Adjoint sensitivity computations for an embedded-boundary Cartesian mesh method

doi:10.1016/j.jcp.2007.11.018

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Adjoint sensitivity computations for an embedded-boundary Cartesian mesh method

2008-02-01

PRE

Nemec, Marian *

Aftosmis, Michael J.

DOI：10.1016/j.jcp.2007.11.018

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Abstract

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We present a new approach for the computation of shape sensitivities using the discrete adjoint and flow-sensitivity methods on Cartesian meshes with general polyhedral cells (cut-cells) at the wall boundaries. By directly linearizing geometric constructors of the cut-cells, an efficient and robust computation of shape sensitivities is achieved for problems governed by the Euler equations. The accuracy of the linearization is verified by the use of a model problem with an exact solution. Verification studies show that the convergence rate of gradients is second-order for design variables that do not alter the boundary shape, and is reduced to first-order for shape design problems. The approach is applied to several three-dimensional problems, including inverse design and shape optimization of a re-entry capsule in hypersonic flow. The results show that reliable approximations of the gradient are obtained in all cases. The approach is well-suited for geometry control via computer-aided design, and is especially effective for conceptual design studies with complex geometry where fast turn-around time is required. (c) 2007 Elsevier Inc. All rights reserved.

Keywords:

aerodynamic shape optimization

Cartesian mesh

adjoint

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