CONSTRUCTION OF WEIGHTED UPWIND COMPACT SCHEME
Abstract
Enormous endeavor has been devoted in spatial high order high resolution schemes in more than twenty five years previously, like total variation diminishing (TVD), essentially non-oscillatory scheme, weighted essentially non-oscillatory scheme for finite difference, and Discontinuous Galerkin methods for finite element and the finite volume. In this dissertation, a high order finite difference Weighted Upwind Compact Scheme has been constructed by dissipation and dispersion analysis. Secondly, a new method to construct global weights has been tested. Thirdly, a methodology to compromise dissipation and dispersion in constructing Weighted Upwind Compact Scheme has been derived. Finally, several numerical test cases have been shown.