Adjoint sensitivity computations for an embedded-boundary Cartesian mesh method

  • Authors:

  • Marian Nemec;Michael J. Aftosmis

  • Affiliations:

  • ELORET Corporation, Sunnyvale, CA 94086, USA and NASA Ames Research Center, MS T27B, Moffett Field, CA 94035, USA;NASA Ames Research Center, MS T27B, Moffett Field, CA 94035, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

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Abstract

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.