Assessment of solving the RANS equations with two-equation eddy-viscosity models using high-order accurate discretization.

A challenge that faces high-order methods for industrial applications generally is turbulence modeling at high Reynolds numbers. Large eddy simulation is studied extensively for high -order methods, nevertheless, its computational cost is enormous for industrial applications. The hybrid LES/RANS compromises the computational cost and the modeling error, however, solving the Reynolds-averaged Navier-Stokes equations is a resilient task for high -order methods, due to the non-smooth profiles of the turbulence quantities. Taking into account the complexity with high-order methods and the fairly large modeling errors of the RANS modeling, low-order methods has proved to be more pragmatic. For instance, in the discontinuous Galerkin framework, the polynomial approximation for these quantities leads to large oscillations that obstructs the non-linear solver. To use the high-order methods for industrial cases it is essential to have reliable implementations of two -equation turbulence models in RANS formulations. In this paper, a RANS discretization based on hybridizable discontinuous Galerkin is presented for the standard, TNT, BSL and SST versions of the k - w model for applications at Reynolds numbers up to 109. A particular focus is given to the treatment of the specific rate of turbulence dissipation w in the high-order framework. The complexity increases with these types of models as the value of w goes to infinity at solid walls. Additionally, with minor modifications to the numerical flux definition, the turbulence model formulation can be solved by discontinuous Galerkin method as well. The results show remarkable improvements regarding the error magnitudes and non-linear convergence rate (iterative error) compared to second-order finite volume based solvers. (c) 2023 Elsevier Inc. All rights reserved.