Rheolef  7.2
an efficient C++ finite element environment
 
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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>
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>
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
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));
}
field lh(Float epsilon, Float t, const test &v)
see the field page for the full documentation
see the form page for the full documentation
see the problem page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
rheolef::details::is_vec dot
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
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.
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
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
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
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
csr< T, sequential > trans(const csr< T, sequential > &a)
trans(a): see the form page for the full documentation
Definition csr.h:455
Definition nu.h:26
void sub_step1(const field &tau_h0, const field &uh0, const field &ph0, field &tau_h, field &uh, field &ph) const
void update_transport_stress(const field &uh) const
void sub_step2(const field &uh0, const field &tau_h1, const field &uh1, field &tau_h, field &uh) const