A Coupled Overset Mesh and Hybridizable Discontinuous Galerkin Algorithm for Pseudo-Compressible Flow

Abstract

Abstract A previously presented overset mesh enabled hybridizable discontinuous Galerkin (HDG) finite element method is extended in this work to an isentropic compressible (pseudo-compressible) fluid. This formulation is a first-principles approach and is complementary to the augmented Lagrangian approach that was utilized in the previous HDG incompressible Navier–Stokes formulations which eliminate the global pressure field. This is the first original presentation combining overset meshes, HDG, and fluid flow, specifically isentropic flow for low Mach number applications. Verification of the code implementation of the proposed overset-HDG formulation is performed via the method of manufactured solutions (MMS) on a successively refined overset mesh configuration containing five meshes, and for order k=1,…,4, Lagrange polynomial elements in both two and three dimensions. Optimal order convergence, k + 1, can be observed in all fields for both the two- and three-dimensional simulations, for each mesh. A two-dimensional benchmark problem is also presented to enable code-to-code comparison as a preliminary validation exercise.