High-order discontinuous Galerkin solver on hybrid anisotropic meshes for laminar and turbulent simulations

Abstract

Efficient and robust solution strategies are developed for discontinuous Galerkin (DG) discretization of the Navier-Stokes (NS) and Reynolds-averaged NS (RANS) equations on structured/unstructured hybrid meshes. A novel line-implicit scheme is devised and implemented to reduce the memory gain and improve the computational efficiency for highly anisotropic meshes. A simple and effective technique to use the modified Baldwin-Lomax (BL) model on the unstructured meshes for the DG methods is proposed. The compact Hermite weighted essentially non-oscillatory (HWENO) limiters are also investigated for the hybrid meshes to treat solution discontinuities. A variety of compressible viscous flows are performed to examine the capability of the present high-order DG solver. Numerical results indicate that the designed line-implicit algorithms exhibit weak dependence on the cell aspect-ratio as well as the discretization order. The accuracy and robustness of the proposed approaches are demonstrated by capturing complex flow structures and giving reliable predictions of benchmark turbulent problems.