TOOLS FOR SIMULATING NONSTATIONARY INCOMPRESSIBLE-FLOW VIA DISCRETELYDIVERGENCE-FREE FINITE-ELEMENT MODELS

We develop simulation tools for the non-stationary incompressible 2D N avier-Stokes equations. The most important components of the finite el ement code are: the fractional step theta-scheme, which is of second-o rder accuracy and strongly A-stable, for the time discretization; a fi xed point defect correction method with adaptive step length-control f or the non-linear problems (stationary Navier-Stokes equations); a mod ified upwind discretization of higher-order accuracy for the convectiv e terms. Finally, the resulting nonsymmetric linear subproblems are tr eated by a special multigrid algorithm which is adapted to the quadril ateral non-conforming discretely divergence-free finite elements. For the graphical postprocess we use a fully non-stationary and interactiv e particle-tracing method. With extensive test calculations we show th at our method is a candidate for a 'black box' solver.