A New Fifth-order Finite Difference WENO Scheme With Immersed Boundary Method For Solving The Compressible Flow

In this thesis,we apply a new fifth-order finite difference weighted essentially non-oscillatory(WENO)scheme with the immersed boundary methods for solving the hyperbolic conservation laws around the complex body surface on structured meshes.One five-point stencil and two two-point stencils are applied for high-order approximation of numerical fluxes in spatial reconstruction procedures and a classical third-order TVD Runge-Kutta time discretization method is applied for time discretization.The advantages of such new WENO scheme are the random choice of positive linear weights with one requirement that their sum is one to achieve fifth-order accuracy in smooth regions and degrade to second-order accuracy near shocks or contact discontinuities simultaneously keeping essentially non-oscillatory property.But such new WENO scheme cannot be directly applied to compute above mentioned problems,since it is dependent on high-quality computational meshes.Comparatively speaking,several immersed boundary methods are very suitable for dealing with complex body surface in numerical simulations.So we can combine both methods to compute the complex subsonic and supersonic flow problems on Cartesian grids.Finally,some benchmark test cases are presented to illustrate the effectiveness and feasibility of these methods.