void
SolveStep::verlet(double delta_t,
int objectNumber,
Object &mainbody,
System &newSystem,
double addtime,
std::string dimension)
{
int i = objectNumber;
System tempSystem = newSystem;
Object &tempBody = tempSystem.objectlist[i];
tempBody.setPosition(mainbody.getPosition()+mainbody.getVelocity()*delta_t +
mainbody.getAcceleration()*delta_t*delta_t*0.5); //pos_i+1
tempSystem.acceleration(tempBody, i, addtime,dimension);
tempBody.setVelocity(mainbody.getVelocity() + 0.5*
(mainbody.getAcceleration()+
tempBody.getAcceleration())*delta_t); //vel_i+1
mainbody.setPosition(tempBody.getPosition());
mainbody.setVelocity(tempBody.getVelocity());
mysolarsystem_.acceleration(mainbody, i, addtime,dimension);
}
void
SolveStep::rk4Step(double delta_t,
int objectNumber,
Object &mainbody,
System &newSystem,
double addtime,
std::string dimension)
{
int i = objectNumber;
System tempSystem = newSystem;
Object &tempBody = tempSystem.objectlist[i];
arma::Col<double> k1Pos(3), k1Vel(3), k2Pos(3), k2Vel(3),
k3Pos(3), k3Vel(3), k4Pos(3), k4Vel(3);
// Calculate k1
arma::Col<double> dPosdt, dVeldt;
dPosdt = tempBody.getVelocity();
dVeldt = tempBody.getAcceleration();
k1Pos = dPosdt*delta_t;
k1Vel = dVeldt*delta_t;
tempBody.setPosition(mainbody.getPosition() + k1Pos*0.5);
tempBody.setVelocity(mainbody.getVelocity() + k1Vel*0.5);
// k2
tempSystem.acceleration(tempBody, i, addtime,dimension);
dPosdt = tempBody.getVelocity();
dVeldt = tempBody.getAcceleration();
k2Pos = dPosdt*delta_t;
k2Vel = dVeldt*delta_t;
tempBody.setPosition(mainbody.getPosition() + k2Pos*0.5);
tempBody.setVelocity( mainbody.getVelocity() + k2Vel*0.5);
// k3
tempSystem.acceleration(tempBody, i, addtime,dimension);
dPosdt = tempBody.getVelocity();
dVeldt = tempBody.getAcceleration();
k3Pos = dPosdt*delta_t;
k3Vel = dVeldt*delta_t;
tempBody.setPosition( mainbody.getPosition() + k3Pos);
tempBody.setVelocity( mainbody.getVelocity() + k3Vel);
// k4
tempSystem.acceleration(tempBody, i, addtime,dimension);
dPosdt = tempBody.getVelocity();
dVeldt = tempBody.getAcceleration();
k4Pos = dPosdt*delta_t;
k4Vel = dVeldt*delta_t;
tempBody.setPosition( mainbody.getPosition() +
1.0/6.0 * (k1Pos + 2.*k2Pos + 2.*k3Pos + k4Pos));
tempBody.setVelocity( mainbody.getVelocity() +
1.0/6.0 * (k1Vel + 2.*k2Vel + 2.*k3Vel + k4Vel));
mainbody.setPosition(tempBody.getPosition());
mainbody.setVelocity(tempBody.getVelocity());
newSystem.acceleration(mainbody, i, addtime,dimension);
}
int
SolveStep::solve(double timestep,
double time,
std::string name,
std::string method,
std::string dimension)
{
/* Solves given system with given parametres using
* given method
* timestep: size of timestep
* time: total simulation time
* name: name of files where the position of the
* particles are saved at some timesteps
* method: verlet or RK4
* dimension: ly or AU
*
* Ditterent timers have not been used at the
* same time.*/
clock_t start, finish;
Distance d;
//declaration and intialisation
omp_set_num_threads(8); //parallelisation
double limit = 60; //definition of bound system
arma::Col<double> center(3), position(3);
center.zeros();
double t = 0.;
System newsystem = mysolarsystem_;
int n = time/timestep;
//file to store energy of the system
std::ofstream energy("energy.m");
energy << "A = [";
//file to store energy of the bound system
std::ofstream bound("BoundEnergy.m");
bound << "A = [";
//update the objects initial acceleration
for (int i = 0 ; i < size() ; ++i)
{
Object &mainbody = newsystem.objectlist[i];
newsystem.acceleration(mainbody, i, 0.0,dimension);
}
// start = clock(); //start timer
//start simulation
for (int k = 0 ; k < n ; ++k)
{
t += timestep;
//file to store position of particles
name.append("t");
std::string filename = name;
filename.append(".m");
std::ofstream fout(filename.c_str());
fout << "t = " << t << "\n A = [";
//variable needed for calculating intermediate steps
double addtime = 0.0;
//simulate all particles for one timestep
#pragma omp parallel for private(i)
for (int i = 0 ; i < size() ; ++i)
{
Object &mainbody = newsystem.objectlist[i];
System tempSystem = mysolarsystem_;
double dt = timestep;
int j = 0;
double maxTimestep;
//chose the smallest timestep
if (mainbody.maxTimestep() < tempSystem.maxTimestep(i))
{
maxTimestep = mainbody.maxTimestep();
}
else
{
maxTimestep = tempSystem.maxTimestep(i);
}
//make sure to use small endough timesteps
while(dt > maxTimestep)
{
dt = dt/2.0;
j += 1;
}
//simulate timesteps
for (int kk = 0 ; kk < std::pow(2,j); ++kk)
{
if (method == "rk4")
{
start = clock(); //start timer
rk4Step(dt, i, mainbody, tempSystem, addtime, dimension);
finish = clock(); //stop timer
std::cout << "time one rk4 step: " <<
static_cast<double>(finish - start)/
static_cast<double>(CLOCKS_PER_SEC ) << " s" << std::endl;
// mainbody.addToFile(name);
addtime += dt;
}
else if(method == "verlet")
{
start = clock(); //start timer
verlet(dt, i, mainbody, tempSystem, addtime, dimension);
finish = clock(); //stop timer
std::cout << "time one verlet step: " <<
static_cast<double>(finish - start)/
static_cast<double>(CLOCKS_PER_SEC ) << " s" << std::endl;
// mainbody.addToFile(name);
addtime += dt;
}
else
{
std::cout << "method must be 'verlet' or 'rk4'" << std::endl;
}
}
mysolarsystem_ = newsystem;
//save position to file
for (int i = 0 ; i < size() ; ++i)
{
Object &mainbody = mysolarsystem_.objectlist[i];
position = mainbody.getPosition();
double dist = d.twoObjects(position,center) ;
if(dist < limit)
{
fout << mainbody.getPosition()(0) << "\t\t" << mainbody.getPosition()(1)
<< "\t\t" << mainbody.getPosition()(2) << "\n";
}
// else
// {
// mysolarsystem_.removeObject(i);
// i-=1;
// }
}
fout << "]; \n";
fout << "plot3(A(:,1), A(:,2),A(:,3), 'o')\n";
fout << "t = " << t ;
fout.close();
}
//write energy of the system to file
bound << t << "\t\t" << mysolarsystem_.boundPotentialEnergy(limit) << "\t\t"
<< mysolarsystem_.boundKineticEnergi(limit) << "\n";
energy << t << "\t\t" << mysolarsystem_.potentialEnergy() << "\t\t"
<< mysolarsystem_.kineticEnergi() << "\n";
if (k % 100 == 0)
{
std::cout << t << std::endl;
}
}
// finish = clock(); //stop timer
// std::cout << "time: " <<
// static_cast<double>(finish - start)/
// static_cast<double>(CLOCKS_PER_SEC ) << " s" << std::endl;
energy << "]; \n";
energy.close();
bound << "]; \n";
bound.close();
for (int i = 0 ; i < size() ; ++i)
{
Object &mainbody = mysolarsystem_.objectlist[i];
mysolarsystem_.acceleration(mainbody, i, 0.0,dimension);
}
//write final postition to file
std::ofstream fout("end.m");
fout << "A = [";
for (int i = 0 ; i < size() ; ++i)
{
Object &mainbody = mysolarsystem_.objectlist[i];
fout << mainbody.getPosition()(0) << "\t\t" << mainbody.getPosition()(1)
<< "\t\t" << mainbody.getPosition()(2) << "\n";
}
fout << "] \n";
fout.close();
return 0;
}
