/* * implementation of euler approximation of the shallow water PDE * @pre: a valid Mesh class instance @mesh * @post: all triangle in the mesh class have new value() = old value - dt/area() * total flux, where total flux is calculated by all three edges of the triangle @return: return total time t+dt */ double hyperbolic_step(MESH& mesh, FLUX& f, double t, double dt) { // Step the finite volume model in time by dt. // Implement Equation 7 from your pseudocode here. for (auto it = mesh.tri_begin(); it!=mesh.tri_end() ; ++it) { // value function will return the flux QVar total_flux=QVar(0,0,0); QVar qm = QVar(0,0,0); // iterate through 3 edges of a triangle auto edgetemp = (*it).edge1(); for (int num = 0; num < 3; num++) { if (num ==0) edgetemp= (*it).edge1(); else if (num==1) edgetemp = (*it).edge2(); else edgetemp = (*it).edge3(); if ( mesh.has_neighbor(edgetemp.index()) ) // it has a common triangle { auto nx = ((*it).norm_vector(edgetemp)).x; auto ny = ((*it).norm_vector(edgetemp)).y; // find the neighbour of a common edge for (auto i = mesh.tri_edge_begin(edgetemp.index()); i != mesh.tri_edge_end(edgetemp.index()); ++i){ if (!(*i==*it)) qm = (*i).value(); } // calculat the total flux total_flux += f(nx, ny, dt, (*it).value(), qm); } else{ // when it doesnt have a neighbour shared with this edge auto nx = ((*it).norm_vector(edgetemp)).x; auto ny = ((*it).norm_vector(edgetemp)).y; qm = QVar((*it).value().h, 0, 0 ); // approximation total_flux += f(nx, ny, dt, (*it).value(), qm); } } (*it).value() += total_flux * (- dt / (*it).area()); } return t + dt; }