Rheolef  7.1
an efficient C++ finite element environment
navier_stokes_solve.icc

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

using namespace std;
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;
}
}
}
field lh(Float epsilon, Float t, const test &v)
see the Float page for the full documentation
see the characteristic page for the full documentation
see the field page for the full documentation
see the form page for the full documentation
see the problem_mixed page for the full documentation
see the space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
class rheolef::details::field_expr_v2_nonlinear_node_unary compose
rheolef::details::is_vec dot
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
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::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.
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
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: sphere.icc:25
Definition: leveque.h:25
Float u(const point &x)