A Parallel, High-Order Direct Discontinuous Galerkin Method for the Navier-Stokes Equations on 3D Hybrid Grids (Communications in Computational Physics, 2018)
A parallel, high-order direct Discontinuous Galerkin (DDG) method hasbeen developed for solving the three dimensional compressible Navier-Stokes equations on 3D hybrid grids. The most distinguishing and attractive feature of DDGmethod lies in its simplicity in formulation and efficiency in computational cost. Theformulation of the DDG discretization for 3D Navier-Stokes equations is detailedly studied and the definition of characteristic length is also carefully examined and evaluatedbased on 3D hybrid grids. Accuracy studies are performed to numerically verify theorder of accuracy using flow problems with analytical solutions. The capability in handling curved boundary geometry is also demonstrated. Furthermore, an SPMD (singleprogram, multiple data) programming paradigm based on MPI is proposed to achieveparallelism. The numerical results obtained indicate that the DDG method can achievethe designed order of accuracy and is able to deliver comparable results as the widelyused BR2 scheme, clearly demonstrating that the DDG method provides an attractivealternative for solving the 3D compressible Navier-Stokes equations.