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**On using artificial compressibility method for solving turbulent flows.**
*(English)*
Zbl 1313.76027

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 2–5, 2012. In honor of the 60th birthday of Michal Křížek. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-60-8/pbk). 163-172 (2012).

The work deals with numerical solutions of incompressible viscous (laminar and turbulent) unsteady flows. The governing system of equations is the system of Navier-Stokes equations for incompressible fluids. In the unsteady case, one of the possibilities is to introduce an artificial time \(\tau\) and apply the artificial compressibility method in this time. In order to simulate turbulent flows, the Reynolds averaging procedure is used leading to the Reynolds-averaged Navier-Stokes (RANS) system of equations. For unsteady simulation it becomes the URANS (unsteady RANS) approach. The Reynolds stress is modelled using a shear stress transport (SST) model and an explicit algebraic Reynolds stress model (EARSM). The extension for the unsteady simulation is considered by increasing an artificial compressibility parameter or by using dual time stepping. Numerical results are given for the three cases. First, a 2D laminar flow around the circular cylinder is considered. In this test case, the Reynolds number is 100. Second, a 3D turbulent flow in synthetic jet generated by a periodical inflow/outflow with zero mean value in the circular nozzle is considered, Re = 13 325. Third, a 3D turbulent flow in a channel with perpendicular branch is considered, Re = 140 000.

For the entire collection see [Zbl 1277.00031].

For the entire collection see [Zbl 1277.00031].

Reviewer: Radka Keslerová (Praha)

### MSC:

76D05 | Navier-Stokes equations for incompressible viscous fluids |

76M12 | Finite volume methods applied to problems in fluid mechanics |

65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |

76F25 | Turbulent transport, mixing |

### Keywords:

artificial compressibility method; steady and unsteady flow; Navier-Stokes equations; incompressible viscous laminar and turbulent flow; dual time stepping method
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\textit{P. Louda} et al., in: Proceedings of the international conference `Applications of mathematics', Prague, Czech Republic, May 2--5, 2012. In honor of the 60th birthday of Michal Křížek. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics. 163--172 (2012; Zbl 1313.76027)

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