A general explicit or semi-explicit algorithm for compressible and incompressible flows

This note presents a rational basis for a unified finite element algorithm capable of dealing with a wide range of fluid flow in both steady and transient cases. It is hoped that empiricism inherent in many previous approaches can be avoided and a sound basis provided. The algorithm permits the use of equal interpolation for all variables by avoiding the need for the Babuska-Brezzi constraints in regions where the flow is nearly incompressible. The success of the algorithm, which here is written for the non-conservative equation form, is demonstrated on several examples ranging from (nearly) incompressible through transonic regions to supersonic flows. Up to mild shocks such as those occurring in the examples presented in this paper, no 'artificial' viscosity is added at any stage. The algorithm extends some concepts introduced in an earlier paper.

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