Overview #

Partial Differential Equations’s are cool, both because of the breadth of things they can model, and because of how hard they can be to solve.

This section is meant to showcase some of the projects that I’ve done over the years as I have been learning how to do this kind of thing. I’ll start with a couple projects that I currently mess around with, but plan to add more of my earlier codes at some point in the future.

PAR2D Solver #

PAR2D (parallel, 2D … I know, very creative), is a code to simulate inviscid gas flows. That is, the compressible Euler equations, or the navier stokes equations without skin friction / thermal conduction. It can solve the regular 2D equations, or can enable a modification to solve the equations in axisymmetric space, i.e. simulating a wedge or a cone based on which option is chosen.

FR1D Solver #

FR1D is a one dimensional code which I use to experiment with the Flux Reconstruction method of HT Hyunh for high-order finite element discretization. It is arbitrary order solver and is written to solve the 1D advection and euler equations. It is arbitrary order solver and is written to solve the 1D advection and euler equations. I’ve used it mainly to learn the FR method, and to experiment with different correction polynomials(they control how FR actually does the flux reconstruction). In the future I think I’m going to be using this to mess around with shock capturing schemes.