[Krishan.aero]

I have been using AUSM for subsonic compressible flow with explicit time integration. But now I am facing problem of convergence and I want to switch to fully implicit time integration for my case.

I need help with following things:

1. How to find F(I+1/2) i.e flux at the face of control volume. As it is compressible flow and flux terms are
in conserved variable form. Do I need to change everything to primitive variables?

2. In AUSM we require left and right variables to be known to compute Mach splitting thus Flux at face. But in Fully Implicit case how would I do it? Compute Mach splitting using information from previous step?

Regards to CFD-online community members,

[sbaffini]

These two references might be useful:

Rinaldi et al., Exact Jacobians for implicit Navier-Stokes simulations of equilibrium real gas flows, J. Comp. Phys. 270, 2014

Colonia et al., Implicit implementation of the AUSM+ and AUSM+up schemes, Int. J. Numer. Meth. Fluids 75, 2014

[Krishan.aero]

Thank you very much @Paolo. I really appreciate your help.

[usv001]

Dear all,

I am trying to implement an implicit finite volume solver using the SLAU flux. I have used a matrix-free method with LU-SGS iteration. The solver works perfectly when I use 1st order upwind schemes on problems like low speed flow (M = 0.01) over cylinder and hypersonic flow (M = 8.1) past blunt body. I obtained very good convergence for both these cases.

However, when I tried to use higher order TVD reconstruction (e.g. van Leer, van Albada, etc.) instead of the 1st order upwind schemes, the solver has trouble converging for both cases. It even starts to produce pressure-velocity decoupling ('checkerboard') in some regions for the low speed flow over cylinder case. There is no such mention of a degradation of performance with increase in order of accuracy in the papers that I've read so far.

I wonder if anyone has faced similar issues and/or perhaps could shed some light on this topic. For your information, I am using OpenFOAM. So, the interpolation schemes should not be the problem. I am interpolating the primitive variables density, velocity and pressure and computing the numerical flux from the reconstructed values.

Thank you for your time.

USV

[naffrancois]

Have you tried first to converge your solution using a simple explicit scheme ?

Venkatakrishnan specifically dealt with poor convergence of Barth and Jespersen limiter on unstructured grids. You may have a look to his papers.

[usv001]

Originally Posted by naffrancois

Have you tried first to converge your solution using a simple explicit scheme ?

Venkatakrishnan specifically dealt with poor convergence of Barth and Jespersen limiter on unstructured grids. You may have a look to his papers.

Thank your for taking your time to answer my question. I ran the two cases (low speed flow past cylinder & hypersonic flow past blunt body) using 1st order explicit Euler time marching with CFL=0.3. The simulations do not converge with TVD reconstructions but they converge steadily with 1st order upwind reconstructions. I forgot about Venkatakrishnan's limiter. Perhaps that might solve the problem. I'll try to implement it and post the results if I manage to do so.

By the way, I have another question for the case of flow past cylinder. I always get a little asymmetry in the results for this case (please see attached image for converged 1st order upwind results). The results reported in the papers always show perfectly symmetric pressure contours but I am not able to reproduce it. Could it be the effect of boundary conditions? I am fixing the values of pressure and velocity at the far field boundary which is located 20R away from the centre of the cylinder. Should I extend the boundary further away from the cylinder, like >40R?

Many thanks,
USV

[usv001]

Hello there,

I have tried implementing Venkatakrishnan's limiter and extending the domain but the solution still does not converge. I have detailed my methods in a new thread that I started (link). I would really appreciate any help toward understanding the two problems:

1. Why is there an asymmetry for the case of nearly incompressible flow past a cylinder?
2. Why does the solver not converge when using high than 1st order methods?

USV