An Efficient DDG/FV Hybrid Method for 3D Viscous Flow Simulations on Tetrahedral Grids (Communications in Computational Physics, 2020)
A new hybrid reconstruction scheme DDG/FV is developed in this workby combining the DDG method and DG/FV hybrid scheme developed in the authors' previous work [1–4] to simulate three-dimensional compressible viscous flow on tetrahedral grids. The extended von Neumann stencils are used in the reconstruction process to ensure the linear stability, and the L2 projection and the least-squares methodare adopted to reconstruct higher order distributions for higher accuracy and robustness. In addition, a quadrature-free L2 projection based on orthogonal basis functionsis implemented to improve the efficiency of reconstruction. Three typical test cases,including the 3D Couette flow, laminar flows over an analytical 3D body of revolutionand over a sphere, are simulated to validate the accuracy and efficiency of DDG/FVmethod. The numerical results demonstrate that the DDG scheme can accelerate theconvergence history compared with widely-used BR2 scheme. More attractively, thenew DDG/FV hybrid method can deliver the same accuracy as BR2-DG method withmore than 2 times of efficiency improvement in solving 3D Navier-Stokes equations ontetrahedral grids, and even one-order of magnitude faster in some cases, which showsgood potential in future realistic applications.