e_u, 'exact_u')
mms.print_hit(e_rhou, 'exact_rhou', rho='${rho}')
mms.print_hit(f_u, 'forcing_u', mu='${mu}', rho='${rho}')
mms.print_hit(e_v, 'exact_v')
mms.print_hit(e_rhov, 'exact_rhov', rho='${rho}')
mms.print_hit(f_v, 'forcing_v', mu='${mu}', rho='${rho}')
mms.print_hit(e_p, 'exact_p')
mms.print_hit(f_p, 'forcing_p', rho='${rho}')
u = 'cos(pi/2 * x)'
vel = u + '* e_i'
p = 'sin(x)'
# Select porosity model
porosity = '0.8'
porosity = '1 - 0.5 * 1 / (1 + exp(-30*(x-1)))'
# Requires smooth_porosity = true in FVKernels
f_u, e_u = mms.evaluate(
'div(vel*rho*u/porosity) - div(mu*porosity*grad(u/porosity)) + porosity*grad(p).dot(e_i)',
u,
variable='u',
vel=vel,
p=p,
porosity=porosity,
scalars=['mu', 'rho'])
f_p, e_p = mms.evaluate('div(vel*rho)',
p,
variable='p',
vel=vel,
scalars=['rho'])
rho = sympy.Symbol('rho')
mms.print_hit(e_u, 'exact_u')
mms.print_hit(f_u, 'forcing_u', mu='${mu}', rho='${rho}')
mms.print_hit(e_p, 'exact_p')
mms.print_hit(f_p, 'forcing_p', rho='${rho}')
u,
variable='u',
vel=vel,
scalars=['mu', 'rho'])
flux_p_left, _ = mms.evaluate('(vel*rho).dot(-e_i)',
p,
variable='p',
vel=vel,
scalars=['rho'])
flux_p_right, _ = mms.evaluate('(vel*rho).dot(e_i)',
p,
variable='p',
vel=vel,
scalars=['rho'])
mms.print_hit(e_u, 'exact_u')
mms.print_hit(f_u, 'forcing_u', mu='${mu}', rho='${rho}')
mms.print_hit(flux_u_left, 'flux_u_left', mu='${mu}', rho='${rho}')
mms.print_hit(flux_u_right, 'flux_u_right', mu='${mu}', rho='${rho}')
mms.print_hit(flux_u_diffusion_left,
'flux_u_diffusion_left',
mu='${mu}',
rho='${rho}')
mms.print_hit(flux_u_diffusion_right,
'flux_u_diffusion_right',
mu='${mu}',
rho='${rho}')
mms.print_hit(e_p, 'exact_p')
mms.print_hit(f_p, 'forcing_p', rho='${rho}')
mms.print_hit(flux_p_left, 'flux_p_left', rho='${rho}')
'div(vel*rho*v/porosity) - div(mu*porosity*grad(v/porosity)) + porosity*grad(p).dot(e_j) + (darcy + forch)*rho*v/porosity',
v,
variable='v',
vel=vel,
p=p,
porosity=porosity,
scalars=['mu', 'rho', 'darcy', 'forch'])
f_p, e_p = mms.evaluate('div(vel*rho)',
p,
variable='p',
vel=vel,
scalars=['rho'])
rho = sympy.Symbol('rho')
mms.print_hit(e_u, 'exact_u')
mms.print_hit(f_u,
'forcing_u',
mu='${mu}',
rho='${rho}',
darcy='${darcy}',
forch='${forch}')
mms.print_hit(e_v, 'exact_v')
mms.print_hit(f_v,
'forcing_v',
mu='${mu}',
rho='${rho}',
darcy='${darcy}',
forch='${forch}')
#!/usr/bin/env python
#* This file is part of the MOOSE framework
#* https://www.mooseframework.org
#*
#* All rights reserved, see COPYRIGHT for full restrictions
#* https://github.com/idaholab/moose/blob/master/COPYRIGHT
#*
#* Licensed under LGPL 2.1, please see LICENSE for details
#* https://www.gnu.org/licenses/lgpl-2.1.html
import mms
fs, ss = mms.evaluate('-div(grad(u))', 'sin(2*pi*x)*sin(2*pi*y)')
mms.print_fparser(fs)
mms.print_hit(fs, 'force')
mms.print_hit(ss, 'exact')
ft, st = mms.evaluate('diff(u,t) - div(grad(u))', 't**3*x*y')
mms.print_fparser(ft)
mms.print_hit(ft, 'force')
mms.print_hit(st, 'exact')
u=u,
vel=vel,
e=e,
p=p,
scalars=['eps'])
_, e_p = mms.evaluate('p',
p,
variable='p',
rho=rho,
rho_et=rho_et,
rho_ud=rho_ud,
ud=ud,
u=u,
vel=vel,
e=e,
p=p,
scalars=['eps'])
mms.print_hit(e_rho, 'exact_rho')
mms.print_hit(f_rho, 'forcing_rho', eps='${eps}')
mms.print_hit(e_rho_ud, 'exact_rho_ud', eps='${eps}')
mms.print_hit(f_rho_ud, 'forcing_rho_ud', eps='${eps}')
mms.print_hit(e_rho_et, 'exact_rho_et')
mms.print_hit(f_rho_et, 'forcing_rho_et', eps='${eps}')
mms.print_hit(e_T, 'exact_T', eps='${eps}')
mms.print_hit(e_eps_p, 'exact_eps_p', eps='${eps}')
mms.print_hit(e_p, 'exact_p', eps='${eps}')
#!/usr/bin/env python3
import mms
f_rho, e_rho = mms.evaluate('div(u*rho) - div(grad(rho))',
'1.1*sin(1.1*x)',
variable='rho',
u='1.1*cos(1.1*x) * e_i')
f_vel, e_vel = mms.evaluate('div(u*vel*rho) - div(grad(vel))',
'1.1*cos(1.1*x)',
variable='vel',
u='1.1*cos(1.1*x) * e_i',
rho='1.1*sin(1.1*x)')
mms.print_hit(f_rho, 'forcing_rho')
mms.print_hit(e_rho, 'exact_rho')
mms.print_hit(f_vel, 'forcing_vel')
mms.print_hit(e_vel, 'exact_vel')
#!/usr/bin/env python3
import mms
f, e = mms.evaluate('-div(grad(u))',
'1.1*sin(0.9*x)*cos(1.2*y)',
variable='u',
transformation='cylindrical',
coordinate_names=('x', 'phi', 'y'))
mms.print_hit(e, 'exact')
mms.print_hit(f, 'forcing')
e = 'rho_et / rho - 0.5 * vel.dot(vel)'
# 0.4 = gamma - 1
p = '0.4 * e * rho'
rho_ht = 'rho_et + p'
ht = 'rho_ht / rho'
gamma = 1.4
R = 8.3145
molar_mass = 29.0e-3
R_specific = R / molar_mass
cp = gamma * R_specific / (gamma - 1.)
cv = cp / gamma
T = 'e / ' + str(cv)
f_rho, e_rho = mms.evaluate('div(mass_flux)', rho, variable='rho', rho_u=rho_u, mass_flux=mass_flux)
f_rho_u, e_rho_u = mms.evaluate('div(mass_flux * u) + grad(p).dot(e_i)', rho_u, variable='rho_u', rho=rho, rho_u=rho_u, mass_flux=mass_flux, u=u, rho_et=rho_et, vel=vel, e=e, p=p)
f_rho_et, e_rho_et = mms.evaluate('div(mass_flux * ht)', rho_et, variable='rho_et', rho_et=rho_et, rho=rho, rho_u=rho_u, mass_flux=mass_flux, u=u, vel=vel, e=e, p=p, rho_ht=rho_ht, ht=ht)
_, e_T = mms.evaluate('T', T, variable='T', rho=rho, rho_et=rho_et, rho_u=rho_u, u=u, vel=vel, e=e, T=T)
_, e_p = mms.evaluate('p', p, variable='p', rho=rho, rho_et=rho_et, rho_u=rho_u, u=u, vel=vel, e=e, p=p)
mms.print_hit(e_rho, 'exact_rho')
mms.print_hit(f_rho, 'forcing_rho')
mms.print_hit(e_rho_u, 'exact_rho_u')
mms.print_hit(f_rho_u, 'forcing_rho_u')
mms.print_hit(e_rho_et, 'exact_rho_et')
mms.print_hit(f_rho_et, 'forcing_rho_et')
mms.print_hit(e_T, 'exact_T')
mms.print_hit(e_p, 'exact_p')
gamma = 1.4
R = 8.3145
molar_mass = 29.0e-3
R_specific = R / molar_mass
cp = gamma * R_specific / (gamma - 1.)
cv = cp / gamma
T = 'e / ' + str(cv)
eps_p = 'eps * p'
f_rho, e_rho = mms.evaluate('div(mass_flux)', rho, variable='rho', eps=eps, rho_ud=rho_ud, mass_flux=mass_flux)
f_rho_ud, e_rho_ud = mms.evaluate('div(mass_flux * u) + eps*grad(p).dot(e_i)', rho_ud, variable='rho_ud', eps=eps, rho=rho, rho_ud=rho_ud, mass_flux=mass_flux, ud=ud, u=u, rho_et=rho_et, vel=vel, e=e, p=p)
f_rho_et, e_rho_et = mms.evaluate('div(mass_flux * ht)', rho_et, variable='rho_et', eps=eps, rho_et=rho_et, rho=rho, rho_ud=rho_ud, mass_flux=mass_flux, ud=ud, u=u, vel=vel, e=e, p=p, rho_ht=rho_ht, ht=ht)
_, e_T = mms.evaluate('T', T, variable='T', eps=eps, rho=rho, rho_et=rho_et, rho_ud=rho_ud, ud=ud, u=u, vel=vel, e=e, T=T)
_, e_eps_p = mms.evaluate('eps_p', eps_p, variable='eps_p', eps=eps, rho=rho, rho_et=rho_et, rho_ud=rho_ud, ud=ud, u=u, vel=vel, e=e, p=p)
_, e_p = mms.evaluate('p', p, variable='p', eps=eps, rho=rho, rho_et=rho_et, rho_ud=rho_ud, ud=ud, u=u, vel=vel, e=e, p=p)
_, e_ud = mms.evaluate('ud', ud, variable='ud', eps=eps, rho_ud=rho_ud, rho=rho)
mms.print_hit(e_rho, 'exact_rho')
mms.print_hit(f_rho, 'forcing_rho')
mms.print_hit(e_rho_ud, 'exact_rho_ud')
mms.print_hit(f_rho_ud, 'forcing_rho_ud')
mms.print_hit(e_rho_et, 'exact_rho_et')
mms.print_hit(f_rho_et, 'forcing_rho_et')
mms.print_hit(e_T, 'exact_T')
mms.print_hit(e_eps_p, 'exact_eps_p')
mms.print_hit(e_p, 'exact_p')
mms.print_hit(e_ud, 'exact_sup_vel_x')
#!/usr/bin/env python
import mms
fs,ss = mms.evaluate('-div(grad(u))', 'sin(2*pi*x)*sin(2*pi*y)')
mms.print_fparser(fs)
mms.print_hit(fs, 'force')
mms.print_hit(ss, 'exact')
ft,st = mms.evaluate('diff(u,t) - div(grad(u))', 't**3*x*y')
mms.print_fparser(ft)
mms.print_hit(ft, 'force')
mms.print_hit(st, 'exact')
#!/usr/bin/env python3
# MooseDocs:start:spatial
import mms
fs, ss = mms.evaluate(('rho * cp * diff(u,t) - div(k*grad(u)) - '
'shortwave*sin(0.5*x*pi)*exp(kappa*y)*sin(1/(hours*3600)*pi*t)'),
't*sin(pi*x)*sin(5*pi*y)',
scalars=['rho', 'cp', 'k', 'kappa', 'shortwave', 'hours'])
mms.print_hit(fs, 'mms_force')
mms.print_hit(ss, 'mms_exact')
# MooseDocs:end:spatial
# MooseDocs:start:temporal
import mms
fs, ss = mms.evaluate(('rho * cp * diff(u,t) - div(k*grad(u)) - '
'shortwave*sin(0.5*x*pi)*exp(kappa*y)*sin(1/(hours*3600)*pi*t)'),
'x*y*exp(-1/32400*t)',
scalars=['rho', 'cp', 'k', 'kappa', 'shortwave', 'hours'])
mms.print_hit(fs, 'mms_force')
mms.print_hit(ss, 'mms_exact')
# MooseDocs:end:temporal
