Efficient and robust algorithms for solution of the adjoint compressible Navier-Stokes equations with applications.

*(English)*Zbl 1161.76035Summary: The complete discrete adjoint equations for an unstructured finite volume compressible Navier-Stokes solver are discussed with respect to the memory and time efficient evaluation of their residuals, and their solution. It is seen that application of existing iteration methods for the nonlinear equation – suitably adjointed – has a property of guaranteed convergence provided that the nonlinear iteration is well behaved. For situations where this is not the case, in particular for strongly separated flows, a stabilization technique based on the recursive projection method is developed. This method additionally provides the dominant eigenmodes of the problem, allowing identification of flow regions that are unstable under the basic iteration. These are found to be regions of separated flow. Finally, an adjoint-based optimization with 96 design variables is performed on a wing-body configuration. The initial flow has large regions of separation, which are significantly diminished in the optimized configuration.

##### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

76N15 | Gas dynamics, general |

76N25 | Flow control and optimization for compressible fluids and gas dynamics |

##### Keywords:

recursive projection method; eigensystem analysis; aerodynamic optimization; wing-body configuration##### Software:

LAPACK
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\textit{R. P. Dwight} and \textit{J. Brezillon}, Int. J. Numer. Methods Fluids 60, No. 4, 365--389 (2009; Zbl 1161.76035)

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