double hyperbolic_step(MESH& m, FLUX& f, double t, double dt, Point ball_loc, int water_tris) {
for (auto tri_it = m.triangle_begin(); (*tri_it).index() != water_tris; ++tri_it) {
QVar sum = QVar(0,0,0);
/* Defines the force of the floating objects by checking its submerged
* cross section of the ball intersects with the centers of adjacent triangles
*/
floatObj obj = floatObj();
if (norm((*tri_it).center()-Point(ball_loc.x, ball_loc.y, 0)) < ball_loc.z)
obj = floatObj(total_mass*grav, M_PI*ball_loc.z*ball_loc.z, density);
Point norm_vec = (*tri_it).normal((*tri_it).node1(), (*tri_it).node2());
// Calcuate flux using adjacent triangle's Q
if ((*tri_it).adj_triangle((*tri_it).node1(), (*tri_it).node2()).is_valid())
sum += f(norm_vec.x, norm_vec.y, dt, (*tri_it).value().q_bar,
(*tri_it).adj_triangle((*tri_it).node1(), (*tri_it).node2()).value().q_bar, obj);
// Boundary conditions
else
sum += f(norm_vec.x, norm_vec.y, dt, (*tri_it).value().q_bar,
QVar((*tri_it).value().q_bar.h, 0, 0), obj);
norm_vec = (*tri_it).normal((*tri_it).node2(), (*tri_it).node3());
// Calcuate flux using adjacent triangle's Q
if ((*tri_it).adj_triangle((*tri_it).node2(), (*tri_it).node3()).is_valid())
sum += f(norm_vec.x, norm_vec.y, dt, (*tri_it).value().q_bar,
(*tri_it).adj_triangle((*tri_it).node2(), (*tri_it).node3()).value().q_bar, obj);
// Boundary conditions
else
sum += f(norm_vec.x, norm_vec.y, dt, (*tri_it).value().q_bar,
QVar((*tri_it).value().q_bar.h, 0, 0), obj);
norm_vec = (*tri_it).normal((*tri_it).node3(), (*tri_it).node1());
// Calcuate flux using adjacent triangle's Q
if ((*tri_it).adj_triangle((*tri_it).node3(), (*tri_it).node1()).is_valid())
sum += f(norm_vec.x, norm_vec.y, dt, (*tri_it).value().q_bar,
(*tri_it).adj_triangle((*tri_it).node3(), (*tri_it).node1()).value().q_bar, obj);
// Boundary conditions
else
sum += f(norm_vec.x, norm_vec.y, dt, (*tri_it).value().q_bar,
QVar((*tri_it).value().q_bar.h, 0, 0), obj);
(*tri_it).value().q_bar2 = ((*tri_it).value().S * dt/(*tri_it).area()) + (*tri_it).value().q_bar -
(sum * dt/(*tri_it).area());
}
/* In order to use original (as opposed to update) q_bar values in the equation above, we have to update
* q_bar values for all triangles after the q_bar values have been calculated.
* Updates the Source term
*/
for (auto tri_it = m.triangle_begin(); (*tri_it).index() != water_tris; ++tri_it){
(*tri_it).value().S = (*tri_it).value().S/(*tri_it).value().q_bar.h*(*tri_it).value().q_bar2.h;
(*tri_it).value().q_bar = (*tri_it).value().q_bar2;
}
return t + dt;
}
double initialize_node_values(MeshType& mesh) const {
double max_height = 0;
for (auto nit = mesh.node_begin(); nit != mesh.node_end(); ++nit) {
if ((*nit).position().x < 0) {
(*nit).value() = QVar(1.75, 0, 0);
}
else {
(*nit).value() = QVar(1, 0, 0);
}
max_height = std::max(max_height, (*nit).value().h);
}
return max_height;
}
/*
* 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;
}
QVar operator+(const QVar& q){
double hnew = h+q.h;
double hunew = hu+q.hu;
double hvnew = hv+q.hv;
//return QVar(h+q.h, hu + q.hu, hv + q.hv);
return QVar(hnew, hunew, hvnew);
}
QVar operator()(double nx, double ny, double dt,
const QVar& qk, const QVar& qm) {
// Normalize the (nx,ny) vector
double n_length = std::sqrt(nx*nx + ny*ny);
nx /= n_length;
ny /= n_length;
// The velocities normal to the edge
double wm = (qm.hx*nx + qm.hy*ny) / qm.h;
double wk = (qk.hx*nx + qk.hy*ny) / qk.h;
// Lax-Wendroff local dissipation coefficient
double vm = sqrt(grav*qm.h) + sqrt(qm.hx*qm.hx + qm.hy*qm.hy) / qm.h;
double vk = sqrt(grav*qk.h) + sqrt(qk.hx*qk.hx + qk.hy*qk.hy) / qk.h;
double a = dt * std::max(vm*vm, vk*vk);
// Helper values
double scale = 0.5 * n_length;
double gh2 = 0.5 * grav * (qm.h*qm.h + qk.h*qk.h);
// Simple flux with dissipation for stability
return QVar(scale * (wm*qm.h + wk*qk.h) - a * (qm.h - qk.h),
scale * (wm*qm.hx + wk*qk.hx + gh2*nx) - a * (qm.hx - qk.hx),
scale * (wm*qm.hy + wk*qk.hy + gh2*ny) - a * (qm.hy - qk.hy));
}
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 initialize_node_values(MeshType& mesh) const {
double max_height = 0;
for (auto nit = mesh.node_begin(); nit != mesh.node_end(); ++nit) {
unsigned H = 0;
if ((*nit).position().x < 0) H = 1;
(*nit).value() = QVar(1 + 0.75 * H * (pow(((*nit).position().x - 0.75), 2) +
pow((*nit).position().y, 2) - 0.15 * 0.15), 0, 0);
max_height = std::max(max_height, (*nit).value().h);
}
return max_height;
}
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;
};
double initialize_node_values(MeshType& mesh) const {
double max_height = 0;
for (auto nit = mesh.node_begin(); nit != mesh.node_end(); ++nit) {
(*nit).value() = QVar(1 - 0.75 * exp(
-80*(pow((*nit).position().x - 0.75, 2) + pow((*nit).position().y, 2))
), 0, 0);
max_height = std::max(max_height, (*nit).value().h);
}
return max_height;
}
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;
}
}
Point post_process(MESH& m, FORCE force, CONSTRAINT& c, double t, double dt, uint water_nodes) {
static double ball_bottom = std::numeric_limits<double>::max();
double water_dis = std::numeric_limits<double>::max();
double dh = 0;
static double submerged_height = 0;
Point bottom_loc;
Point water_loc;
for (auto n_it = m.node_begin(); n_it != m.node_end(); ++n_it) {
// handles the shallow water
if ((*n_it).index() < water_nodes) {
double sum_area = 0;
QVar value = QVar(0,0,0);
for (auto tri_it = m.adj_triangle_begin((*n_it).uid()); tri_it != m.adj_triangle_end((*n_it).uid()); ++tri_it) {
value += (*tri_it).value().q_bar * (*tri_it).area();
sum_area += (*tri_it).area();
}
(*n_it).value().q = value * 1.0/(sum_area);
}
// handles the ball
else {
(*n_it).set_position((*n_it).position() + (*n_it).value().velocity*dt);
dh = (*n_it).value().q.h - (*n_it).position().z;
(*n_it).value().q.h = (*n_it).position().z;
(*n_it).value().velocity += force(m,(*n_it),t)*dt/(*n_it).value().mass;
if ((*n_it).value().q.h < ball_bottom) {
ball_bottom = (*n_it).position().z;
bottom_loc = (*n_it).position();
}
}
}
// find the water node closest to the bottom of the ball
for (auto n_it = m.node_begin(); (*n_it).index() != water_nodes; ++n_it) {
if (norm(Point((*n_it).position().x,(*n_it).position().y,0)-Point(bottom_loc.x,bottom_loc.y,0)) < water_dis){
water_dis = norm(Point((*n_it).position().x,(*n_it).position().y,0)-Point(bottom_loc.x,bottom_loc.y,0));
water_loc = Point((*n_it).position().x,(*n_it).position().y,(*n_it).value().q.h);
}
}
// apply contraints of neccessary
c(m,ball_bottom);
// determines if the ball fell below shallow water and updates height submerged
if (bottom_loc.z < water_loc.z)
submerged_height += dh;
return Point(bottom_loc.x, bottom_loc.y, submerged_height);
}
/*
* post process of a mesh instance to update the values of all the nodes values
* @pre: a valid mesh instance
* @post: update the nodes values based on approximation of the average of neighbours values
refer to equation 9 on the notes
*/
void post_process(MESH& m) {
// Translate the triangle-averaged values to node-averaged values
// Implement Equation 8 from your pseudocode here
// iterate through all the nodes
for ( auto it = m.node_begin(); it!= m.node_end(); ++it)
{
QVar sum = QVar(0,0,0);
double sumTriArea = 0;
// for each node, iterate through its adjacent triangles
for (auto adji = m.vertex_begin((*it).index()); adji != m.vertex_end((*it).index()); ++ adji)
{
auto tri = (*adji);
sum += tri.area() * tri.value();
sumTriArea += tri.area();
}
(*it).value() = sum/sumTriArea; // update nodes value
}
}
QVar operator()(double nx, double ny, double dt,
const QVar& qk, const QVar& qm) {
double e_length = sqrt(nx*nx + ny*ny);
nx /= e_length;
ny /= e_length;
// The velocities normal to the edge
double wm = (qm.hu*nx + qm.hv*ny) / qm.h;
double wk = (qk.hu*nx + qk.hv*ny) / qk.h;
// Lax-Wendroff local dissipation coefficient
double vm = sqrt(grav*qm.h) + sqrt(qm.hu*qm.hu + qm.hv*qm.hv) / qm.h;
double vk = sqrt(grav*qk.h) + sqrt(qk.hu*qk.hu + qk.hv*qk.hv) / qk.h;
double a = dt * std::max(vm*vm, vk*vk);
// Helper values
double scale = 0.5 * e_length;
double gh2 = 0.5 * grav * (qm.h*qm.h + qk.h*qk.h);
// Simple flux with dissipation for stability
return QVar(scale * (wm*qm.h + wk*qk.h) - a * (qm.h - qk.h),
scale * (wm*qm.hu + wk*qk.hu + gh2*nx) - a * (qm.hu - qk.hu),
scale * (wm*qm.hv + wk*qk.hv + gh2*ny) - a * (qm.hv - qk.hv));
}
QVar operator()(double nx, double ny, double dt,
const QVar& qk, const QVar& qm, floatObj obj = floatObj()) {
double e_length = sqrt(nx*nx + ny*ny);
nx /= e_length;
ny /= e_length;
// The velocities normal to the edge
double wm = (qm.hu*nx + qm.hv*ny) / qm.h;
double wk = (qk.hu*nx + qk.hv*ny) / qk.h;
// Lax-Wendroff local dissipation coefficient
double vm = sqrt(grav*qm.h) + sqrt(qm.hu*qm.hu + qm.hv*qm.hv) / qm.h;
double vk = sqrt(grav*qk.h) + sqrt(qk.hu*qk.hu + qk.hv*qk.hv) / qk.h;
double a = dt * std::max(vm*vm, vk*vk);
// Helper values which accounts for floating objects (MODIFIED EQN HERE)
double scale = 0.5 * e_length;
double gh2 = (0.5 * grav) * (qm.h*qm.h + qk.h*qk.h) + (obj.F/(obj.A * obj.ro)*(qm.h+qk.h));
// Simple flux with dissipation for stability
return QVar(scale * (wm*qm.h + wk*qk.h) - a * (qm.h - qk.h),
scale * (wm*qm.hu + wk*qk.hu + gh2*nx) - a * (qm.hu - qk.hu),
scale * (wm*qm.hv + wk*qk.hv + gh2*ny) - a * (qm.hv - qk.hv));
}
TriData():Q(QVar()), F(3, QVar()){}
int main(int argc, char* argv[])
{
// Check arguments
if (argc < 3) {
std::cerr << "Usage: shallow_water NODES_FILE TRIS_FILE\n";
exit(1);
}
MeshType mesh;
// HW4B: Need node_type before this can be used!
#if 1
std::vector<typename MeshType::node_type> mesh_node;
#endif
// Read all Points and add them to the Mesh
std::ifstream nodes_file(argv[1]);
Point p;
while (CS207::getline_parsed(nodes_file, p)) {
// HW4B: Need to implement add_node before this can be used!
#if 1
mesh_node.push_back(mesh.add_node(p));
#endif
}
// Read all mesh triangles and add them to the Mesh
std::ifstream tris_file(argv[2]);
std::array<int,3> t;
while (CS207::getline_parsed(tris_file, t)) {
// HW4B: Need to implement add_triangle before this can be used!
#if 1
mesh.add_triangle(mesh_node[t[0]], mesh_node[t[1]], mesh_node[t[2]]);
#endif
}
// Print out the stats
std::cout << mesh.num_nodes() << " "
<< mesh.num_edges() << " "
<< mesh.num_triangles() << std::endl;
// HW4B Initialization
// Set the initial conditions according the type of input pattern
if(argv[2][5]=='d'){
Dam<MeshType> init;
for(auto it= mesh.node_begin(); it != mesh.node_end(); ++it)
init(*it);
}
else if((argv[2][5]=='p')){
Pebble<MeshType> init;
for(auto it= mesh.node_begin(); it != mesh.node_end(); ++it)
init(*it);
}
else{
Wave<MeshType> init;
for(auto it= mesh.node_begin(); it != mesh.node_end(); ++it)
init(*it);
}
// Set triangle values
for (auto it=mesh.triangle_begin(); it!=mesh.triangle_end(); ++it) {
(*it).value().Q = QVar(0.0,0.0,0.0);
(*it).value().Q += (*it).node(0).value().Q;
(*it).value().Q += (*it).node(1).value().Q;
(*it).value().Q += (*it).node(2).value().Q;
(*it).value().Q /= 3.0;
}
// Launch the SDLViewer
CS207::SDLViewer viewer;
viewer.launch();
// HW4B: Need to define Mesh::node_type and node/edge iterator
// before these can be used!
#if 1
auto node_map = viewer.empty_node_map(mesh);
viewer.add_nodes(mesh.node_begin(), mesh.node_end(),
CS207::DefaultColor(), NodePosition(), node_map);
viewer.add_edges(mesh.edge_begin(), mesh.edge_end(), node_map);
#endif
viewer.center_view();
// HW4B: Timestep
// CFL stability condition requires dt <= dx / max|velocity|
// For the shallow water equations with u = v = 0 initial conditions
// we can compute the minimum edge length and maximum original water height
// to set the time-step
// Compute the minimum edge length and maximum water height for computing dt
double min_edge_length =( *mesh.edge_begin()).length();
for (auto it=mesh.edge_begin(); it!=mesh.edge_end(); ++it) {
if ((*it).length() < min_edge_length) {
min_edge_length = (*it).length();
}
}
double max_height = 0.0;
for (auto it=mesh.node_begin(); it!=mesh.node_end(); ++it) {
if ((*it).value().Q.h > max_height) {
max_height = (*it).value().Q.h;
}
}
#if 1
double dt = 0.25 * min_edge_length / (sqrt(grav * max_height));
#else
// Placeholder!! Delete me when min_edge_length and max_height can be computed!
double dt = 0.1;
#endif
double t_start = 0;
double t_end = 10;
// Preconstruct a Flux functor
EdgeFluxCalculator f;
// Begin the time stepping
for (double t = t_start; t < t_end; t += dt) {
//print(mesh, t);
// Step forward in time with forward Euler
hyperbolic_step(mesh, f, t, dt);
// Update node values with triangle-averaged values
post_process(mesh);
// Update the viewer with new node positions
// HW4B: Need to define node_iterators before these can be used!
#if 1
viewer.add_nodes(mesh.node_begin(), mesh.node_end(),
CS207::DefaultColor(), NodePosition(), node_map);
#endif
viewer.set_label(t);
// These lines slow down the animation for small meshes.
// Feel free to remove them or tweak the constants.
if (mesh.num_nodes() < 100)
CS207::sleep(0.05);
}
return 0;
}
int main(int argc, char* argv[]) {
// Check arguments
if (argc < 5) {
std::cerr << "Usage: final_project NODES_FILE TRIS_FILE ball.nodes ball.tris \n";
exit(1);
}
MeshType mesh;
std::vector<typename MeshType::node_type> mesh_node;
// Read all water Points and add them to the Mesh
std::ifstream nodes_file(argv[1]);
Point p;
uint water_nodes = 0;
while (CS207::getline_parsed(nodes_file, p)) {
mesh_node.push_back(mesh.add_node(p));
water_nodes++;
}
// Read all water mesh triangles and add them to the Mesh
std::ifstream tris_file(argv[2]);
std::array<int,3> t;
int water_tris = 0;
while (CS207::getline_parsed(tris_file, t)) {
mesh.add_triangle(mesh_node[t[0]], mesh_node[t[1]], mesh_node[t[2]]);
water_tris++;
}
uint water_edges = mesh.num_edges();
std::ifstream nodes_file2(argv[3]);
double radius = 1 * scale;
while (CS207::getline_parsed(nodes_file2, p)) {
p *= scale;
p.z += + start_height;
mesh_node.push_back(mesh.add_node(p));
}
// Read all ball mesh triangles and add them to the mesh
std::ifstream tris_file2(argv[4]);
while (CS207::getline_parsed(tris_file2, t)) {
mesh.add_triangle(mesh_node[t[0]+water_nodes], mesh_node[t[1]+water_nodes], mesh_node[t[2]+water_nodes]);
}
// Print out the stats
std::cout << mesh.num_nodes() << " "
<< mesh.num_edges() << " "
<< mesh.num_triangles() << std::endl;
/* Set the initial conditions */
// Set the initial values of the nodes and get the maximum height double
double max_h = 0;
double dx = 0;
double dy = 0;
auto init_cond = Still();
auto b_init_cond = Cone();
// Find the maximum height and apply initial conditions to nodes
for (auto it = mesh.node_begin(); it != mesh.node_end(); ++it) {
auto n = *it;
if (n.index() < water_nodes){
n.value().q = init_cond(n.position());
n.value().b = b_init_cond(n.position());
max_h = std::max(max_h, n.value().q.h);
}
else {
n.value().q = QVar(n.position().z, 0, 0);
n.value().mass = total_mass/(mesh.num_nodes() - water_nodes);
n.value().velocity = Point(0.0,0.0,0.0);
}
}
// Set the initial values of the triangles to the average of their nodes and finds S
// Set the triangle direction values so that we can determine which
// way to point normal vectors. This part assumes a convex shape
Point center = get_center(mesh);
for (auto it = mesh.triangle_begin(); it != mesh.triangle_end(); ++it) {
auto t = *it;
if (t.index() < water_tris){
t.value().q_bar = (t.node1().value().q +
t.node2().value().q +
t.node3().value().q) / 3.0;
t.value().q_bar2 = t.value().q_bar;
double b_avg = (t.node1().value().b +
t.node2().value().b +
t.node3().value().b) / 3.0;
// finds the max dx and dy to calculate Source
dx = std::max(dx, fabs(t.node1().position().x - t.node2().position().x));
dx = std::max(dx, fabs(t.node2().position().x - t.node3().position().x));
dx = std::max(dx, fabs(t.node3().position().x - t.node1().position().x));
dy = std::max(dy, fabs(t.node1().position().y - t.node2().position().y));
dy = std::max(dy, fabs(t.node2().position().y - t.node3().position().y));
dy = std::max(dy, fabs(t.node3().position().y - t.node1().position().y));
t.value().S = QVar(0, -grav * t.value().q_bar.h * b_avg / dx, -grav * t.value().q_bar.h * b_avg / dy);
}
else
set_normal_direction((*it),center);
}
// Calculate the minimum edge length and set edge inital condititons
double min_edge_length = std::numeric_limits<double>::max();
uint count = 0;
for (auto it = mesh.edge_begin(); it != mesh.edge_end(); ++it, count++){
if (count < water_edges)
min_edge_length = std::min(min_edge_length, (*it).length());
else {
(*it).value().spring_constant = spring_const;
(*it).value().initial_length = (*it).length();
}
}
// Launch the SDLViewer
CS207::SDLViewer viewer;
viewer.launch();
auto node_map = viewer.empty_node_map(mesh);
viewer.add_nodes(mesh.node_begin(), mesh.node_end(),
Color(water_nodes), NodePosition(), node_map);
viewer.add_edges(mesh.edge_begin(), mesh.edge_end(), node_map);
// adds solid color-slows down program significantly
//viewer.add_triangles(mesh.triangle_begin(), mesh.triangle_end(), node_map);
viewer.center_view();
// CFL stability condition requires dt <= dx / max|velocity|
// For the shallow water equations with u = v = 0 initial conditions
// we can compute the minimum edge length and maximum original water height
// to set the time-step
// Compute the minimum edge length and maximum water height for computing dt
double dt = 0.25 * min_edge_length / (sqrt(grav * max_h));
double t_start = 0;
double t_end = 10;
Point ball_loc = Point(0,0,0);
double dh = 0;
// double pressure = gas_const/(4/3*M_PI*radius*radius*radius);
// add listener
my_listener* l = new my_listener(viewer,mesh,dt);
viewer.add_listener(l);
// Preconstruct a Flux functor
EdgeFluxCalculator f;
// defines the constraint
PlaneConstraint c = PlaneConstraint(plane_const);
// Begin the time stepping
for (double t = t_start; t < t_end; t += dt) {
// define forces on ball
GravityForce g_force;
BuoyantForce b_force = BuoyantForce(dh, ball_loc.z);
WindForce w_force;
MassSpringForce ms_force;
// PressureForce p_force = PressureForce(pressure);
// DampingForce d_force = DampingForce(mesh.num_nodes());
auto combined_forces = make_combined_force(g_force, b_force, w_force, ms_force);
// Step forward in time with forward Euler
hyperbolic_step(mesh, f, t, dt, ball_loc, water_tris);
// Update node values with triangle-averaged values
ball_loc = post_process(mesh, combined_forces, c, t, dt, water_nodes);
// Update the viewer with new node positions
viewer.add_nodes(mesh.node_begin(), mesh.node_end(),
Color(water_nodes), NodePosition(), node_map);
// viewer.add_triangles(mesh.triangle_begin(), mesh.triangle_end(), node_map);
viewer.set_label(t);
// find radius of cross sectional radius of ball submerged
dh = ball_loc.z;
if (dh > 2*radius)
dh = 2 * radius;
ball_loc.z = cross_radius(radius, dh);
// These lines slow down the animation for small meshes.
if (mesh.num_nodes() < 100)
CS207::sleep(0.05);
}
return 0;
}
QVar operator/ (double n){
return QVar(h/n, hu/n, hv/n);
}
QVar operator()(Point p) {
if (pow(p.x-0.75,2) + pow(p.y,2) - pow(0.15,2) < 0)
return QVar(1.75,0,0);
else
return QVar(1.0,0,0);
}
QVar operator()(Point p) {
return QVar(1.0 - 0.75*exp(-80*(pow((p.x-0.75),2) + pow(p.y,2))), 0, 0);
}
int main(int argc, char* argv[])
{
// Check arguments
if (argc < 3) {
std::cerr << "Usage: shallow_water NODES_FILE TRIS_FILE\n";
exit(1);
}
auto start = std::chrono::high_resolution_clock::now();
MeshType mesh;
// HW4B: Need node_type before this can be used!
std::vector<typename MeshType::node_type> mesh_node;
// Read all Points and add them to the Mesh
std::ifstream nodes_file(argv[1]);
Point p;
while (CS207::getline_parsed(nodes_file, p)) {
mesh_node.push_back(mesh.add_node(p));
}
// Read all mesh triangles and add them to the Mesh
std::ifstream tris_file(argv[2]);
std::array<int,3> t;
while (CS207::getline_parsed(tris_file, t)) {
// HW4B: Need to implement add_triangle before this can be used!
mesh.add_triangle(mesh_node[t[0]], mesh_node[t[1]], mesh_node[t[2]]);
}
// Print out the stats
std::cout << mesh.num_nodes() << " "
<< mesh.num_edges() << " "
<< mesh.num_triangles() << std::endl;
//Start of nearest neighor. Put all positions that you want inspected in a vector of type double
std::vector<double> pos;
for (auto it = mesh.node_begin(); it != mesh.node_end(); ++it )
pos.push_back((*it).position().z);
unsigned num_neighbors = 10; //num of neighors to return
unsigned object_idx = 5; // do this if you want to examine the neighbors of a specific idx
MeshType::NearestNeighbor a = mesh.calculateNearestNeighbors(num_neighbors ,pos);
auto idx = mesh.getNeighbors(a,object_idx);
auto dist = mesh.getNeighborDistances(a,object_idx);
/*auto all_n = mesh.getAllNeighbors(a);
auto all_d = mesh.getAllNeighborDistances(a);*/
for (unsigned i = 0; i < idx.size(); ++i)
std::cout << "Node " << object_idx << "'s " << i << " neighbor is: node " << idx[i] << " with distance of " << dist[i] << endl;
/*//Uncomment to view results for all nodes
for (unsigned j = 0; j < pos.size(); ++j){
std::cout << endl;
for (unsigned i = 0; i < num_neighbors; ++i)
std::cout << "For node " << j << " neighbor " << i << " is index " << all_n[i+j*num_neighbors] << " and distance is " << all_d[i+j*num_neighbors] << endl;
}*/
// HW4B Initialization
// Set the initial conditions
int wave = 0, peddle=0, dam=1;
if (wave){
for ( auto it = mesh.node_begin(); it!= mesh.node_end(); ++it){
auto x = (*it).position().x;
auto y = (*it).position().y;
double h = 1-0.75 * exp(-80 * ( (x-0.75)*(x-0.75) + y*y ));
mesh.value((*it),QVar( h,0,0));
}
}
else if (peddle){
for ( auto it = mesh.node_begin(); it!= mesh.node_end(); ++it){
auto x = (*it).position().x;
auto y = (*it).position().y;
double h = (x-0.75)*(x-0.75) + y*y -0.15*0.15 ;
int H =0;
if (h < 0)
H = 1;
mesh.value((*it), QVar(1+0.75*H,0,0));
}
}
else if (dam){
for ( auto it = mesh.node_begin(); it!= mesh.node_end(); ++it){
auto x = (*it).position().x;
int H =0;
if (x < 0)
H = 1;
mesh.value((*it), QVar(1+0.75*H,0,0));
}
}
// Perform any needed precomputation
// initialize triangle
for (auto it = mesh.tri_begin(); it != mesh.tri_end(); ++it ) {
(*it).value() = ((*it).node1().value() + (*it).node2().value() + (*it).node3().value())/3.0;
}
// Launch the SDLViewer
CS207::SDLViewer viewer;
viewer.launch();
// HW4B: Need to define Mesh::node_type and node/edge iterator
// before these can be used!
auto node_map = viewer.empty_node_map(mesh);
viewer.add_nodes(mesh.node_begin(), mesh.node_end(),
CS207::DefaultColor(), NodePosition(), node_map);
viewer.add_edges(mesh.edge_begin(), mesh.edge_end(), node_map);
viewer.center_view();
// HW4B: Timestep
// CFL stability condition requires dt <= dx / max|velocity|
// For the shallow water equations with u = v = 0 initial conditions
// we can compute the minimum edge length and maximum original water height
// to set the time-step
// Compute the minimum edge length and maximum water height for computing dt
auto min_length = *std::min_element(mesh.edge_begin(), mesh.edge_end(), EdgeComparator);
auto max_h = *std::max_element(mesh.node_begin(), mesh.node_end(), HeightComparator);
double dt = 0.25 * min_length.length() / (sqrt(grav * max_h.value().h));
double t_start = 0;
double t_end = 0.1;
// Preconstruct a Flux functor
EdgeFluxCalculator f;
// Begin the time stepping
for (double t = t_start; t < t_end; t += dt) {
// Step forward in time with forward Euler
hyperbolic_step(mesh, f, t, dt);
// Update node values with triangle-averaged values
post_process(mesh);
// Update the viewer with new node positions
// HW4B: Need to define node_iterators before these can be used!
viewer.add_nodes(mesh.node_begin(), mesh.node_end(),
CS207::DefaultColor(), NodePosition(), node_map);
viewer.set_label(t);
// These lines slow down the animation for small meshes.
// Feel free to remove them or tweak the constants.
if (mesh.num_nodes() < 100)
CS207::sleep(0.05);
}
auto elapsed = std::chrono::high_resolution_clock::now() - start;
long long microseconds = std::chrono::duration_cast<std::chrono::microseconds>(elapsed).count();
cout << microseconds << endl;
return 0;
}
QVar operator-(const QVar& q){
return QVar(h-q.h, hu - q.hu, hv - q.hv);
}
QVar operator*(double n, QVar& q){
return QVar(n*q.h,n*q.hu,n*q.hv);
}
QVar operator()(Point p) {
if (p.x < 0)
return QVar(1.75,0,0);
else
return QVar(1.0,0,0);
}
QVar operator* (double n){
return QVar(h*n, hu*n, hv*n);
}
QVar operator()(Point p) {
(void) p;
return QVar(1.0,0,0);
}
QVar operator/(double n,QVar& q) {
return QVar(n/q.h, n/q.hu, n/q.hv);
}
