Numerical Simulation Of High-Order Discontinuous Galerkin Method Based On Rotating Coordinate System

In this paper, unsteady numerical simulations of rotating fluid problems are carried out. The Euler equations are obtained based on the rotating coordinate system, and then solved by numerical discretization of a parallel high order discontinuous Galerkin method(DGM) to obtain the highly accurate solutions of the flow fields in different states. Discontinuous Galerkin method combines the advantages of the finite element method(FEM) and the finite volume method(FVM), and become a research focus in the recent years due to its fast convergence and advantages in dealing with complex geometries, h/p adaptivity and parallel implementation. The rotating coordinate system has great advantages in dealing with the rotating flow in fluid mechanics, and can simplify the computational complexity and improve the computational efficiency.The completely curved mesh is generated to ensure the accurate expression of the real geometry of the solid wall based on elastic theory. The method of explicit artificial viscosity is used for shock capturing. In the part of the steady simulations, based on the data structure characteristics of the DGM and the METIS grid partition library, a parallel high-order DGM computing strategy is designed on the unstructured grid. Unsteady calculation is on the basis of the steady simulations with the same grid partition method, a parallel four-stage Runge-Kutta time-stepping scheme is designed for the Euler equations in rotating coordinate system. We first carry on the numerical simulations of the steady flow problems(i.e., the rotation angle velocity is zero). The numerical simulations of the steady flow fields of the symmetrical airfoil NACA0012 in subsonic flow and the supercritical airfoil RAE2822 in transonic flow are conducted respectively. Then the numerical simulations of unsteady flow fields of the symmetric airfoil NACA0012, thin airfoil NACA64a010 and supercritical airfoil NLR7301 are carried out based on the steady-state results. The numerical simulation results indicate that the parallel DG method based on the rotating coordinate system is very efficient and competitive in dealing with the rotating fluid problems, and highly accurate solutions can be obtained even on very sparse grids.