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Magesh July 17, 2003 10:19

Roe upwind fluxes!!
I am trying to solve a simple 2-D test case viz Poisuelle flow using my quadratic reconstruction based finite volume solver(all this is probbaly irrelevant for my current question..but i just provide the info to make it complete). I use Roe's Riemann solver for the convective part and a central discretization for the diffusive part. My convereged solution using the solver does not match with the exact solution..I tried to probe it.for a simple 2d-poisuelle flow problem when i try to probe where this disturbance comes from(i print out the state increments, convective and diffusive fluxes..) i realised that whatever increments I have strictly comes from this Upwind part.. and diffusive fluxes are simply zero(note i started with exact soln) The problem I have is very simple and fundamental..when you explicitly write down the Upwind part of the fluxes for a flow where velocity is aligned in the channel direction leading to <v,n> =0 (velocity dot normal) then the fluxes from the left and right side are directly zero..but in the upwind part of the flux estimate you have eigen values mod(<v,n>+c) and mod(<v,n>-c)(app 10e+02) multiply by enthalphy term leading to a significant non-zero term..and non-physical gradinet in the channel normal direction..) but if i switch off the upwind part of the flux computation my code breaks.. (no probs in scalar convection-diffusion case..) what i have desribed is the classical problem
: all the upwind schemes have; a heavy dose of dissipation. my diffusive fluxes must dampen it isn't it.. made me wonder whether am trapped into some kind of non-zero gradients which are not captured(akin to checker board problem..) though it is not exactly a odd-even decoupling..i have non-zero gradients which are introduced by the conv flux discretization which are not captured by my diffusion scheme.. Is there any special tricks people use wrt to solving NS eqns..

Tom July 17, 2003 11:24

Re: Roe upwind fluxes!!
It appears to me that your code must be calculating the pressure incorrectly - for poisuelle flow the balance is between the driving pressure gradient and the diffusion. If you've got this right the convection terms, if discretized correctly, will vanish no matter what scheme you use,


Magesh July 17, 2003 11:35

Re: Roe upwind fluxes!!
What you say is right..i have wrong pressure gradients in the normal direction..but when i probed where does it come from it comes from the generation of y momentum..thats what i had explained when i tried to debug my code i discovered that these incre ments come from the upwind part which my diffusive fluxes does not capture and still not sure whether i am being clear if you could write to me i could probaly explain better.. hope i ambeing clear enough

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