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_R-U_L)

preconditioning: F = 0.5*(F_L+F_R)+0.5*P*abs[(P^-1)*A]*(U_R-U_L)

or F = 0.5*(F_L+F_R)+0.5*P*abs[(P^-1)*A*M]*(Up_R-Up_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?

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

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?

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(nx-1) Neumann condition.

Besides, I used MUSCL and 3-stage Runge kutta.

But it didn't convergence.

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 Weiss-Smith 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

Dear ganesh:

First, thanks for your answer about the convergene

problem.

I solve the problem about channel flow. But in the

back-ward-facing-step 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_R-Up_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 97-0644 'recent Enhanecements to OVERFLOW'

Can you give me some suggestions?

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

lower the time-step