Entropy-Based Drag-Error Estimation and Mesh Adaptation in Two Dimensions

Abstract

This paper presents a method for estimating the drag error in two-dimensional computational fluid dynamics simulations using a method that does not require auxiliary adjoint solutions. The error of interest is that caused by the numerical discretization, including effects of finite mesh size and approximation order. The target output is a drag calculation based on a farfield integration of the entropy. The error estimate is motivated by an interpretation of entropy variables as adjoint solutions to an entropy balance output. As entropy variables are obtained by a direct transformation of the state, no separate adjoint solution is required. The method is shown to be applicable not only to inviscid and laminar flows, but also to turbulent Reynolds-averaged Navier-Stokes flows, for which entropy variables generally lose their symmetrization property. Since the proposed drag error estimate is based on an integral of a weighted residual over the computational domain, it can be localized to provide an adaptive indicator over each element. Adaptive results for several flows of aerodynamic interest show that the error estimate is effective and that the method performs on par with adjoint-based methods. ∗Assistant Professor, AIAA Senior Member †Graduate Research Assistant ‡Professor, AIAA Fellow