Space–time discontinuous Galerkin method for the compressible Navier–Stokes equations

Abstract

A space-time discontinuous Galerkin finite element method for the compressible Navier-Stokes equations is presented. We explain the space-time setting, derive the weak formulation and discuss our choices for the numerical fluxes. The resulting numerical method allows local grid adaptation as well as moving and deforming boundaries, which we illustrate by computing the flow around a 3D delta wing on an adapted mesh and by simulating the dynamic stall phenomenon of a 2D airfoil in rapid pitch-up maneuver.

Error Estimation and Adaptive Mesh Refinement for Aerodynamic Flows

“…The delta wing has a sloped and sharp leading edge and a blunt trailing edge. A similar case has previously been considered in [81]. The geometry of the delta wing can be seen from the initial surface mesh in Figure 67 number equal to 0.3, at an angle of attack α = 12.5 • , and Reynolds number Re = 4000 with isothermal no-slip wall boundary condition imposed on the wing geometry.…”

Polymorphic nodal elements and their application in discontinuous Galerkin methods

“…The extension to problems of viscous gas dynamics was initiated in [3,5] and this again has lead to several related formulations [28,34,16] for the compressible Navier-Stokes equations. Many examples and further details along these lines can be found in [8,29] and [25].…”

Output-Based Space-Time Mesh Adaptation for Unsteady Aerodynamics

“…Specifically, the discontinuous Galerkin (DG) method is used in both space and time. Such a discretization has been studied previously, [8][9][10][11][12][13] and although computationally expensive, it shows potential for high accuracy and flexibility in the solution space. The latter point is important for mesh adaptation, which may require hanging nodes or variation in order throughout the space-time domain.…”