A high-order Discontinuous Galerkin solver for the incompressible RANS and k–ω turbulence model equations

In this work a Discontinuos Galerkin (DG) solver for the incompressible Navier–Stokes equations has been extended to deal with the Reynolds-Averaged Navier–Stokes (RANS) equations coupled with the k–ω turbulence model. A distinguishing feature of the method is the formulation of the inviscid interface numerical fluxes, based on an exact Riemann solver for the incompressible Euler equations with a relaxed incompressibility constraint. The turbulence model has been implemented in a non-standard way employing the variable \tilde{\omega} = log(ω) instead of ω and enforcing the fulfilment of realizability conditions for the modeled turbulent stresses.The reliability, robustness and accuracy of the proposed implementation have been assessed by computing several turbulent test cases: (i) the flow past a flat plate for a Reynolds number Re = 11.1×10^6, (ii) the flow around a NACA 0012 airfoil at different angles of attack α = {0°,10°,15°} and Reynolds numbers Re = {2.88×10^6, 6.0×10^6}, with comparisons with experimental and CFD benchmark data, and (iii) the flow through a rotating vertical axis wind turbine.