Residual Smoothing works?
 

Hi,

Residual smoothing is a kind of averaging of the residuals over the neighboring cells, right? Well, It doesn't work with my FV code (steady 2D Compressible Euler).

It is to increase the support of the stencil and increase the stability so that one can use a larger time step. But can it also contaminate the residuals? because you're altering the residuals. I'd like to understand the idea more completely. Can anyone justify the residual averaging? Does it really work?

Thanks,

Sid

Re: Residual Smoothing works?
 

I'm not a code writer but I have used a CFD code that uses residual averaging (smoothing) and it did work for me. The difficulty with it is that it's supposed to allow you to increase the time step also and in multi-dimensions it is difficult to evaluate the increased time step you can get with it. You may have convergence problems with it. I can't say. The original references on it I know about are some papers in the 80s by Jameson and his colleagues. These articles are "classics" so you should be able to find them in an engineering library. As you probably know residual smoothing works by applying a Laplacian smoother to the flowfield at each time step. The idea is that,ideally, at convergence the residual is smooth (i.e. very close to zero), however, during convergence the residual is not smooth due to the necessarily incorrect initial conditions. So to improve convergence the residual is smoothed repeatedly. The combination of residual smoothing and the increased time step should increase convergence but the combination of stronger smoothing and increased time step can lead to instability the limits of which can be difficult to evaluate. Efforts in this area are ongoing from my own investigation. To be convservative you can apply smoothing without increasing the time step and see what happens, it has worked for me. You may also want to use less strong smoothing.