Let's assume atmospheric flow enter a very low pressure vessel, e.g. about 100 pascal. Can current scheme like TVD scheme solve this problem easily? If not, is there any method to solve this?

Thanks.

details need details but tvd scheme should work

The simplest mathmetical model is the well known shock-tube problem. Any method of predicting shock wave, for example, TVD, ENO and artificail scheme, can be used.

Z. Lei

The ENO or WENO schemes are better then TVD. But if you use viscous model then stability condition for time step for explicit scheme may be strong due to low density (see,for example, MacCormack's works): Delta_t < const*(Delta_x)^2*density/viscosity. Because of it use implicit scheme at least for viscous part.

Best regards.

What are TVD, ENO and WENO schemes?

The TVD scheme (total variation diminising ) or TVNI ( total variation nonincreasing) was first developed by Ami Harten (see J. Comp. Phys. v.49 (1983) pp. 357-393). The ENO scheme (essentially nonoscillatory) schemes started with the paper A.Harten, B.Engquist, and others, J. Comp. Phys. v.71 (1987) pp. 231-303. A lot of information about ENO and WENO (weighted ENO) you can get from Shu's lectures notes: ICASE Report No.97-65 (see www.icase.edu)

Best regars.

Alexey Ignatiev.