Simulation Of Unsteady Flow Based On High-order Discontinuous Galerkin Method

Turbulent flow is simulated with a two-dimensional Detached Eddy Simulation(DES)model using high-order discontinuous Galerkin method.The discontinuous Galerkin method(DG)is a hybrid method of finite volume method(FVM)and finite element method(FEM).The DG method describes the conservative variables by piece-wise high-order polynomials.And up-wind schemes,which is common in FVM,are adopted to overcome the discontinuity between elements.Since its high-order accuracy,small stencils,easy implementation of adaptivity and parallelism,it has become the most promising high-order method in CFD.The DES model is also a hybrid method of the average Reynolds stress equations(RANS)and large eddy simulation(LES)method.The flow is simulated with RANS near the wall boundaries and the LES method in other regions of the field.Such method combines the advantages of the RANS and LES method,and thereby being capable of simulating the separate flow without a large amount of mesh.The approximation accuracy of wall surfaces is proved to be a crucial effect on high-order method,hence,in this paper firstly we have to develop the generation of valid curvilinear mesh.Using hybrid mesh helps to reduce the amount of mesh and the difficulty of mesh generation effectively.The discontinuous Galerkin method is adopted in the spatial discretization of the DES method based on SA model.An implicit dual time stepping method is deployed in the temporal discretization.The generalized minimum residual method(GMRES)based on ILU preconditioning is used to solve the large linear system generated in each time step.In order to improve the calculation speed,METIS grid partitioning technology and MPICH parallel strategy are adopted.The numerical simulation of flow around a cylinder,single airfoil separation and multi-element airfoil slats unsteady flow verify the modifications of the length scale in two-dimensional cases is effective.When compared with results of the SA model,it shows an obvious improvement in the simulation ability of separation flow.With the help of the high-order discontinuous Galerkin method,results of very high accuracy can be obtained on very coarse grids.