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 diaw September 30, 2005 03:39

Methods to quantify 'numerical viscosity'

As part of my research, I have been investigating the 'numeric viscosity' of a few different schemes.

Are there any standard recognised techniques, or benchmarks that could be of use? I would really value some links.

I have developed a simple test which seems to show up the inherent 'numerical viscosity' in the main Finite Element research solver I use. In my case, it seems to point to a numeric viscosity which is rather large.

I wss wondering what other benchmarks are around.

Thanks.

diaw...

 Scott Shaw October 2, 2005 10:39

Re: Methods to quantify 'numerical viscosity'

I would be interested in any standard benchmarks you come across.

Currently in our work we use potential flow around an airfoil and evaluate the drag. D'Alemberts paradox tells us the drag should be zero so any drag must be related to numerical viscosity.

We have also been looking at convection of a 2D vortex - again inviscid flow theory tells us that the vortex strength and structure should be maintained so variations in circulation or peak vorticity must be due to numerical viscosity.

Scott

 diaw October 2, 2005 10:56

Re: Methods to quantify 'numerical viscosity'

Thanks Scott,

I would guess that you are working in the high-speed, inviscid region. Those would appear to be excellent benchmarks up at that scale. Thanks for that.

I am currently working down at the other end of the scale - with slightly compressible gas flow inside micro-channels.

I have been working with a 'standard 1x1 square' & test the model against increasing entry velocity. When the system blows up, then I record that velocity against the number of cells in the model. Very interesting things happen. At a certain point, the u,max & cell number are related. I use this to estimate that numerical viscosity of the model. At the bottom end, it becomes a measure of the model 'stiffness' - at the top end, a measure of the solver viscosity.

I will also look for solid benchmarks down at this 'low end' against which I can validate & calibrate the model/solver.