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ayt September 21, 1999 04:09

flow into vacuum
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?


clifford bradford September 21, 1999 10:36

Re: flow into vacuum
details need details but tvd scheme should work

Zhong Lei September 21, 1999 20:58

Re: flow into vacuum
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

Alexey September 23, 1999 08:40

Re: flow into vacuum
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.

Yangang Bao September 28, 1999 15:28

Re: flow into vacuum
What are TVD, ENO and WENO schemes?

Alexey Ignatiev October 7, 1999 18:33

Re: flow into vacuum
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

Best regars.

Alexey Ignatiev.

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