# Euler equations in 2d

As an assignment in college, I did a 1d simulation. The problem statement was to solve 1d shock tube problem involving compressible ideal gas as working fluid. For this problem, I solved system of Eulers equations using Roe's Riemann solver. I want to know, to solve the Euler's equations in 2 or 3 dimensions, where should I start? Which is the test problem, i should consider first? (Please don't suggest commercial solvers. I want to write my own code) just I need some help in writing my own code.

What are the good resources that introduce 2d problem in the most practical way?

• Recently I learned the rotational invariance property of the Euler's equations, can that be used for 2d coding? Such the first we align the coordinate system perpendicular to a face, and solve 1d problem, then rotate the frame perpendicular to orthogonal face and repeat? – Subodh Jun 4 '12 at 7:56
• I recommend Chapters 18-21 of LeVeque's FV book: depts.washington.edu/clawpack/book.html The only drawback to this is that the approach is based on fluctuations rather than fluxes (the latter are more mainstream). – David Ketcheson Jun 4 '12 at 18:10