A Spalart–allmaras Turbulence Model Implementation for High-order Discontinuous Galerkin Solution of the Reynolds-averaged Navier-stokes Equations

Abstract

A novel and robust approach has been proposed for the high-order discontinuous Galerkin (DG) discretization of the Reynolds-averaged Navier-Stokes (RANS) equations with the turbulence model of Spalart-Allmaras (SA). The solution polynomials of the SA equation are reconstructed by the Hermite weighted essentially non-oscillatory (HWENO) scheme. Several practical techniques are suggested to simplify and extend a positivity-preserving limiter to further guarantee the positivity of SA working variable. The resulting positivity-preserving HWENO limiting method is compact and easy to implement on arbitrary meshes. Typical turbulent flows are conducted to assess the accuracy and robustness of the present method. Numerical experiments demonstrate that with the increasing grid or order resolution, the limited results of the working variable are getting closer to the unlimited ones. And the most obvious improvement with proposed method is on the computation of the working variable field in wake regions.