A staggered semi-implicit discontinuous Galerkin method for the two dimensional incompressible Navier-Stokes equations

摘要: In this paper we propose a new spatially high order accurate semi-implicit discontinuous Galerkin (DG) method for the solution of two dimensional incompressible Navier-Stokes equations on staggered unstructured curved meshes. While discrete pressure is defined primal grid, velocity vector field an edge-based dual grid. The flexibility DG methods meshes allows to discretize even complex physical domains rather coarse grids. Formal substitution momentum equation into continuity yields one sparse block four-diagonal linear system only scalar unknown, namely pressure. computationally efficient, since resulting not very but also symmetric and positive definite appropriate boundary conditions. Furthermore, all volume surface integrals needed by scheme presented in depend geometry polynomial degree basis test functions can therefore be precomputed stored preprocessor stage, which leads savings terms computational effort time evolution part. way extension fully isoparametric approach becomes natural affects preprocessing step. validated degrees up $p=3$ solving some typical numerical problems comparing results with available analytical solutions or other experimental reference data.