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 ∼ = 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.

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