Problems of numerical instability because of high gradients
I use CFD in the development of high voltage circuit breaker. In this field, the fluid flow is transient, turbulent, compressible with Mach number from 0.2 to 5. Our CFD codes are of finite volume and time stepping methods. There are extremely large gradient of temperature from 300K to 20000K and large gradient of pressure from 1 bar to 100 bar. Therefore, we suffer the problem of numerical instability because of these extremely large gradients. We must often strongly reduce the time step, but then we get an extreme long calculation time. Are there any people who have experience to treat such problem and know robust schemes for the discretizations and for the artificial viscosity?

Re: Problems of numerical instability because of high gradients
As I understand your problem, I may offer two solutions First is to use regularizations schemes, for example Il'in scheme. Second is to use adaptive grids  grids with variable step.
{calculate with constant step; while (solution is bad) { change your grid  condence in areas with large gradients in your solution(in bad sulution); recalculate on this grid; } } 
Re: Problems of numerical instability because of high gradients
Thank you very much for your tips. Would you please recommend me the literature of the regularizations schemes you mentioned?
X. Ye 
Re: Problems of numerical instability because of high gradients
Here are two titles: 1.Uniform numerical methods for problems with initial and boundary layers / E.P.Doolan, J.J.H.Miller, W.H.A.Schilders (Dublin 1980)
2.Shear flow in surface oriented coordinates./Ernst Heinrich Hirschel, Wilhelm Kordula (Wiesbaden 19811986) At the first book you can find many references, and what about adaptive grids? 
Re: Problems of numerical instability because of high gradients
Thank youu very much for your recommendation of literature. I will read them firstly. We do'nt have adaptive grids in our code, because for finite volume method this technique is not very convenient. But we will consider to use it.
X. Ye 
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