Assessment of a high-order discontinuous Galerkin method for incompressible three-dimensional Navier–Stokes equations: Benchmark results for the flow past a sphere up to Re=500

This paper deals with the implementation of the high-order Discontinuous Galerkin (DG) artificial compressibility flux method into a three-dimensional incompressible Navier–Stokes (INS) solver. The method is fully implicit in time and its distinguishing feature is the formulation of the inviscid interface flux, which is based on the solution of the Riemann problem associated with a local artificial compressibility-like perturbation of the equations. The code has been tested on a wide range of flow regimes considering the flow past a sphere at moderate Reynolds numbers. In order to asses the code reliability and its accuracy in space, up to the sixth order polynomial approximation, and in time, up to the fourth order, both steady (Re = 20, 200, 250) and unsteady (Re = 300, 500) problems have been approached. With the largest Reynolds number here considered the flow exhibits a complex behavior, even if it still laminar, since undergoes the transition from a regular to an almost chaotic system. For this problem, for which the flow field characteristics are not completely well established and no many data are available in the present literature, detailed results are reported in this paper.