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 Vinod Venugopalan July 21, 2004 13:41

ENO scheme asymmetry

Hi,

I am coding a 3rd order ENO scheme (F.D) to solve Euler equations for a flow in a 2D tube. I have induced a shock by adding a large source term over a small symmetric area in the center of the flow. While ENO handes the shock, the reflection and the gradients very well... the trouble is that the flow pattern being created is slightly asymmetrical.

When I zoom into the energy input area, I see that the center of the property contours has shifted by exactly one grid point in y-direction & is probably causing the asymmetry.

I've seen results from Dr Laney's Computational Gas Dynamics and also the results from my codes for simple conservation laws, eg. advection equation in pages 533-535. There is a bit of asymmetry in the results.

Is this an inherent prob with the ENO scheme? Any way of fixing this?

geometry: X:[-10 27.5] Y:[-6 6 ] Nx =250 Ny = 80. cfl =0.1 Using 3rd order R-K time integration, Lax fredrich flux splitting..

Thank you

Vinod

 Junseok Kim July 21, 2004 17:01

Re: ENO scheme asymmetry

For an asymmetry problem, it could be generated by under resolved grid, or numerical error even if the solver is not asymmetric. You may want to solve the problem on the symmetric domain if the problem is symmetric in nature or put more grids.

 Vinod Venugopalan July 21, 2004 17:40

Re: ENO scheme asymmetry

hi,

I tried increasing grid resolution, went from del_x &del_y of 0.15 to 0.075 .. the solution still has an asymmetry.. Again the center of the contour plots is shifted by one grid point.

I don't want to reduce grid size further because of really long run times.

 Hrvoje Jasak July 22, 2004 06:42

Re: ENO scheme asymmetry

I have seen something like this before and the differencing scheme I use has got the same property. In my opinion, symmetry is an additional constraint which is not inherently present in ENO, so when you derive a new scheme it may or may not behave symmetrically.

I have a vague memory that some (not all?) of the TVD schemes are properly symmetrical - it may be useul to repeat your test with the van Leer scheme and see if the symmetry is preserved (I think it should be).

Hrv

 Praveen July 22, 2004 07:00

Re: ENO scheme asymmetry

This could be related to conservation. Are you using a finite volume scheme ? If yes are you starting with cell-averaged initial conditions ?

 Vinod Venugopalan July 22, 2004 13:06

Re: ENO scheme asymmetry

I am using a finite difference scheme..

The reason I was wondering if the asymmetry is because of the scheme is because of earlier results from solution of scalar conservation laws.. U can see them in Dr Laney's book "Computational Gas Dynamics" pages 53 -535

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