Discrete Adjoint Approximations with Shocks

By M. Giles. 2003

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Optimization and Computational Fluid Dynamics (2008, methodology): “He also presented the analytical solutions of the adjoint equations using Green’s functions [56], an exact approach for the solution of the adjoint equations [22], a shock wave reduction method in external aerodynamics [21] and the harmonic approach to turbomachinery steady and unsteady designs [11,”
Adjoint and defect error bounding and correction for functional estimates (2003, background): “In this case, numerical results [33] indicate that the ‘‘discrete’’ adjoint approach does not necessarily yield convergent results, unless one uses numerical dissipation that leads to an increasing smoothing of the shock as the mesh is refined.”