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Tensor universal serendipity elements and unsteady Taylor-Galerkin finite element method. (English) Zbl 0854.76055

Summary: A new kind of universal serendipity element (USE) – the tensor universal serendipity element (TUSE) – is constructed by using both tensor force finite elements and the basic idea of USE. The formulation of shape functions and their derivatives for TUSE is presented. TUSE can be used to study steady and unsteady transonic flow fields when combined with Taylor-Galerkin finite element methods, the NND scheme in FDM, and four-stage Runge-Kutta methods. As numerical examples, the transonic flow in cascades and one kind of complex unsteady transonic axisymmetric flows engineering are studied.

MSC:

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

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