Numerical solutions of a steady 2-D incompressible flow in a rectangular domain with wall slip boundary conditions using the finite volume method

• Autorzy: Ambethkar V. , Srivastava M. K.

Identyfikatory

DOI

10.17512/jamcm.2017.2.01

• Języki publikacji: EN

Abstrakty

EN

In this study, a finite volume method (FVM) is suitably used for solving the problem of a fully coupled fluid flow in a rectangular domain with slip boundary conditions. Numerical solutions for the flow variables, viz. velocity, and pressure have been computed. The FVM, with an upwind scheme, has been implemented to discretize the governing equations of the present problem. The well known SIMPLE algorithm is employed for pressure-velocity coupling. This was executed with the aid of a computer program developed and run in a C-compiler. Computations have been performed for unknown variables with Reynolds numbers (Re) = 50, 100, 250, 500, 750 and 1000. The behavior of steady-state solutions of velocity and pressure of the fluid along horizontal and vertical through geometric center of the rectangular domain have been illustrated. We observed that, with the increase of the Reynolds number, the absolute value of velocity components decreases whereas the pressure value increases.

Słowa kluczowe

EN

finite volume method; numerical solutions; pressure; Reynolds number; SIMPLE algorithm; staggered grid; u-velocity; v-velocity

PL

przepływy cieczy; metoda objętości skończonej; metody numeryczne; liczba Reynoldsa; algorytm SIMPLE; metoda siatek przesuniętych

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2017
• Tom: Vol. 16, nr 2
• Strony: 5--16
• Opis fizyczny: Bibliogr. 22 poz., rys.

Twórcy

autor

Ambethkar V.

• Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, India

autor

Srivastava M. K.

• Delhi College of Arts & Commerce, University of Delhi, Delhi, India

Bibliografia

• [1] Patankar S.V., Numerical Heat Transfer and Fluid Flow, Hemisphere, New York 1980.
• [2] Anderson D.A., Pletcher R.H., Tannehill J.C., Computational Fluid Mechanics and Heat Transfer, Second ed., Taylor and Francis, Washington D.C. 1997.
• [3] Bozeman J.D., Dalton C., Numerical study of viscous flow in a cavity, Journal of Computational Physics 1973, 12, 348-363.
• [4] Ghia U., Ghia K.N., Shin C.T., High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, Journal of Computational Physics 1982, 48, 387-411.
• [5] Bruneau C.H., Jouron C., An efficient scheme for solving steady incompressible Navier-Stokes equations, Journal of Computational Physics 1990, 89, 389-413.
• [6] Mansour M.L., Hamed A., Implicit solution of the incompressible Navier-Stokes equations on non-staggered grid, Journal of Computational Physics 1990, 86, 147-167.
• [7] Spotz W.F., Accuracy and performance of numerical wall boundary conditions for steady 2-D incompressible stream function vorticity, International Journal for Numerical Methods in Fluids 1998, 28, 737-757.
• [8] Boivin S., Cayre F., Herard J.M., A finite volume method to solve the Navier-Stokes equations for incompressible flows on structured meshes, International Journal of Thermal Sciences 2000, 39, 806-825.
• [9] Kalita J.C., Dalal D.C., Dass A.K., Fully compact higher-order computation of steady-state natural convection in a square cavity, Physical Review E 2001, 64, 066703.
• [10] Liakos A., Discretization of the Navier-Stokes equations with slip boundary condition, Numerical Methods for Partial Differential Equations 2001, 17, 26-42.
• [11] Piller M., Stalio E., Finite-volume compact schemes on staggered grids, Journal of Computational Physics 2004, 197, 299-340.
• [12] Oztop H.F., Dagtekin I., Mixed convection in two-sided lid-driven differentially heated square cavity, International Journal of Heat and Mass Transfer 2004, 47, 1761-1769.
• [13] Erturk E., Corke T.C., Gokcol C., Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers, International Journal for Numerical Methods in Fluids 2005, 48, 747-774.
• [14] Young D.L., Jane S.J., Fan C.M., Murugesan K., Tsai C.C., The method of fundamental solutions for 2D and 3D Stokes problems, Journal of Computational Physics 2006, 211, 1-8.
• [15] Droniou J., Eymard R., A mixed finite volume scheme for anisotropic diffusion problems on any grid, Numer. Math. 2006, 105, 35-71.
• [16] Salem S.A., On the numerical solution of the incompressible Navier-Stokes equations in primitive variables using grid generation techniques, Mathematical and Computational Applications 2006, 11, 127-136.
• [17] Mencinger J., Zun I., On the finite volume discretization of discontinuous body force field on collocated grid: Application to VOF method, Journal of Computational Physics 2007, 221, 524- 538.
• [18] Bharti R.P., Chhabra R.P., Eswaran V., A numerical study of steady forced convection heat transfer from an unconfined circular cylinder, Heat Mass Transfer 2007, 43, 639-648.
• [19] Hokpunna A., Manhart M., Compact fourth-order finite volume method for numerical solutions of Navier-Stokes equations on staggered grids, Journal of Computational Physics 2010, 229, 7545-7470.
• [20] Sathiyamoorthy M., Chamkha A.J., Effect of magnetic field on natural convection flow in a liquid gallium filled square cavity for linearly heated side wall(s), International Journal of Thermal Sciences 2010, 49, 1856-1865.
• [21] Versteeg H.K., Malalsekra W., An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Second ed., Pearson, India 2007.
• [22] Patankar S.V., Spalding D.B., A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, Int. J. Heat Mass. Transfer 1972, 15, 1787.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).