Space-Time Discontinuous Galerkin Finite Element Method with Dynamic Grid Motion for Inviscid Compressible Flows.

摘要

A new space-time discontinuous Galerkin finite element method with dynamic grid motion for the solution of the Euler equations of gas dynamics is presented. The discontinuous Galerkin discretization presented in this paper results in an efficient upwind finite element method, which satisfies the Geometric Conservation Law, and provides an algorithm which requires significantly less flux calculations than discontinuous Galerkin discretizations using Gauss quadrature rules for the flux integrations. In addition, a less general but more efficient, discontinuous Galerkin discretization using a translating-rotating reference frame is discussed. This method is especially suited for problems with solid body rotation, but without grid deformation. An efficient implicit time integration method is discussed, where the non-linear equations of the implicit discretization are solved with a full approximation storage multigrid scheme. The formulation of a multigrid algorithm for both discontinuous Galerkin methods receives special attention. Simulations of a delta wing in pitching oscillation are used to demonstrate the numerical algorithms. delta wing in pitching oscillation are used to demonstrate the numerical algorithms.