Advances in control-volume-based finite-element methods for compressible flows

Recent developments in the application of a control-volume-based finite-element method, that has proven successful in solving incompressible flow problems, to the solution of compressible flow problems are presented. The finite Element Differential Scheme (FIELDS) is demonstrated to retain the pressure checker boarding problem for the case of Euler flow under certain conditions of flow. The source of this is investigated and remedies are provided that surmount this problem for all flows including Euler flows. Success is demonstrated for incompressible flow and a formulation is provided for extension to compressible flows. One dimensional testing on a supersonic converging-diverging nozzle exhibits extremely high accuracy of flow prediction including both shock strength and sharpness of resolution.

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