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Tools for simulating non-stationary incompressible flow via discretely divergence-free finite element models. (English) Zbl 0794.76051
We develop simulation tools for the non-stationary incompressible two- dimensional Navier-Stokes equations. The most important components of the finite element code are: the fractional step \(\vartheta\)-scheme, which is of second-order accuracy and strongly \(A\)-stable, for the time discretization; a fixed point defect correction method with adaptive step length control for the nonlinear problems (stationary Navier-Stokes equations); a modified upwind discretization of higher-order accuracy for the convective terms. Finally, the resulting nonsymmetric linear subproblems are treated by a special multigrid algorithm which is adapted to the quadrilateral non-conforming discretely divergence-free finite elements.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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