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oldroyd_theta_scheme3.h

The Oldroyd problem by the theta-scheme – class body.

The Oldroyd problem by the theta-scheme – class body

template <class P>
void oldroyd_theta_scheme<P>::sub_step1 (
const field& tau_h0, const field& uh0, const field& ph0,
field& tau_h, field& uh, field& ph) const
{
update_transport_stress (uh0);
field gamma_h = inv_mt*(th*tau_h0 - thb);
test v (Xh), xi (Th);
field lh = lambda*integrate (dot(uh0,v))
+ b*(c1*tau_h0 + c2*gamma_h);
ph = ph0;
uh.set_u() = uh0.u();
stokes.solve (lh, field(Qh,0), uh, ph);
field Duh = inv_mt*integrate(ddot(D(uh),xi));
tau_h = c1*tau_h0 + c2*gamma_h + 2*c3*Duh;
}
template <class P>
void oldroyd_theta_scheme<P>::sub_step2 (
const field& uh0,
const field& tau_h1, const field& uh1,
field& tau_h, field& uh) const
{
uh = (1-theta)/theta*uh1 - (1-2*theta)/theta*uh0;
test xi (Th);
if (We == 0) {
field Duh = inv_mt*integrate(ddot(D(uh),xi));
tau_h = 2*alpha*Duh;
return;
}
update_transport_stress (uh);
form th_nu = th + nu*mt;
typename P::tau_upstream tau_up (Th.get_geo(), We, alpha);
field lh = integrate (ddot(c4*tau_h1 + 2*c5*D(uh1),xi))
+ integrate ("boundary",
max(0, -dot(uh,normal()))*ddot(tau_up,xi));
problem transport (th_nu);
transport.solve (lh, tau_h);
}
template <class P>
void
oldroyd_theta_scheme<P>::update_transport_stress (const field& uh) const {
typename P::tau_upstream tau_up (Th.get_geo(), We, alpha);
trial tau (Th); test xi (Th);
auto ma = 0.5*((1-a)*grad(uh) - (1+a)*trans(grad(uh)));
auto beta_a = tau*ma + trans(ma)*tau;
th = integrate (ddot(grad_h(tau)*uh + beta_a,xi))
+ integrate ("boundary", max(0, -dot(uh,normal()))*ddot(tau,xi))
+ integrate ("internal_sides",
- dot(uh,normal())*ddot(jump(tau),average(xi))
+ 0.5*abs(dot(uh,normal()))*ddot(jump(tau),jump(xi)));
thb = integrate ("boundary", max(0, -dot(uh,normal()))*ddot(tau_up,xi));
}
lh
field lh(Float epsilon, Float t, const test &v)
Definition burgers_diffusion_operators.icc:25
field
see the field page for the full documentation
form
see the form page for the full documentation
problem
see the problem page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
mkgeo_ball.a
int a
Definition mkgeo_ball.sh:151
rheolef::details::dot
rheolef::details::is_vec dot
rheolef::grad
std::enable_if< details::has_field_rdof_interface< Expr >::value, details::field_expr_v2_nonlinear_terminal_field< typenameExpr::scalar_type, typenameExpr::memory_type, details::differentiate_option::gradient > >::type grad(const Expr &expr)
grad(uh): see the expression page for the full documentation
Definition field_expr_terminal.h:930
rheolef::D
std::enable_if< details::has_field_rdof_interface< Expr >::value, details::field_expr_v2_nonlinear_terminal_field< typenameExpr::scalar_type, typenameExpr::memory_type, details::differentiate_option::gradient > >::type D(const Expr &expr)
D(uh): see the expression page for the full documentation.
Definition field_expr_terminal.h:988
rheolef::ddot
T ddot(const tensor_basic< T > &a, const tensor_basic< T > &b)
ddot(x,y): see the expression page for the full documentation
Definition tensor.cc:278
rheolef::grad_h
std::enable_if< details::has_field_rdof_interface< Expr >::value, details::field_expr_v2_nonlinear_terminal_field< typenameExpr::scalar_type, typenameExpr::memory_type, details::differentiate_option::gradient > >::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
Definition field_expr_terminal.h:968
rheolef::normal
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Definition field_expr_terminal.h:432
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&!is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition integrate.h:211
rheolef::trans
csr< T, sequential > trans(const csr< T, sequential > &a)
trans(a): see the form page for the full documentation
Definition csr.h:455
lambda
Definition yield_slip_circle.h:34
nu
Definition nu.h:26
oldroyd_theta_scheme::sub_step1
void sub_step1(const field &tau_h0, const field &uh0, const field &ph0, field &tau_h, field &uh, field &ph) const
Definition oldroyd_theta_scheme3.h:26
oldroyd_theta_scheme::update_transport_stress
void update_transport_stress(const field &uh) const
Definition oldroyd_theta_scheme3.h:65
oldroyd_theta_scheme::sub_step2
void sub_step2(const field &uh0, const field &tau_h1, const field &uh1, field &tau_h, field &uh) const
Definition oldroyd_theta_scheme3.h:42