Pathologies of Simple Flux Jacobian Approximation
 

Hi everyone,

I am working on a CFD code that has a very simple approximation to A (let's write the Euler equations as Q_t + AQ_x = 0, A is the flux Jacobian). If we're iterating on a time step, it currently simply approximates A^(k+1) with A^(k) from the previous iteration with a simple limiter to prevent Gibbs. It's been more or less functional for what this code does, but I suspect this not going to hold up well under various supersonic conditions. Thing is, I'm so used to more advanced methods that I no longer remember why this is a bad idea.

What sort things should I expect to be going wrong with this method and look for in order to compare it with Roe and other more sophisticated methods? The most obvious thing is that it won't handle shock tube problems very well, or any other problem with a moving shock, but what about steady-state problems?