Implicit high-order Discontinuous Galerkin solution of turbulent flows with an Explicit Algebraic Reynolds Stress Model

In this work we present an implicit high-order Discontinuous Galerkin (DG) implementation of the Explicit Algebraic Reynolds Stress Model (EARSM) of Wallin and Johansson [21]. The aim is to investigate the numerical issues related to the EARSM implementation in the framework of a very high-order DG discretization and to assess the modelling capabilities of EARSM when dealing with turbulent flows of aeronautical interest. The EARSM model has been implemented in the implicit high-order DG code MIGALE [5] and employs the κ-ω model as the two-equation underlying model. The κ-ω model of the DG code MIGALE has been extensively tested on several problems and in this investigation it has been used without any recalibration of the model constants. The realizability constraint of our standard κ-ω implementation has not been used with EARSM, as this model already provides realizable Reynolds stresses. Both 2d and 3d test cases of aeronautical flows, proposed within the EU IDIHOM project, are used to assess the behaviour of the EARSM in the context of high-order DG discretization of the RANS and κ-ω equations.