Adjoint-based error estimation and adaptive mesh refinement for the RANS and k–ω turbulence model equations

Abstract In this article we present the extension of the a posteriori error estimation and goal-oriented mesh refinement approach from laminar to turbulent flows, which are governed by the Reynolds-averaged Navier–Stokes and k – ω turbulence model (RANS- kω ) equations. In particular, we consider a discontinuous Galerkin discretization of the RANS- kω equations and use it within an adjoint-based error estimation and adaptive mesh refinement algorithm that targets the reduction of the discretization error in single as well as in multiple aerodynamic force coefficients. The accuracy of the error estimation and the performance of the goal-oriented mesh refinement algorithm is demonstrated for various test cases, including a two-dimensional turbulent flow around a three-element high lift configuration and a three-dimensional turbulent flow around a wing-body configuration.