some puzzles on Boundary condition transformation
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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:
Attachment 12550 1) on the physical outflow boundary the condition like ux(imax,j)=ux(imax1,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 secondorder 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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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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