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WENO accuracy study, a 2D test case?

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Old   June 28, 2013, 07:16
Default WENO accuracy study, a 2D test case?
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Faraz
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Hi,

Is there a standard 2D test case to perform accuracy study of WENO without using periodic boundary conditions?

I know that people do tests with periodic BC, but I would like to understand if the boundary effects could decrease convergence rate significantly.

Say, for example in a scalar convection case?
Is there a paper or a reference to check with that?

Thanks
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Old   October 16, 2017, 16:45
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Aranya Dan
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Try with 2D Reimann problems.

A large list can be found in the paper "Solution of 2d Reimann problems for Gas Dynamics without Reimann Problem Solvers" -A. Kurganov, E. Tadmor
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Old   October 17, 2017, 03:01
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Hello,

The advantage of periodic bc is that you can simulate a long time/distance advection case and then more easily show the less diffusive properties of high order schemes. Without periodic bc, you would need a much wider grid and computational time would be much higher.

If you do not want to work with such a bc, you can still perform accuracy test with advection equation to check the formal order of accuracy of your scheme. But you have to be very careful on the treatment of the limit as indeed it will spoil the observed order of accuracy for finer grids. What I am used to do is to prescribe the exact Riemann state (from the exact solution) at the face gauss nodes and let the Riemann solver do the job.

François
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