The Navier-Stokes equations for incompressible isothermal flow of a Newtonian fluid are at the core of fluid dynamics. Since analytical solutions are only available in very special cases, numerical algorithms are essential for computing fluid flow simulations of complex, real-life applications with sufficient accuracy and efficiency. This is known as computational fluid dynamics (CFD), which belongs to the field of scientific computing.

There is currently no software package available that can handle any kind of fluid flow problem in arbitrary domains. The difficulty arises from the huge field of different flow phenomena and the numerical problems arising from simulations in complex domains, e.g. transient domains.

In this talk, numerical simulation techniques for Newtonian and some class of non-Newtonian incompressible fluid flow problems in stationary and transient domains, possibly coupled with other physical effects such as fluid-structure interaction, are presented. In particular, the efficiency of discrete projection methods for the time integration in conjunction with an algebraic multigrid solver is demonstrated. Accuracy, efficiency, easy extensibility, and applicability to real life problems are the main objectives of the presented methods.