A high order HLLC Riemann solver is implemented within a finite volume procedure for solving the Euler equations on unstructured grids. The traditional HLLC form is modified slightly to ensure satisfactory performance on stretched meshes and an appropriate limiter is employed to ensure stability and robustness. A Delaunay anisotropic mesh adaptation strategy is introduced with the objective of improving solution accuracy with an optimum number of mesh points, a suitable points inserting

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... m is proposed as well as a Delaunay kernel modification. The electiveness of the proposed approach is demonstrated by application to a number of test examples and the results produced are compared with experiment. Nomenclature