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The first step towards establishing credibility in computational physics simulations involves code verification, which is typically performed using exact and manufactured solutions. However, exact solutions are typically limited, and manufactured solutions generally require the invasive introduction of an artificial forcing term within the source code, such that the code solves a modified problem for which the solution is known. For some physics phenomena, such as non-decomposing ablation, there are many possible exact solutions to the governing equations, but the boundary conditions may render these impractical and eliminate such conveniences as separation of variables. For such phenomena, however, we can manufacture the terms that comprise the boundary conditions to obtain exact solutions. In this paper, we present a nonintrusive method for manufacturing solutions for non-decomposing ablation in two dimensions, which does not require the addition of a source term.

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Currently, the usefulness of proper orthogonal decomposition (POD) is limited to computational domains with fixed meshes and fixed boundaries. This paper presents a new POD method that enables the modeling of flow through computational domains with deforming meshes and/or moving boundaries. To achieve this goal, the solution is approximated using basis functions which, although not explicitly functions of time, depend on parameters associated with flow unsteadiness. Results are shown for transonic flow through the Tenth Standard Configuration. Comparisons are made between this method and the standard approach for on-and off-reference flow conditions. This method properly captured flow nonlinearities and shock motion for cases in which the classical POD method failed.