double hyperbolic_step(MESH& m, FLUX& f, double t, double dt) {
// HW4B: YOUR CODE HERE
// Step the finite volume model in time by dt.
// Pseudocode:
// Compute all fluxes. (before updating any triangle Q_bars)
// For each triangle, update Q_bar using the fluxes as in Equation 8.
// NOTE: Much like symp_euler_step, this may require TWO for-loops
/* 1. Initialize a vector temp_Q of size @a m.num_triangles() for storing all temp Q_bar values
* 2. Use a TriangleIterator to iterate through all the triangles, for each tri_it:
* a. Compute the sum of fluxes sum_fluxes
* b. temp_Q[(*it).index()] = sum_fluxes
* 3. Use indices of triangles to do another for loop, for each triangle(i):
* a. triangle_i.value().Q_bar = temp_Q[i]
*/
std::vector<QVar> temp_fluxes(m.num_triangles(), QVar());
for (auto tri_it = m.triangle_begin(); tri_it != m.triangle_end(); ++tri_it) {
auto qk = (*tri_it).value();
QVar F_k(0, 0, 0);
for (size_type i = 0; i < 3; ++i) {
auto edge = (*tri_it).edge(i);
QVar qm(0, 0, 0);
if (m.adj_triangle1_index(edge) == -1 || m.adj_triangle2_index(edge) == -1) {
//set_boundary_conditions
qm = QVar(qk.h, 0, 0);
} else {
size_type adj_tri_idx = m.adj_triangle1_index(edge) == (*tri_it).index() ?
m.adj_triangle2_index(edge) : m.adj_triangle1_index(edge);
auto adj_triangle = m.triangle(adj_tri_idx);
qm = adj_triangle.value();
}
auto norm_ke = m.out_norm((*tri_it), edge);
F_k = F_k + f(norm_ke.x, norm_ke.y, dt, qk, qm);
}
// print_triangle(m, (*tri_it), f, t, dt);
temp_fluxes[(*tri_it).index()] = qk - F_k * (dt / (*tri_it).area());
}
for (auto tri_it = m.triangle_begin(); tri_it != m.triangle_end(); ++tri_it) {
(*tri_it).value() = temp_fluxes[(*tri_it).index()];
}
return t + dt;
}
double get_volume(MESH& m) {
double volume = 0.0;
for(auto it = m.triangle_begin(); it != m.triangle_end(); ++it){
auto tri = (*it);
Point normal = get_normal_surface(tri);
double area = tri.area();
volume += normal.z * area * (tri.node(0).position().z + tri.node(1).position().z + tri.node(2).position().z) / 3.0;
}
return volume;
}
double hyperbolic_step(MESH& m, FLUX& f, double t, double dt) {
// HW4B: YOUR CODE HERE
// Step the finite volume model in time by dt.
// Pseudocode:
// Compute all fluxes. (before updating any triangle Q_bars)
// For each triangle, update Q_bar using the fluxes as in Equation 8.
// NOTE: Much like symp_euler_step, this may require TWO for-loops
// Implement Equation 7 from your pseudocode here.
for(auto i = m.edge_begin(); i != m.edge_end(); ++i){
if ((*i).triangle1().index() != (unsigned) -1 && (*i).triangle2().index() != (unsigned) -1 ){
MeshType::Triangle trik = (*i).triangle1();
MeshType::Triangle trim = (*i).triangle2();
unsigned int edge_k = 0;
unsigned int edge_m = 0;
//which edge (*i) is in trik and trim
while(trik.node(edge_k).index()== (*i).node1().index()
|| trik.node(edge_k).index()== (*i).node2().index() )
++edge_k;
while(trim.node(edge_m).index()== (*i).node1().index()
|| trim.node(edge_m).index()== (*i).node2().index() )
++edge_m;
QVar flux = f(trik.normal(edge_k).x, trik.normal(edge_k).y, dt, trik.value().Q, trim.value().Q);
trik.value().F[edge_k] = flux;
trim.value().F[edge_m] = -flux;
}
else{
MeshType::Triangle trik;
if ((*i).triangle1().index() != (unsigned) -1)
trik = (*i).triangle1();
else
trik = (*i).triangle2();
unsigned int edge_k = 0;
while(trik.node(edge_k).index()== (*i).node1().index()
|| trik.node(edge_k).index()== (*i).node2().index() )
++edge_k;
QVar flux = f(trik.normal(edge_k).x, trik.normal(edge_k).y, dt, trik.value().Q, QVar(trik.value().Q.h, 0, 0));
trik.value().F[edge_k] = flux;
}
}
for(auto i = m.triangle_begin(); i != m.triangle_end(); ++i){
QVar sum = QVar(0, 0, 0);
for (int j = 0; j < 3; ++j){
sum += (*i).value().F[j];
}
(*i).value().Q = (*i).value().Q-dt/(*i).area()*sum;
}
return t + dt;
};
void post_process(MESH& m) {
// HW4B: Post-processing step
// Translate the triangle-averaged values to node-averaged values
// Implement Equation 9 from your pseudocode here
for (auto it = m.node_begin(); it != m.node_end(); ++it){
double sumarea=0;
QVar sumQ = QVar(0, 0, 0);
for(auto j = m.triangle_begin(*it); j != m.triangle_end(*it); ++j){
sumarea += (*j).area();
sumQ += (*j).value().Q * (*j).area();
}
(*it).value().Q = sumQ/sumarea;
}
}