I am simulating a flow through a membrane module, with a pressure inlet and pressure outlet. A standard k-e turbulence model is used. The flow does not involve any high Mach-number flow. My mesh is tetrahedral, as a complex geometry with alot of curves is involved. I used a segregated solver.

My question concerns the order of discretization. When I choose first order discretization scheme for the convective terms of the governing equations, my residuals are stable (even though they dont converge), ie. they don't go up and down alot, However, when I change the order of discretization to second order, the residuals wiggles violently, suggesting an unstable calculation.

I am wondering, when it is necessary to use the 2nd order discretization, when the calculation using the 1st order is already stable? I am aware that the manual says that, while the first-order discretization generally yields better convergence than the second-order scheme, it generally will yield less accurate results, especially on tri/tet mesh. The problem in applying this sentence is that, we have no experimental values to validate our result.

If it is ALWAYS necessary to check for convergence and stability with the second order, then I am hoping someone could give some suggestions as to how i can improve the stability when 2nd order discretization is turned on.

[k_tafazoli]

Hi, I've got a fortran code for solving 2D compressible flow over an airfoil with the method of first order van leer flux vector splitting . I have to change it to second order van leer flux vector splitting method . Can you please help me on how to do it? It's also possible for me to solve this project with the method of AUSM+ . Are you familiar with this method? can you help me with it please?
Thanks a lot in advance

[blackmask]

In my experience, 2nd order discretization is necessary. I have used a simple 2D wavy channel flow to study mesh convergence behavior with high- and low- order discretization. The simulation is assumed steady and turbulence model are used. Other settings than the discretization schemes are kept unchanged. The number of mesh nodes range from around 8k to 700k. The pressure drop from inlet to outlet is used as the indicator. I have never been able to obtain a grid independent solution use first order discretization. The pressure drop changed by 6~10% after each refinement. On the other hand, the pressure drop given by 17k-nodes-mesh differs only by 0.4% from the 700k-nodes-mesh with 2nd order discretization.

We know that the discretization error decreases with reduced grid spacing. In my study the pressure drop do approach to the "true value" (given by the finest mesh with 2nd order schemes) with increased grids number using 1st order discretization. However, the result of 700k-nodes-mesh with 1st order discretization is approximately as accurate as that of the 11k-nodes-mesh with 2nd order discretization, which is about 2% higher than the "true value".

I didn't differentiate the discretization of momentum equations and turbulence equations. They switched to the 2nd order discretization at the same time in my study. But I believe that the higher order discretization of the momentum equation is critical.