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

• Published in: Computers & fluids 2014-07, Vol.98, p.54-68
• Main Authors: Bassi, F., Ghidoni, A., Perbellini, A., Rebay, S., Crivellini, A., Franchina, N., Savini, M.
• Format: Article
• Language: English
• Subjects: Aerodynamics; Computational fluid dynamics; Discontinuous Galerkin; Fluid flow; High-order accurate space discretization; Incompressible RANS equations; k–ω turbulence model; Mathematical analysis; Mathematical models; Navier-Stokes equations; Turbulence; Turbulent flow
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2014.02.028

•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 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.