Need help to justify artificial viscosity

[alvesker]

Hi,

When solving for example Shallow Water Equations, the system itself is hyperbolic. Usually when dealing with non smooth solutions people add artificial diffusion to the momentum equation. Can anyone suggest papers or book, where they explain why it helps and why we can consider such solutions as solutions of the initial systems?

 

[bigfooted]

Try the book of Lomax and Pulliam, Fundamentals of CFD. They are really going over all the details of numerical methods, including artificial diffusion methods and the Lax-Wendroff method. The basic idea is to make the equation stable by smearing out the solution a bit in a controllable way. The diffusion term makes the numerical method more stable. Note that the artificial dissipation method is one of the methods to add a diffusion term to the equation, another being simply using a first order explicit scheme, but this is generally a bad idea - well, the book explains why.

If you are writing your own numerical code and you are into CFD, this is a nice book to have.