Finite Difference Weighted Essentially Non-oscillatory Schemes With Ghost Cell Immersed Boundary Method On Structured Meshes

A series of finite difference weighted essentially non-oscillatory (WENO3, WENO5, WENO7)schemes for solving the hyperbolic conservation laws on the structured meshes are applied in thisthesis. By computing the values of the interpolation polynomials at the different mesh points, thelinear weights, smooth indicators and nonlinear weights, we could get the high order accurate semidiscrete schemes spatially. Then, by using the TVD Runge-Kutta time discrete method, we couldobtain the fully discrete scheme both in space and time.After that, the ghost cell method couples with the numerical schemes are used to deal with theproblems for the flow over a complex body in this thesis. We apply such methodology to simulate theforward facing step problem and the supersonic flow past a physical body problem, etc.. By doing so,we could validate that such methodology is suitable for the problems of the flow past an intricatephysical body on the structured meshes.