The Application Of High Order HWENO Scheme And Immersed Boundary Method On Cartesian Grid

In this thesis,we construct a third order finite volume HWENO(Hermite weighted essentially non-oscillatory)scheme with TVD Runge-Kutta time discretization method and Lax-Wendroff time discretization method on Cartesian grids.Comparing with the popular Runge-Kutta time discretization method,the Lax-Wendroff time discretization method can achieve arbitrary high order accuracy in time and make the spatial stencils more compact;on the other hand,it can shorten the computing CPU time and improve the computing efficiency of the associated numerical schemes.Since the non-physical oscillations will occur at the boundary regions of complex objects on Cartesian grids which result in the calculation processes break down,such finite volume schemes can't be directly adopted to simulate the compressible transonic flow problems containing complex objects on Cartesian grids.So we should remedy such drawback with the application of high quality computing meshes.As it is well known,the immersed boundary method is a good way of dealing with the sophisticated body surface conditions and is applicable on different types of computing meshes.Hence we apply such high order HWENO schemes together with the immersed boundary method to solve the transonic flow problems around complex objects on Cartesian grids.Finally,some benchmark numerical examples are presented to illustrate the good performance of these methods.