The present work addresses several aspects associated with the generation and an efficient use of high-order meshes together with a high-order spectral difference (SD) method for the simulation of compressible flows. Flows of interest are assumed to be adequately modeled by the two-dimensional Euler equations. Issues associated with the use of curved boundaries are discussed. In particular, the problem of auto-intersecting cells is assessed for the special cases in which highly stretched meshes are required. Further developments on the generation of meshes with arbitrary order, given a linear initial mesh, are also discussed. The use of radial basis functions and of mesh optimization techniques are discussed as a means of rearranging and accommodating the interior nodes in the case of cell inversion due to high-order boundary treatment. Validation test cases for curved and highly stretched meshes are addressed in order to demonstrate the capability implemented.
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