navier_stokes_solve.icc

The Navier-Stokes equations with the method of characteristics – solver function

using namespace std;
int navier_stokes_solve (
Float Re, Float delta_t, field l0h, field& uh, field& ph,
size_t& max_iter, Float& tol, odiststream *p_derr=0) {
const space& Xh = uh.get_space();
const space& Qh = ph.get_space();
string label = "navier-stokes-" + Xh.get_geo().name();
integrate_option iopt;
iopt.set_family(integrate_option::gauss_lobatto);
iopt.set_order(Xh.degree());
trial u (Xh), p (Qh);
test v (Xh), q (Qh);
form m = integrate (dot(u,v), iopt);
form a = integrate (2*ddot(D(u),D(v)) + 1.5*(Re/delta_t)*dot(u,v), iopt);
form b = integrate (-div(u)*q, iopt);
problem_mixed stokes (a, b);
if (p_derr != 0) *p_derr << "[" << label << "] #n |du/dt|" << endl;
field uh1 = uh;
for (size_t n = 0; true; n++) {
field uh2 = uh1;
uh1 = uh;
field uh_star = 2.0*uh1 - uh2;
characteristic X1 ( -delta_t*uh_star);
characteristic X2 (-2.0*delta_t*uh_star);
field l1h = integrate (dot(compose(uh1,X1),v), iopt);
field l2h = integrate (dot(compose(uh2,X2),v), iopt);
field lh = l0h + (Re/delta_t)*(2*l1h - 0.5*l2h);
stokes.solve (lh, field(Qh,0), uh, ph);
field duh_dt = (3*uh - 4*uh1 + uh2)/(2*delta_t);
Float residual = sqrt(m(duh_dt,duh_dt));
if (p_derr != 0) *p_derr << "[" << label << "] "<< n << " " << residual << endl;
if (residual < tol) {
tol = residual;
max_iter = n;
return 0;
}
if (n == max_iter-1) {
tol = residual;
return 1;
}
}
}
rheolef::div
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::divergence >>::type div(const Expr &expr)
div(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:1031
form
see the form page for the full documentation
field
see the field page for the full documentation
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
problem_mixed
see the problem_mixed page for the full documentation
space
see the space page for the full documentation
rheolef::details::compose
class rheolef::details::field_expr_v2_nonlinear_node_unary compose
p
Definition: sphere.icc:25
navier_stokes_solve
int navier_stokes_solve(Float Re, Float delta_t, field l0h, field &uh, field &ph, size_t &max_iter, Float &tol, odiststream *p_derr=0)
Definition: navier_stokes_solve.icc:26
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
a
Definition: diffusion_isotropic.h:25
lh
field lh(Float epsilon, Float t, const test &v)
Definition: burgers_diffusion_operators.icc:25
mkgeo_sector.m
m
Definition: mkgeo_sector.sh:118
characteristic
see the characteristic page for the full documentation
test
see the test page for the full documentation
u
Definition: leveque.h:25
Float
see the Float 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
u
Float u(const point &x)
Definition: transmission_error.cc:26
mkgeo_ball.b
b
Definition: mkgeo_ball.sh:152
mkgeo_ball.n
n
Definition: mkgeo_ball.sh:150
trial
see the test page for the full documentation
rheolef::details::dot
rheolef::details::is_vec dot