Fast time implicit-explicit discontinuous Galerkin method for the compressible Navier-Stokes equations

摘要

An efficient and robust time integration procedure for a high-order discontinuous Galerkin method is introduced for solving the unsteady compressible Navier-Stokes equations. The time discretization is based on an explicit formulation for the convective fluxes and an implicit formulation for the viscous fluxes. The implicit procedure uses a fast iterative algorithm based on a partial uncoupling of variables in neighboring elements introduced in previous works by the authors. In the present work, the method is associated to a Newton-Krylov Jacobian-free method. This association allows to reduce memory requirements and operation counts by avoiding the complete construction of the Jacobian matrix and solving a problem of reduced size. Numerical examples in two space dimensions indicate that the performance of the present method is seen to be significantly improved in terms of CPU time.