An Unsteady Adaptation Algorithm for Discontinuous Galerkin Discretizations of the RANS Equations

Abstract

An adaptive method for high-order discretizations of the Reynolds-averaged NavierStokes (RANS) equations is examined. The RANS equations and Spalart-Allmaras (SA) turbulence model are discretized with a dual consistent, discontinuous Galerkin discretization. To avoid oscillations in the solution in under-resolved regions, particularly the edge of the boundary layer, artificial dissipation is added to the SA model equation. Two adaptive procedures are examined: a standard output-based adaptation algorithm that requires the steady state solution to estimate the error and a new, unsteady approach that allows the mesh to be adapted without requiring a steady state solution. Results show that the combination of a dual consistent discretization with artificial dissipation and adaptation has significant promise as a practical method for obtaining high-order RANS solutions.