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ANISOTROPIC SIMPLEX MESH ADAPTATION BY METRIC OPTIMIZATION FOR HIGHER-ORDER DG DISCRETIZATIONS OF 3D COMPRESSIBLE FLOWS

Yano, Masayuki; Darmofal, David L.;

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We extend our optimization-based framework for anisotropic simplex mesh adaptation to three dimensions and apply it to high-order discontinuous Galerkin discretizations of steady-state aerodynamic flows. The framework iterates toward a mesh that minimizes the output error for a given number of degrees of freedom by considering a continuous optimization problem of the Riemannian metric field. The adaptation procedure consists of three key steps: sampling of the anisotropic error behavior using element-wise local solves; synthesis of the local errors to construct a surrogate error model in the metric space; and optimization of the surrogate model to drive the mesh toward optimality. The anisotropic adaptation decisions are entirely driven by the behavior of the a posteriori error estimate. As a result, the method handles any discretization order, naturally incorporates both the primal and adjoint solution behaviors, and robustly treats irregular features. Numerical results demonstrate the effectiveness of the adaptive high-order discretization applied to the compressible Navier-Stokes equations in three dimensions.

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Palavras-chave: anisotropic adaptation, discontinuous Galerkin method, higher-order, dualweighted residual, compressible Navier-Stokes,

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DOI: 10.5151/meceng-wccm2012-18538

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Como citar:

Yano, Masayuki; Darmofal, David L.; "ANISOTROPIC SIMPLEX MESH ADAPTATION BY METRIC OPTIMIZATION FOR HIGHER-ORDER DG DISCRETIZATIONS OF 3D COMPRESSIBLE FLOWS", p. 1770-1785 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18538

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