I'm trying to reproduce a model of stratified spin-up from rest from a 2002 paper. The spacial discretization scheme is all central differences and I am finding that stability is lost after a certain number of time steps. The paper is not that well written but having re-read it recently I am pretty certain that I need to include a fourth order derivative explicit artificial dissipation term to keep the stability under control. However, I am struggling to find good information about implementing explicit artificial dissipation. All I have been able to find so far are either journal papers which discuss advanced topics in the subject area and assume a high level of background knowledge which I don't have, or I have found CFD books that mention the subject briefly without ever describing how it is implemented properly.
Could anyone please point me in the right direction for some quality information regarding the theory and implementation of explicit artificial dissipation?
Thank you in advance.
Some authors to look for are:
Antony Jameson (http://aero-comlab.stanford.edu/jame...tion_list.html), focus of earlier Euler work is on explicit methods
Tom Pulliam (http://people.nas.nasa.gov/~pulliam/...lications.html), however the focus is on implicit methods
R. C. Swanson (ntrs.nasa.gov)
An example of implementing a non linear scaler model is in:
Jameson, A., Schmidt, W., and Turkel, E., "Numerical Solution of the Euler Equations by Finite Volume Methods using Runge-Kutta Time-Stepping Schemes," AIAA Paper 81-1259, June 1981.
You can also search for titles with "artificial dissipation" at ntrs.nasa.gov
"Artificial dissipation and central difference schemes for the Euler and Navier-Stokes equations" might work for you.
There is also "Comparison of Several Dissipation Algorithms for Central Difference Schemes" by R. C. Swanson, R. Radespiel, and E. Turkel. You can find that at ntrs.
The titles above are titles I used in developing my solver. I can't say they are the best out there. But it is a starting point.
What would happen if you increase the viscocity, say to 100 times its actual value or (1/100), in your current programme
Thanks and good luck
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