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\title{Numerical Solution of Unsteady Incompressible Flows}
\tocauthor{P. Louda} \author{} \institute{}
{\large \underline{Petr Louda}}\\
Czech Technical University in Prague\\
\\ \vspace{4mm}{\large Jaromir P\v{r}\'{\i}hoda}\\
Institute of Thermomechanics, Czech Academy of Sciences\\
\\ \vspace{4mm}{\large Karel Kozel}\\
Czech Technical University in Prague\\
The work deals with numerical solution of 2D and 3D laminar and
turbulent unsteady flows of incompressible fluid. Flows with
self-induced as well as forced unsteadiness are considered, namely:
laminar flow over backward facing step at higher Reynolds numbers,
laminar flow around cylinder, turbulent synthetic free and impinging
jet and turbulent flow through branched channel. The numerical methods
are based either on a projection method using the Poisson equation for
pressure or on artificial
compressibility approach. The time discretization uses multi-stage
Runge-Kutta methods or implicit methods, the space discretization is
done by higher order upwind finite volume methods. The turbulent flows
are approximated by unsteady RANS method with two-equation turbulence
models. Results of different methods for same case are discussed and
also comparison with measurements.
{\sc K. Kozel and P. Louda and J. P\v{r}\'\i{h}oda}. {Numerical methods of higher order of accuracy for incompressible flows}. Mathematics and Computers in Simulation 80(8):1734--1745 (2010).