p -Multigrid High-Order Discontinuous Galerkin Solution of Compressible Flows

Discontinuous finite element methods are finding widespread use in a wide range of scientific and technical applications since they are among the few available methods for the approximation of partial differential problems that combines high-order accuracy, geometric flexibility, and robustness. The price to pay for the robustness, accuracy, and flexibility of these methods is their high computational cost and storage requirement. However, the computational efficiency of discontinuous finite element methods can be substantially improved by resorting to multilevel solution techniques. This chapter presents the application of a p-multigrid high-order accurate discontinuous finite element method to the numerical solution of compressible laminar viscous flows (compressible Navier–Stokes equations) and to compressible turbulent flows modeled with the Reynolds-Averaged Navier–Stokes equations coupled with the k- ω turbulence model.