In this work we briefly survey the numerical solution of non linear convection diffusion equations using relaxed methods. We consider several approaches to the construction of approximating relaxation systems, studying the numerical properties of the resulting relaxed schemes. The unified approach proposed here includes BGK-based diffusive relaxation methods, but also allows for the construction of new relaxed methods. A stability analysis for the new methods is sketched and high order extensions are provided. Finally several numerical tests in one and two dimensions are shown.
|Titolo della pubblicazione ospite||Numerical Methods for Balance Laws|
|Numero di pagine||40|
|Stato di pubblicazione||Pubblicato - 2010|
- Relaxation schemes
- convection-diffusion problems