Advantages of static condensation in implicit compressible Navier-Stokes DGSEM solvers

摘要

We consider implicit time-marching schemes for the compressible Navier-Stokes equations, discretised using the Discontinuous Galerkin Spectral Element Method with Gauss-Lobatto nodal points (GL-DGSEM). We compare classic implicit strategies for the full Jacobian system to our recently developed static condensation technique for GL-DGSEM Rueda-Ramirez et al.(2019), A Statically Condensed Discontinuous Galerkin Spectral Element Method on Gauss-Lobatto Nodes for the Compressible Navier-Stokes Equations [1]. The Navier-Stokes system is linearised using a Newton-Raphson method and solved using an iterative preconditioned-GMRES solver. Both the full and statically condensed systems benefit from a Block-Jacobi preconditioner.