Study On Implicit Large Eddy Simulation Based On High-order Discontinuous Galerkin Method

Unsteady compressible turbulent flow is simulated with Implict Large Eddy Simulation method(ILES)based on Discontinuous Galerkin method(DG)in this thesis.The DG method has become one of the most popular high-order methods in the field of computational fluid dynamics since it possesses an excellent ability to describe flow-fields containing complicated vortices.Since the DG method has favorable dispersion and dissipation properties,its discretizations have been found well suited for ILES and the grid itself can filter high-frequency information.Firstly,unstructured tetrahedral mesh is used in the mesh generation,and a curved mesh generation method is deployed on the boundary of the solid wall in order to ensure the accuracy of expressions of the solid wall.The spatial discretization of the Navier-Stokes equations is then implemented with the DG method.The famous Local Lax-Friedrichs scheme is adopted for the convective flux and the BR2 scheme is employed for the viscous flux.An implicit time integration method is adopted for the unsteady temporal discretization in order to improve the calculation speed and the huge linear system generated during the iterations is solved using the preconditioned GMRES method.METIS grid partitioning technology as well as parallel strategy are adopted to accelerate convergence.The unsteady flow of the three-dimensional cylinder is numerically simulated by the method developed in this thesis.The accurate results are obtained on the coarse mesh and the correctness of the code as well as the effectiveness and high accuracy of the methods for large separation flow are verified.Finally,the numerical simulation of the unsteady flow of the three-dimensional 30P30 N multi-segment wing at high Reynolds number has been tried to carry out,which proves the feasibility of the developed method in the simulation of complex shape flow problems.