High Order Numerical Schemes For PDEs And Applications To CFD

Abstract

In the past two decades, many efforts have been made in developing high-order schemes with high resolution, such as compact scheme, essentially non-oscillatory scheme (ENO), weighted essentially non-oscillatory scheme (WENO).The present dissertation comprises the analysis and numerical testing of two high order methods. The first one refers to the modification of pseudo spectral method which can be used to partial differential equations(PDEs) with non-periodic boundary conditions. The second one is in high order finite difference class and is the mixing of weighted non-oscillatory scheme and compact scheme (MWCS) with using global weights instead of local ones. Numerical tests are performed for one dimensional and two dimensional cases and results are compared with some well-established numerical schemes.