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

Abstract

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 ω∼=logω 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=11.1×106, (ii) the flow around a NACA 0012 airfoil at different angles of attack α=0°,10°,15° and Reynolds numbers Re=2.88×106,6.0×106, with comparisons with experimental and CFD benchmark data, and (iii) the flow through a rotating vertical axis wind turbine.