Computation Of Flow Field With Complex Boundary And Study Of Acoustic Resolution Properties Of DG Scheme

This dissertation mainly studies the numerical simulation of the flow field with complex boundary,the acoustic resolution properties of discontinuous Galerkin(DG)method and its relationship with the central difference scheme and DRP scheme.This work is made up of two parts.The first part consists of the second chapter and the third chapter.The numerical simulation of an incompressible flow field with a complex elastic boundary and com-pressible flow field with complex rigid boundary are studied respectively.The difficulty of solving this kind of problems lies in the efficient treatment of boundary conditions.Firstly,the immersed boundary method is combined with the finite difference WENO scheme and applied to the numerical simulation of incompressible flow field with elas-tic boundary.Based on the immersed boundary framework,the algorithm maintains the simple and effective processing of the moving interface,and adopts the weighted essen-tially non oscillatory(WENO)method and Hodge decomposition technique in the fluid domain without the interface to achieve high-order accuracy.Numerical examples show the effectiveness of the algorithm.Compared with the traditional immersed boundary method,the proposed method has better volume conservation properties.In addition,the high-order inverse Lax-Wendroff(ILW)boundary scheme for solving complex mov-ing boundary problems on a fixed Cartesian grid is studied,and the moving rigid body with complex boundary under shock wave impact in compressible inviscid flow field is numerically studied.Different from the ILW method only considering rigid body translation proposed in previous work(Tan and Shu,J.Compute.Physics.230:6023-60362011),we consider both rigid body translation and rotation in this paper.Numeri-cal examples of cylinder,elliptic cylinder and NACA0012 airfoil are given to show the effectiveness and robustness of the proposed method.The second part is about the acoustic resolution properties of DG methods and its comparison with DRP scheme.The acoustic resolution properties of DG schemes are discussed in detail and compared with some central difference schemes and DRP scheme.The analysis shows that although the DG scheme has some dissipation,its overall dispersion and dissipation properties are equivalent to that of DRP scheme on the same stencil.In order to compare with FD scheme directly,we write DG scheme into block finite difference scheme.We have done a series of numerical experiments including nozzle flow.The results show that the DG scheme and DRP scheme with the same stencil can get the comparable numerical results.Due to the flexibility of DG scheme on unstructured grids,DG scheme is a good candidate in computational aeroacoustics,especially in complex geometric conditions.