Efficient Residual-Based Mesh Adaptation for 1D and 2D CFD Applications

Abstract

This work examines different approaches for driving mesh adaptation on 1D and 2D structured grids. Arguments are made for truncation error-based adaptation since it serves as the local source of the discretization error. While the equivalency of the truncation error and discrete or continuous residuals is discussed, analytic truncation error expressions are derived and used in the current work. Derivation of truncation error (TE) expressions for 1D and 2D Burgers equation is discussed. TE expressions are presented for a finite volume formulation of the quasi-1D nozzle problem employing the 1D Euler equations with a central flux scheme stabilized with numerical damping. Examination of the truncation error expressions in generalized coordinates provides insight into the effects of mesh quality (mesh stretching in 1D and mesh stretching, mesh skewness and curvature in 2D) on the discretization error. Numerical results for 1D Burgers equation using four different approaches for driving mesh adaption are presented: solution gradients, solution curvature (i.e., Hessian), discretization error, and truncation error. Numerical results for 2D Burgers equation using five different mesh adaption approaches based upon truncation error, discretization error, Laplacian, Hessian and discrete residual are presented. Results from truncation error-based adaption and feature-based adaption are presented and compared for the quasi-1D nozzle problem.