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A second order finite element method for the solution of the transonic Euler and Navier-Stokes equations. (English) Zbl 0840.76030
A finite element approach is proposed in which the fourth-order dissipation is recast as the difference of two Laplacian operators, allowing the use of bilinear elements. The Laplacians of the primitive variables of the first-order scheme are thus balanced by additional terms obtained from the governing equations themselves, tensor identities or other forms of nodal averaging. To demonstrate formally the accuracy of this scheme, an exact solution is introduced which satisfies the continuity equation identically and the momentum equations through forcing functions. The solutions of several transonic and supersonic inviscid and laminar viscous test cases are also presented and compared to other available numerical data.

76M10 Finite element methods applied to problems in fluid mechanics
76H05 Transonic flows
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