Test problem for 1D isothermal Euler equations
 

Hi All,

Could someone suggest a test problem for the 1D Isothermal Euler equations?

I know that the 1D Riemann (shock tube) problem is generally used.. but am having difficulty in understanding the "link" between pressure and density in the isothermal case.. can someone help me with this ?

also please suggest any other test problems?

thanks

Hi,

I know it has been a long time but I was wondering if you got a reply to your answer with regards to test cases?

Also were you coding this?

Thanks!

A typical test is the Sod shock tube:

http://en.wikipedia.org/wiki/Sod_shock_tube

I am not sure about what you consider as "isothermal" flow... for example the "isoentropic" flow can be defined as the case in which the entropy is constant along the trajectory of a fluid particle, that is on the characteristic curve dx/dt = u. In this case spatial gradient of entropy are allowed (ds/dt + u ds/dx = 0).

In the classic Sod test you have one family of characteristic waves were the flow is omoentropic and Riemann invariant can be used, then the contact discontinuity and the shock wave are the other regions involved.

What test are you looking for?

I'm looking for a test case that involves the Euler equations (with or without energy).