Hello, I have a vortex which is defined by analytical function and then compute it with Euler code. The questions are: 1. Should the vortex shape and strength

change? 2. How can I verify the computational result? Thank you.

gecko

Depends on the vortex distribution function. In general the vortex will change shape. This is a non-linear problem so I doubt you can find an analytical solution for it. You just have to do a grid independence check. If you are using grid-based methods, make sure your domain is large enough to reduce the effect of the far field boundary condition.

Adrin Gharakhani

The vortex will initially relax to a steady state, and if there is no viscosity and no shear in the flow, then the vortex should be rather steady. You might want to check that you conserve vorticity in the absence of viscosity. While the maximum amplitude of the vortex and its shape might change initially (during the initial relaxation period), the vorticity of the whole flow should not change. The actual change of the vorticity over a long period of time should give you the accuracy of the numerical scheme you are using. It is like checking if your scheme conserves energy and momemtum - here you want to check that your scheme conserves vorticity.

Patrick

Checking for the conservation of vorticity, impulse, etc. is of course always recommended and necessary. However, I think looking at such integral quantities alone without checking other "geometric" features is a mistake (and misleading). I think it is very possible that a solution will conserve vorticity but will have the wrong vorticity field _distribution_!

Adrin Gharakhani

Well, at least to check the conservation of vorticity is a start. However, to check 'geometric' features one needs to know what to expect (a 'flat top' vortex? or a more 'spiky' one? etc... ).

This is a very interesting test. Can you tell me where I can get details of this test case ? Is it a compressible flow ?