Introduction

The method I chose for practice writing a higher dimension code is the 1st order accurate, split scheme, Godunov + Exact Riemann Solver to solve the 2D Euler equations for a cylindrical explosion. This method begins by initializing a 2D Cartesian grid

Upsides / Downsides

The good aspects of this method are: 1) accurate resolution of shear waves, 2) simple to construct.

The downside is: 1) not higher order (if wanted to add this - code could become quite complex to take into account the addition of shears into the TVD algorithms)