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some puzzles on Boundary condition transformation

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Old   April 14, 2012, 09:44
Post some puzzles on Boundary condition transformation
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YeChen
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Hello,everyone. I want to simulate a supersonic (Ma=4.0) flow fleid around a circular body and check for the shock/boundary profiles. I choose to use the finite difference method(FDM),and hence I do a grid transformation from physical domain(x,y) to computational domain(ξ,η). And there comes some puzzles:
Fig.jpg
1) on the physical outflow boundary the condition like ux(imax,j)=ux(imax-1,j) such interpolations, how to convert this to the computational domain ?

2) what scheme is suitable for super/hypersonic problems like this, MacCormack seems have strong oscilations around the shock. what about Ausm series?

3) During the grid transformation, is second-order estimation of Jacobians like Xξ sufficient?

Thank you very much for advises, my friends. I am looking forward for your help.
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Old   April 14, 2012, 10:59
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Serge A. Suchkov
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2) what scheme is suitable for super/hypersonic problems like this, MacCormack seems have strong oscilations around the shock. what about Ausm series?
In your case you need one of shock-capturing schemes http://en.wikipedia.org/wiki/Shock_capturing_methods
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Old   April 15, 2012, 09:00
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In your case you need one of shock-capturing schemes http://en.wikipedia.org/wiki/Shock_capturing_methods
Thank you for your reply and useful website.
for the puzzle 1 listed , can you give me some advices. I guess my code work fails largely on this boundary condition transformation.
Explicitly to say, like a adiabatic left wall boundary in physical plane(x,y),we may use T(1,j)=T(2,j) to specify, after the transformation on the computational plane (ξ,η), what the left wall boundary then should look like , it's a mathe problem in fact.
Thank you in advance.
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