The Application Of Finite Volume Weighted Essentially Non-oscillatory Scheme With Ghost Cell Immersed Boundary Method On Structured Meshes

A finite volume weighted essentially non-oscillatory scheme for solving the hyperbolicconservation laws on the structured meshes is used in this thesis. Firstly, we construct a high orderdegree interpolation polynomial on the big stencil. Then, we divide the big stencil into some smallerstencils each has the target cell and construct different interpolation polynomials on different smallstencils that match the cell averages of the physical variables on the cells of the same small stencil.After that, we calculate the linear weights, smoothness indicators and nonlinear weights, respectively.Lastly, by using the TVD Runge-Kutta time discrete method, we could obtain the fully discretescheme both in space and time.For the purpose of utilizing the proposed scheme to simulate the problems for the flow over thecomplex body, we find that there are no any flow values on the structured meshes inside the body andthen use the ghost cell immersed boundary method to deal with the associated boundary conditions.The key idea of such method is the immersed boundary condition obtained from the ghost cell withinthe vicinity of the solid wall into the flow field. Then two different kinds of the ghost cell methods areapplied in this thesis. Lastly, the extensive numerical tests show that the methods applied here candeal with the simulations of the flow over the complex body convincingly and precisely.