Ascent-beta

Lorenz.h

#pragma once

#include "ascent/Link.h"
#include "Eigen/Dense"

class Lorenz : public asc::Module
{
public:
   Eigen::Vector3d x = Eigen::Vector3d::Zero();
   Eigen::Vector3d xd = Eigen::Vector3d::Zero(); // derivative of x

   const double sigma = 10.0;
   const double R = 28.0;
   const double b = 8.0 / 3.0;

   Lorenz(size_t sim);

protected:
   void update();
};

Lorenz.cpp

The update() method defines the system of differential equations.

#include "Lorenz.h"

Lorenz::Lorenz(size_t sim) : asc::Module(sim)
{
   addIntegrator(x, xd);

#define ascNS Lorenz
   ascVar(x)
}

void Lorenz::update()
{
   xd[0] = sigma*(x[1] - x[0]);
   xd[1] = R*x[0] - x[1] - x[0] * x[2];
   xd[2] = -b*x[2] + x[0] * x[1];
}

Initializing and Running

Main.cpp

#include "Lorenz.h"

int main()
{
   Lorenz lorenz(0);
   lorenz.name<Lorenz>("lorenz");
   lorenz.x = Eigen::Vector3d(10.0, 1.0, 1.0); // initial conditions

   lorenz.track("t");
   lorenz.track("x");

   lorenz.run(0.01, 50.0); // time step and simulation end time

   lorenz.outputTrack();

   return 0;
}

Generated File

lorenz.csv

t,lorenz x
0,10.000000,1.000000,1.000000
0.01,9.269483,3.563663,1.190859
0.02,8.841946,5.921403,1.583097
0.03,8.672069,8.135682,2.148331
0.04,8.724232,10.257212,2.880594
0.05,8.970418,12.323869,3.789982
continued...

3D Plotted Results: