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

• DG solution of the incompressible RANS and k–ω turbulence model eq. is presented.
• The inviscid interface numerical fluxes is based on an exact Riemann solver.
• Exact Riemann solver with a relaxed incompressibility constraint.
• The formulation of the governing equations in a relative reference frame is discussed.
• The method is validated by considering three testcases (steady and unsteady).

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 ωω 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=11.1×106Re=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}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.