A Hybrid Adjoint/Error Transport Approach to Error Estimation, Adaptation, and Higher-Order Solutions for Computational Fluid Dynamics

摘要

Computational fluid dynamics is an invaluable tool for both the design and analysis of aerospace vehicles. Accurate error estimation techniques as well as effective adaptation schemes are needed to ensure that simulation results are accurate enough to use in the decision-making process. In this work, a framework for estimating error and improving solution accuracy is presented. A linearized error transport equation (ETE) is used to determine local discretization errors. Requirements for accurate truncation error estimation are discussed. A new approach to driving an adjoint-based adaptation scheme is proposed with the goal of targeting multiple functionals during the adaptation process. Equivalence between adjoint and ETE methods is reiterated. Using adjoint/ETE equivalence, ETE error estimates are shown to increase the order of accuracy of the entire primal solution, and by extension all solution hinctionals. Computational gains of this hybrid adjoint/error transport approach are discussed. This framework is evaluated using the quasi-lD nozzle problem.