Adjoint-based anisotropic mesh adaptation for Discontinuous Galerkin Methods Using a Continuous Mesh Model

• ID: 2746, RIV: 10360273
• ISSN: not specified, ISBN: 978-1-62410-506-7
• source: 23rd AIAA Computational Fluid Dynamics Conference
• keywords: Adjoint-based anisotropic mesh adaptation; Discontinuous Galerkin Methods; Continuous Mesh Model
• authors: Vít Dolejší, Ajay Mandyam Rangarajan, Georg May
• authors from KNM: Dolejší Vít

Abstract

In this paper we propose an adjoint-based mesh optimization method for conservation laws, which may be used with any numerical method based on piecewise polynomials. The method uses a continuous mesh framework, where a global optimization scheme was formulated with respect to the error in the numerical solution, measured in any $L^q$ norm. The novelty of the present work is the extension to more general optimization targets. Here, any solution-dependent functional, which is compatible with an adjoint equation, may be the target of the continuous-mesh optimization. We present the rationale behind the formulation of the optimization problem, with particular emphasis on the continuous mesh model, and the relevant adjoint-based error estimate. We also present numerical results, demonstrating the viability of the scheme.