oldroyd_theta_scheme3.h
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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));
}
form
see the form page for the full documentation
bdf::alpha
Float alpha[pmax+1][pmax+1]
Definition: bdf.icc:28
mkgeo_contraction.c2
c2
Definition: mkgeo_contraction.sh:199
field
see the field page for the full documentation
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:439
nu
Definition: nu.h:26
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:202
rheolef::grad
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::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:911
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
lh
field lh(Float epsilon, Float t, const test &v)
Definition: burgers_diffusion_operators.icc:25
test
see the test page for the full documentation
problem
see the problem page for the full documentation
rheolef::D
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::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:969
mkgeo_ball.b
b
Definition: mkgeo_ball.sh:152
mkgeo_ball.a
a
Definition: mkgeo_ball.sh:151
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
rheolef::grad_h
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::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:949
trial
see the test page for the full documentation
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
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
rheolef::details::dot
rheolef::details::is_vec dot
lambda
Definition: yield_slip_circle.h:34