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OpenFOAM discretization schemes

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Old   May 23, 2017, 03:14
Default OpenFOAM discretization schemes
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Hello OpenFOAMers. As you know from the CFD theory, there are several discretization schemes such as Upwind, Hybrid and Power-Law.

I mostly select linear of OpenFOAM as it is second order scheme. When I am solving laminar and high Re number flows, such as Re = 2000 for empty channel, I am facing with convergence problems. However, if I select Upwind, there is no convergence problem.

This is one of the advantage of Upwind scheme when there is strong convective effect. However, as it is first-order scheme, there is false diffusion risk. What are your suggestions for this kind of flows? As I know, there is no power-law scheme in OpenFOAM, which scheme should I select at high Re and laminar flows?
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Old   May 23, 2017, 03:23
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That depends on the term you are trying to discretise...

For the convective term, 'linear' is asking for trouble as far as I know.
'upwind' works, but is diffusive.
'vanLeer' (and other flux-limiters) are the best of both worlds: second-order in all of space, except for the critical regions like shocks where it switches to first-order to maintain a stable simulation.

For the Laplacian (momentum diffusion / viscosity) terms, I tend to always go for 'linear', but I don't know if it really matters. The convective term seems to be the most critical one.
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Old   May 23, 2017, 09:46
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Thank you so much for your answer. I try to discretize U term. I don't know why but when Re high, even channel flow with good quality mesh, only upwind scheme works for me. What might be a reason behind this? I use OpenFOAM 4.1.
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Old   May 23, 2017, 13:10
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It is the wrong way the reach numerical stability by using less exact models.

The first thing to analyse is the reason for instability. Often it ist the mesh or wrong boundary conditions. Only in real complicated problems the physics need taken into account. The last one may be if there are shock waves and other transient effects of large size.

To analyse the mesh it may be helpful to write result every time step. These result indicate the region where the instability starts to grow. Look at these regions first.

If you need to handle physical stiffness of you problem, it may be much better to use relaxation in the solution process but second order schemes. In this case the final, stable solution is correct (if there is any), but the course to it get smeared. If you use less exact models you don't get a correct solution for any simulated time.
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Uwe Pilz
Die der Hauptbewegung überlagerte Schwankungsbewegung ist in ihren Einzelheiten so hoffnungslos kompliziert, daß ihre theoretische Berechnung aussichtslos erscheint. (Hermann Schlichting, 1950)
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openfoam 4.1, upwind

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