A higher-order error estimation framework for finite-volume CFD

Computational fluid dynamics is an invaluable tool for both the design and analysis of aerospace vehicles. Reliable error estimation techniques are needed to ensure that simulation results are accurate enough to be used in engineering decision-making processes. In this work, a framework for estimating error and improving solution accuracy is presented. A linearized error transport equation (ETE) is used to estimate local discretization errors. A truncation error estimation technique is proposed which combines aspects of higher-order residual methods and continuous residual methods. The equivalence between adjoint and ETE methods for functional error estimation is demonstrated. Using adjoint/ETE equivalence, the higher-order properties of adjoint methods are extended to ETE methods. Consequently, ETE error estimates are shown to converge to the true discretization error at a higher-order rate. ETE error estimates are then used to correct the entire primal solution, and by extension, all output functionals, to higher order. The computational advantages of this ETE approach are discussed. Results are presented for 1D and 2D inviscid and viscous flow problems on grids with smoothly varying and non-smoothly varying grid metrics. (C) 2019 Elsevier Inc. All rights reserved.