Mathematical modelling of flow around obstacles with complex geometric configuration in a viscous incompressible medium

  • A. Issakhov
  • A. A. Shaibekova

Abstract

In this paper, we numerically investigate flow around obstacles with complex geometric configuration in a viscous incompressible environment. The Navier-Stokes equations were used to modeling the flow around obstacles with complex geometric configuration. The numerical algorithm was constructed by using projection method. At the first stage the intermediate speed is determined by the 5-step Runge-Kutta method. At the second stage the results of intermediate velocity used to determine the pressure field. Poisson equation for the pressure field is solved numerically by using the Jacobi method.
The numerical algorithm is tested at flow around the square cylinder and compared with experimental data, which gives good results. Also, in this work simulated non-stationary flow around one and two
cylinders obstacles arranged opposite each other.

References

1. Chung T.J. Computational fluid dynamics // Cambridge University Press. – 2002. – 1012 p.
2. Fletcher K. Computational Methods in Fluid Dynamics (Russian) – Moscow, 1991. –552 p.
3. Madhavan S. Transition to three-dimensional models for flow past a confined square cylinder. PhD thesis, University of Alberta, Edmonton, AB. – Canada, 2011.
4. Anderson D., Tannehill John., Pletcher R. Computational fluid mechanics and heat transfer (Russian). – М., 1990. – 337 p.
5. Kozlov I. M., Dobergo K. V., Gnesdilov N. N. Application Of RES methods for computation of hydrodynamic flows by an example of 2D flow past a circular cylinder for Re=5-200 // International Journal of Heat and Mass Transfer. – 2011. – Vol. 54. – P. 887-893.
6. Belov I. Interaction of the Non-Uniform Flows with the Obstacles. – М.: Engineering, 1983. – 166 p.
7. Issakhov A., Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power plant // International Journal of Nonlinear Science and Numerical Simulation. – 2015. – Vol. 16, No 5. – P. 229–238, doi:10.1515/ijnsns-2015-0047.
8. Issakhov A., Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power plant under various operational capacities // Applied Mathematical Modelling. – 2016. – Vol. 40, No 2. – P. 1082–1096
9. Issakhov A. Large eddy simulation of turbulent mixing by using 3D decomposition method // J. Phys.: Conf. Ser. – 2011. – Vol. 318, No 4. – P. 1282-1288, doi:10.1088/1742-6596/318/4/042051.
10. Chorin A.J. Numerical solution of the Navier-Stokes equations // Math. Comp. –1968. – Vol. 22. – P. 745-762.
Published
2016-06-27
How to Cite
ISSAKHOV, A.; SHAIBEKOVA, A. A.. Mathematical modelling of flow around obstacles with complex geometric configuration in a viscous incompressible medium. International Journal of Mathematics and Physics, [S.l.], v. 7, n. 1, p. 40-45, june 2016. ISSN 2409-5508. Available at: <http://ijmph.kaznu.kz/index.php/kaznu/article/view/158>. Date accessed: 21 may 2018. doi: https://doi.org/10.26577/ijmph.v7i1.158.

Keywords

The Navier-Stokes equations, finite volumes method, Karman vortex shedding, an aerodynamic tube.