Automated finite-difference time evolution code for conservation laws
R. David Todd
Brigham Young University
Jalen Morgan
Brigham Young University
Abstract
Time evolution of initial data in Partial Differential Equations (PDEs) plays an important role in understanding physical phenomena, and is of particular interest in determining the long term dynamics of perturbed unstable waves. In this paper, we describe the Python package we have developed for carrying out time evolution studies. This package allows the user to input a conservation law or reaction-diffusion equation in one spatial dimension in system form. The Python program then generates the MATLAB driver and system specific files to be used in carrying out time evolution using the Crank-Nicolson scheme. We demonstrate the performance of this package in three example systems: Burgers' equation, nonisentropic Navier-Stokes, and reactive Navier-Stokes (rNS). The rNS study suggests the way in which instability of traveling waves is manifested in that system.
