def navierstokes():
domain, geom = mesh.rectilinear( [numpy.linspace(0,1,9)] * 2 )
ubasis, pbasis = function.chain([
domain.basis( 'std', degree=2 ).vector(2),
domain.basis( 'std', degree=1 ),
])
dofs = function.DerivativeTarget( [len(ubasis)] )
u = ubasis.dot( dofs )
p = pbasis.dot( dofs )
viscosity = 1
inertia = model.Integral( (ubasis * u).sum(-1), domain=domain, geometry=geom, degree=5 )
stokesres = model.Integral( viscosity * ubasis['ni,j'] * (u['i,j']+u['j,i']) - ubasis['nk,k'] * p + pbasis['n'] * u['k,k'], domain=domain, geometry=geom, degree=5 )
residual = stokesres + model.Integral( ubasis['ni'] * u['i,j'] * u['j'], domain=domain, geometry=geom, degree=5 )
cons = domain.boundary['top,bottom'].project( [0,0], onto=ubasis, geometry=geom, ischeme='gauss2' ) \
| domain.boundary['left'].project( [geom[1]*(1-geom[1]),0], onto=ubasis, geometry=geom, ischeme='gauss2' )
lhs0 = model.solve_linear( dofs, residual=stokesres, constrain=cons )
for name in 'direct', 'newton', 'pseudotime':
@unittest( name=name, raises=name=='direct' and model.ModelError)
def res():
tol = 1e-10
if name == 'direct':
lhs = model.solve_linear( dofs, residual=residual, constrain=cons )
elif name == 'newton':
lhs = model.newton( dofs, residual=residual, lhs0=lhs0, freezedofs=cons.where ).solve( tol=tol, maxiter=2 )
else:
lhs = model.pseudotime( dofs, residual=residual, lhs0=lhs0, freezedofs=cons.where, inertia=inertia, timestep=1 ).solve( tol=tol, maxiter=3 )
res = residual.replace( dofs, lhs ).eval()
resnorm = numpy.linalg.norm( res[~cons.where] )
assert resnorm < tol
def res():
if name == 'direct':
lhs = model.solve_linear( dofs, residual=residual, constrain=cons )
else:
lhs = model.newton( dofs, residual=residual, lhs0=cons|0, freezedofs=cons.where ).solve( tol=1e-10, maxiter=0 )
res = residual.replace( dofs, lhs ).eval()
resnorm = numpy.linalg.norm( res[~cons.where] )
assert resnorm < 1e-13
def res():
tol = 1e-10
if name == 'direct':
lhs = model.solve_linear( dofs, residual=residual, constrain=cons )
elif name == 'newton':
lhs = model.newton( dofs, residual=residual, lhs0=lhs0, freezedofs=cons.where ).solve( tol=tol, maxiter=2 )
else:
lhs = model.pseudotime( dofs, residual=residual, lhs0=lhs0, freezedofs=cons.where, inertia=inertia, timestep=1 ).solve( tol=tol, maxiter=3 )
res = residual.replace( dofs, lhs ).eval()
resnorm = numpy.linalg.norm( res[~cons.where] )
assert resnorm < tol
def navierstokes():
domain, geom = mesh.rectilinear([numpy.linspace(0, 1, 9)] * 2)
ubasis, pbasis = function.chain([
domain.basis('std', degree=2).vector(2),
domain.basis('std', degree=1),
])
dofs = function.DerivativeTarget([len(ubasis)])
u = ubasis.dot(dofs)
p = pbasis.dot(dofs)
viscosity = 1
inertia = model.Integral((ubasis * u).sum(-1),
domain=domain,
geometry=geom,
degree=5)
stokesres = model.Integral(viscosity * ubasis['ni,j'] *
(u['i,j'] + u['j,i']) - ubasis['nk,k'] * p +
pbasis['n'] * u['k,k'],
domain=domain,
geometry=geom,
degree=5)
residual = stokesres + model.Integral(ubasis['ni'] * u['i,j'] * u['j'],
domain=domain,
geometry=geom,
degree=5)
cons = domain.boundary['top,bottom'].project( [0,0], onto=ubasis, geometry=geom, ischeme='gauss2' ) \
| domain.boundary['left'].project( [geom[1]*(1-geom[1]),0], onto=ubasis, geometry=geom, ischeme='gauss2' )
lhs0 = model.solve_linear(dofs, residual=stokesres, constrain=cons)
for name in 'direct', 'newton', 'pseudotime':
@unittest(name=name, raises=name == 'direct' and model.ModelError)
def res():
tol = 1e-10
if name == 'direct':
lhs = model.solve_linear(dofs,
residual=residual,
constrain=cons)
elif name == 'newton':
lhs = model.newton(dofs,
residual=residual,
lhs0=lhs0,
freezedofs=cons.where).solve(tol=tol,
maxiter=2)
else:
lhs = model.pseudotime(dofs,
residual=residual,
lhs0=lhs0,
freezedofs=cons.where,
inertia=inertia,
timestep=1).solve(tol=tol, maxiter=3)
res = residual.replace(dofs, lhs).eval()
resnorm = numpy.linalg.norm(res[~cons.where])
assert resnorm < tol
def res():
if name == 'direct':
lhs = model.solve_linear(dofs,
residual=residual,
constrain=cons)
else:
lhs = model.newton(dofs,
residual=residual,
lhs0=cons | 0,
freezedofs=cons.where).solve(tol=1e-10,
maxiter=0)
res = residual.replace(dofs, lhs).eval()
resnorm = numpy.linalg.norm(res[~cons.where])
assert resnorm < 1e-13
def res():
tol = 1e-10
if name == 'direct':
lhs = model.solve_linear(dofs,
residual=residual,
constrain=cons)
elif name == 'newton':
lhs = model.newton(dofs,
residual=residual,
lhs0=lhs0,
freezedofs=cons.where).solve(tol=tol,
maxiter=2)
else:
lhs = model.pseudotime(dofs,
residual=residual,
lhs0=lhs0,
freezedofs=cons.where,
inertia=inertia,
timestep=1).solve(tol=tol, maxiter=3)
res = residual.replace(dofs, lhs).eval()
resnorm = numpy.linalg.norm(res[~cons.where])
assert resnorm < tol
