High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

We describe in detail some techniques to construct high order MUSCL type schemes on general meshes : the ENO and WENO type schemes. Special attention is given to the reconstruction step. Extesio to Hamilton Jacobi equations is sketched. We also present some hybrid techniques that use simple modifications of classical TVD schemes yielding in a very clear improvements of the accuracy. We discuss means of improving the efficiency using Harten’s multiresolution analysis. We provide several numerical examples and comparisions with more conventional schemes.