| Abstract: | We develop simulation tools for the non-stationary incompressible 2D Navier--Stokes equations. The most important components of the finite element code are: the fractional step ?-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 non-linear 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. For the graphical postprocess we use a fully non-stationary and interactive particle-tracing method. With extensive test calculations we show that our method is a candidate for a ‘black box’ solver. |
