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OUTPUT-BASED HP-ADAPTATION APPLIED TO AERODYNAMIC FLOWS

Ceze, Marco; Fidkowski, Krzysztof;

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We present a method for concurrent mesh and polynomial-order adaptation with the objective of direct minimization of output error using a selection process for choosing the optimal refinement option from a discrete set of choices that includes directional spatial resolution and approximation order increment. The scheme is geared towards compressible viscous aerodynamic flows, in which solution features make certain refinement options more efficient compared to others. No attempt is made, however, to measure the solution anisotropy or smoothness directly or to incorporate it into the scheme. Rather, mesh anisotropy and approximation order distribution arise naturally from the optimization of a merit function that incorporates both an output sensitivity and a measure of the computational cost of solving on the new mesh. An adjoint state is used to translate the residual perturbation resulting from each refinement option into an output sensitivity with respect to each mesh modification option. Two measures of computational cost are explored: a generic measure that accounts for the number of degrees of freedom of the discrete state, and one that accounts for the number of floating-point operations involved in solving the discrete problem. We restrict the mesh refinement mechanics to quadrilateral and hexahedral meshes. Many such meshes and associated meshing programs exist from the structured CFD community, and these can be leveraged to produce the starting meshes for the proposed adaptation. Additionally, we discuss implementation challenges of hp-adaptive methods for aerodynamic problems, such as load balancing on distributed-memory systems. The method is applied to output-based adaptive simulations of laminar and Reynolds-averaged compressible Navier-Stokes equations on body-fitted meshes in two and three dimensions. Two-dimensional results show significant reduction in the degrees of freedom and computational time to achieve output convergence when the discrete choice optimization is used compared to uniform h or p adaptation. Threedimensional results show that the presented method is an affordable way of achieving output convergence on notoriously difficult cases such as the third Drag Prediction Workshop W1 configuration.

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Palavras-chave: hp-adaptation, computational fluid dynamics, discontinuous Galerkin.,

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DOI: 10.5151/meceng-wccm2012-18038

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Como citar:

Ceze, Marco; Fidkowski, Krzysztof; "OUTPUT-BASED HP-ADAPTATION APPLIED TO AERODYNAMIC FLOWS", p. 608-627 . 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-wccm2012-18038

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