For the finite volume scheme we need the value of the conservative variables on the faces of the cell. For this as stated in Jameson, 1981, we use the average of the value on either side of the face (i.e. center difference). Can we use the second order upwind for the same? What the effects will be?
By second order upwind, I meaning for the face (i+1/2), using (i+1) and (i+2) value in the forward predictor step and using i and (i-1) in the backward corrector step.
I take it that you wish to solve Euler or NS. A proper stability analysis will then determine if it is a stable scheme. Presumably it is a consistent choice. Unless someone has carried out the analysis for your particular scheme, there is no simple answer.
Thank you for your reply.
I am solving Euler Solver using explicit formulation. Actually, I was looking if someone has done any analysis on this. In literature, I have seen they have use the center difference. One reason, i was seeing was, MacCormach being central scheme, we use center difference.
Actually MacCormack is a two step process. In finite volume formulation, we require the face value. But, here we take the cell value as per the forward or backward step. Also, in the Jameson, 1981 MacCormack method has not been used. So, please if any one can correct me, I am understanding that we do not require any extrapolation to the face values. But, for non-uniform grid or unstructured grid, will it be applicable.
Hi
I recommend you to read the course Of Collela and Puckett:
"Modern Numerical Methods for fluid Flow"
Free available on the Web :
It simply explains the Consistency, Stability and convergence notion. Details are given for classical schemes as Upwing Centered lax Wendroff , Godunov ...
http://www.engineering108.com/Data/Engineering/Mechanical/COMPUTATIONAL_FLUID_DYNAMICS/modern-numerical-methods-for-fluid-flow.pdf
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