HIGH-ORDER DDG/FV HYBRID METHOD FOR VISCOUS FLOW SIMULATION ON UNSTRUCTURED/HYBRID GRIDS

In recent years, the discontinuous Galerkin method (DGM) has become one of the most popular high-order methods on unstructured/hybrid grids due to its excellent features: high accuracy, compact stencils and high parallelizability. At the same time, DGM is recognized as computationally intensive with respect to both computational costs and storage requirements. When it simulates the flow over 3D realistic complex configuration with large-scale grid, the huge memory requirements and high computational costs of DG method are usually unbearable. Recently, based on the idea of `hybrid reconstruction', a class of DG/FV hybrid schemes has been proposed and developed, which can successfully reduce the expensive computational costs and memory requirements. In this work, we introduce the efficient viscous term discretization method DDG into DG/FV method, and get a new hybrid scheme named as DDG/FV in order to further improve the efficiency of DG/FV scheme for simulating viscous flow problems. A variety of typical 2D laminar cases are tested, including Couette flow, laminar flow over a flat plate, steady flow over a cylinder, unsteady flow over a cylinder, and laminar flow over a NACA0012 airfoil. According to these cases, we select proper coefficients for DDG formulation, verify the order of accuracy and computational efficiency of DDG/FV for the simulation of steady and unsteady viscous flow, and compare the simulation results and computational efficiency with the widely used BR2-DG scheme. The numerical results demonstrate that the new DDG/FV hybrid scheme can achieve the designed order of accuracy. It can achieve the same accuracy as BR2-DG scheme with efficiency increased by more than 2 times for steady problems with implicit time scheme and by 1.6 times for unsteady problems with explicit time scheme in solving Navier-Stokes equations on unstructured/hybrid grids. And in some cases, the DDG/FV scheme has stronger robustness than the BR2-DG scheme. Because of the improvement of efficiency and robustness, the DDG/FV hybrid scheme shows good potential in future applications.