Roe implement about preconditioning
Dear all:
I used weiss and smith's preconditioning in my compressible code. But I still confused about the Roe scheme. Original Roe: F = 0.5*(F_L+F_R)+0.5*abs(A)*(U_RU_L) preconditioning: F = 0.5*(F_L+F_R)+0.5*P*abs[(P^1)*A]*(U_RU_L) or F = 0.5*(F_L+F_R)+0.5*P*abs[(P^1)*A*M]*(Up_RUp_L) here M = partial(U)/partial(Up) U = [rho rho*U rho*E] Up = [P U T]; T = P/rho Which is correct for preconditioning? 
Re: Roe implement about preconditioning
Hi, THe second form is the correct one  you want to work entirely with the Up vector. See recent articles from Hosangadi et al or Whitfield et al.
ajs 
Re: Roe implement about preconditioning
Thank you for your answer,AJS.
I try the first and the second form in my code. But It still didn't convergence. Can you give some reference ? In Eigenvalues and Eigenvector, I used AIAA papre about Overflow code. I check many times and I think it was right. Why it did't covergence? 
Re: Roe implement about preconditioning
Sorry, I forget write my BC.
I test the flow in a channel. The inlet velocity is 0.46 m/s. The outlet condition is Pressure = 1atm. In the wall, P(nx)=P(nx1) Neumann condition. Besides, I used MUSCL and 3stage Runge kutta. But it didn't convergence. 
Re: Roe implement about preconditioning
Dear Ricklee,
If you are having problems with convergence, you can try the following 1. Use the preconditioned Roe scheme itself to run a compressible flow problem, say at M=0.4, switching off the preconditioning option, if you like to. This would help you to find if the preconditioned Roe scheme works well or not. 2. If things are working fine, and you have some problems of convergence, try the following. There is a quantity Uref used in the modified eigen values. Try out the following way of defining Uref rather than the one in WeissSmith paper (In fact they are not very different) Uref = min(a,max(q,K*q_inf)) where a is the local sonic velocity, q is the local velocity( sqrt(u**2 + v**2) and q_inf is the freestream velocity. K is a constant which is generally taken 1. Try this with K=1 and higher K. I am nearly sure things will get sorted out, becasue it worked for me this way. For a liitle more details, look at New Features in CFL 3D. You can get this by just googling it Hope this helps Regards, Ganesh 
Re: Roe implement about preconditioning
Dear ganesh:
First, thanks for your answer about the convergene problem. I solve the problem about channel flow. But in the backwardfacingstep model, it didn't covergence. In the reverse flow region, the velocity profile has oscillation. I used the MUSCL , Roe scheme , three stage Runge Kutta , Weiss and smith preconditioning. Roe implement: F = 0.5*(F_L+F_R)+0.5*P*abs[(P^1)*A*M]*(Up_RUp_L) here M = partial(U)/partial(Up) U = [rho rho*U rho*V rho*W rho*E] Up = [P U V W T]; T = P/rho In the eigenvalues and eigenvectors. I used the AIAA paper about Overflow. AIAA 970644 'recent Enhanecements to OVERFLOW' Can you give me some suggestions? 
Re: Roe implement about preconditioning
Dear Ricklee,
I also had problems initially about convergence. Some problems converged well, but others did not. It was then that I came across the CFL3D: New Features section, where the issue of a constsnt in the reference velocity was discussed, as in my earlier post. I have sucessfully solved lid driven cavity, backward facing step, flow past airfoil and flow past cylinder among others. Just make sure that your code first runs for a compressible flow problem (as I have said in my earlier post) and then try increasing the constant, to improve the convergence. You could also try a coarser grid and see if the problem persists. Hope this helps Regards, Ganesh 
Re: Roe implement about preconditioning
lower the timestep

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