Numerical solution of two-dimensional problems of incompressible fluid convection in irregular domains
https://doi.org/10.29235/1561-2430-2025-61-3-231-243
Abstract
A finite-difference computational algorithm for solving the equations of convective flows of incompressible fluid in two-dimensional irregular domains using generalized curvilinear coordinates is constructed. The physical domain is mapped into a computational domain (unit square) in the space of generalized coordinates. The equations of mixed convection in primitive variables are written in generalized curvilinear coordinates and approximated in the computational domain on uniform non-staggered grids. The constructed computational algorithm is based on splitting difference schemes. The obtained results are mapped onto a nonuniform difference grid in the physical domain. The results of solving boundary value problems of heat and mass transfer of incompressible fluid in domains of complex shape are presented.
About the Authors
M. M. Chuiko
Institute of Mathematics of the National Aca demy of Sciences of Belarus
Belarus
Belarus
Mikhail M. Chuiko – Ph. D. (Physics and Mathematics), Leading Researcher of the Department of Computational Mathematics
11, Surganov Str., 220072, Minsk
O. M. Korolyova
Belarusian National Technical University
Belarus
Belarus
Olga M. Korolyova – Ph. D. (Physics and Mathematics), Associate Professor of the Department of Higher Mathematics
65, Nezavisimosti Ave., 220013, Minsk
References
1. Polezhaev V. I., Bune A. V., Verezub N. A., Glushko G. S., Gryaznov V. L., Dubovik K. G. [et al.]. Mathematical Modelling of Convective Heat and Mass Transfer on the Basis of the Navier-Stokes Equations. Moscow: Nauka Publ., 1987. 272 p. (in Russian).
2. Roache P. J. Computational Fluid Dynamics. Hermosa, Albuquerque, 1976. 446 p.
3. Berkovsky B. M., Polevikov V. K. Computational Experiment in Convection. Minsk, Universitetskoe Publ., 1988. 167 p. (in Russian).
4. Armfield S. W. Finite difference solutions of the Navier-Stokes equations on staggered and nonstaggered grids. Computers & Fluids, 1991, vol. 20, no. 1, pp. 1–17. https://doi.org/10.1016/0045-7930(91)90023-B
5. Chung M.-H. Cartesian cut cell approach for simulating incompressible flows with rigid bodies of arbitrary shape. Computers & Fluids, 2006, vol. 35, no. 6, pp. 607–623. https://doi.org/10.1016/j.compfluid.2005.04.005
6. Ye T., Mittal R., Udaykumar H. S., Shyy W. An accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries. Journal of Computational Physics, 1999, vol. 156, no. 2, pp. 209–240. https://doi.org/10.1006/jcph.1999.6356
7. Li Z. An overview of the immersed interface method and its applications. Taiwanese Journal of Mathematics, 2003, vol. 7, no. 1, pp. 1–49. https://doi.org/10.11650/twjm/1500407515
8. Fletcher C. A. J. Computational Techniques for Fluid Dynamics. Vol. 2. Springer, 1988. 494 p.
9. Anderson D., Tannehill J., Pletcher R. Computational Fluid Mechanics and Heat Transfer. New York, Hemisphere Publ., 1984. 599 p.
10. Zang Y., Street R. L., Koseff J. R. A non-staggered grid, fractional step method for time-dependent incompressible Navier-Stokes equations in general curvilinear coordinate systems. Journal of Computational Physics, 1994, vol. 114, no. 1, pp. 18–33. https://doi.org/10.1006/jcph.1994.1146
11. Koshizuka S., Oka Y., Kondo S. A staggered differencing technique on boundary-fitted curvilinear grids for incompressible flows along curvilinear or slant walls. Computational Mechanics, 1990, vol. 7, pp. 123–136. https://doi.org/10.1007/BF00375926
12. Thompson J. F., Warsi Z. U. A., Mastin C W. Numerical Grid Generation: Foundations and Applications. Elsevier North-Holland, 1985. 483 p.
13. Chuiko M. M., Korolyova O. M. Solution of the mixed boundary problem for the Poisson equation on two-dimensional irregular domains. Informatika = Informatics, 2023, vol. 20, no. 2, pp. 111−120 (in Russian). https://doi.org/10.37661/18160301-2023-20-2-111-120
14. Chuiko M. M., Korolyova O. M. Numerical solution of the mixed boundary value problem for the heat equation in two-dimensional domains of complex shape. Vestsі Natsyyanal’nai akademіі navuk Belarusі. Seryya fіzіka-matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 2024, vol. 60, no. 3, pp. 216–224 (in Russian). https://doi.org/10.29235/1561-2430-2024-60-3-216-224
15. Vabishchevich P., Pavlov V., Churbanov A. Numerical methods for unsteady incompressible flows using primitive variables and non-staggered grids. Matematicheskoe modelirovanie = Mathematical Models and Computer Simulation, 1996, vol. 8, no. 7, pp. 81–108 (in Russian).
16. Chuiko M., Lapanik A. Incompressible fluid flow computation in an arbitrary two-dimensional region on nonstaggered grids. Computational Methods in Applied Mathematics, 2005, vol. 5, no. 3, pp. 242−258. https://doi.org/10.2478/cmam-2005-0012
17. Samarskii A. A. The Theory of Difference Schemes. New York, 2001. 786 p.
18. Schneider G. E., Zedan M. A modified strongly implicit procedure for the numerical solution of field problem. Numerical Heat Transfer, 1981, vol. 4, no. 1, pp. 1–19. https://doi.org/10.1080/01495728108961775
19. Samarskii A., Vabishchevich P. Computational Heat Transfer. Vol. 2. The Finite Difference Methodology. Wiley, 1996. 432 p
20. Li J., Yu B., Wang M. Benchmark solutions for two-dimensional fluid flow and heat transfer problems in irregular regions using multigrid method. Advances in Mechanical Engineering, 2015, vol. 7, no. 11, pp. 1–17. https://doi.org/10.1177/1687814015618611
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