• DOI:10.2514/1.37149
• Corpus ID: 122703828

2-D Euler Shape Design on Nonregular Flows Using Adjoint Rankine-Hugoniot Relations

@article{Baeza20082DES,
  title={2-D Euler Shape Design on Nonregular Flows Using Adjoint Rankine-Hugoniot Relations},
  author={Antonio Baeza and Carlos Castro and Francisco Palacios and E. Zuazua},
  journal={AIAA Journal},
  year={2008},
  volume={47},
  pages={552-562}
}

• A. Baeza, C. Castro, +1 author E. Zuazua
• Published 7 January 2008
• Mathematics
• AIAA Journal

Optimal Shape Design (OSD) aims at flnding the minimum of a functional by controlling the Partial Difierential Equation (PDE) modeling the ∞ow using surface (domain boundaries) deformation techniques. As a solution to the enormous computational resources required for classical shape optimization of functionals of aerodynamic interest, one of the best strategies is to use methods inspired in control theory. To do this, one assumes that a given aerodynamic surface is an element that produces lift or drag by controlling or modifying the ∞ow. One of the key ingredients in the application of control methods relies on the use of the adjoint system techniques to simplify the computation of gradients. In this paper we will restrict our attention to optimal shape design in 2D systems governed by the Euler equations with discontinuities in the ∞ow variables (an isolated normal shock wave). We flrst review some facts on control theory applied to optimal shape design, and recall the 2D Euler equations (including Rankine-Hugoniot relations). We then study the adjoint formulation, providing a detailed exposition of how the derivatives of functionals may be obtained when a discontinuity appears. Further on, adjoint equations will be discretized and analyzed and some novel numerical experiments with adjoint RankineHugoniot relations will be shown. Finally, we expose some conclusions about the viability of a rigorous approach to the continuous Euler adjoint systems with discontinuities in the ∞ow variables.