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A modified finite element method for solving the time-dependent, incompressible Navier-Stokes equations. I: Theory. (English) Zbl 0559.76030

Beginning with the Galerkin finite element method and the simplest appropriate isoparametric element for modelling the Navier-Stokes equations, the spatial approximation is modified in two ways in the interest of cost-effectiveness: the mass matrix is ”lumped” and all coefficient matrices are generated via 1-point quadrature. After appending an hour-glass correction term to the diffusion matrices, the modified semi-discretized equations are integrated in time using the forward explicit Euler method in a special way to compensate for that portion of the time truncation error which is intolerable for advection- dominated flows. The scheme is completed by the introduction of a subcycling strategy that permits less frequent updates of the pressure field with little loss of accuracy.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
76M99 Basic methods in fluid mechanics

Citations:

Zbl 0559.76031
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References:

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