tneuer / NBodySolver

Some solvers for ODE's and PDE's implemented

ODESolver

Description

This is a full set of solvers for the gravitational N-Body problems, solved for small systems with the typical Integrators Leapfrog, Runge-Kutta 2 and Runge-Kutta 4.

• The NBody_Solver.py file implements a parent class for all the others, which handles initialization (read-in) of the initial values, the time step and the reuse of older initial values . The children need to implement a get_next_steps(self, steps) method, where positions and velocities are calculated. In the for-loop the save_system_information(self, positions, velocities) needs to be called after every iteration.

• The LeapFrog.py module implements the leapfrog method solver.

• The RungeKutta2.py module implements the Runge-Kutta 2 solver.

• The RungeKutta4.py module implements the Runge-Kutta 4 solver.

  if __name__ == "__main__":
      dt = 60*60*24
      RK4 = N_Body_Gravitation_RK4(dt, "./default_initial_short.json", verbose=True)
      results = RK4.evolve(steps=365, saveOnly=270)
      RK4.plot_trajectories(draw_forces=True, draw_energies=False, show=True, save=True)

  • The saveOnly options declares how many positions are saved

    

• The Comparator.py module implements a class which compares the performance of the solvers in terms of energy and runtime. As input it takes a dictonary of solvers, the timestep and the number of steps.

  • The compare method evaluates the solvers for the given steps
  • Planet Earth is shown as comparison planet for the trajectories
  • The results can be directly saved

• The DashSimulation.py implements a high level simulation of the N-Body system. It is based on the Dash library so it needs to be installed like describe in the dependencies below. Dash runs the application in the webbrowser, similar to Java.

  In this application user-defined bodies can be entered, the step size, the sun mass and the drag of every body can be changed dynamically.

  

Features

• Variable drag
• Variable mass of central star
• Automatic recognition of unused dimensions
  • Third dimension input is closed if all default planets have no z-entries

Dependencies

For the normal solvers:

• json

# Color package
>> pip install json

For the Dash simulation

• Dash

# Dash (from https://dash.plot.ly/installation, 2018/10/04)
>> pip install dash==0.28.5  # The core dash backend
>> pip install dash-html-components==0.13.2  # HTML components
>> pip install dash-core-components==0.35.1  # Supercharged components

TODO

• Implements logartihmic mass scaling for point size
• Dark background colour
• Change mass of sun
• planets get smaller with bigger scale
• refactor with Superclass ODESOLVER
• Comparison to true values in sun-earth system --> error calculation
• Different Solver in one plot or all in different
• Timestep input
• Automatic update to two body dimension
• show planet position before adding
• draw every quarter year where earth should be
• Restart message
• body error message
• No fail if body is added during runtime
• Body collision