The algebraic moments of vorticity. Theory and numerical tests
Abstract
The paper presents the method of algebraic vorticity moments. It may be used to solve problems of viscous liquid motion in 2-D and 3-D cases. Its essence lies in the integration of a set of ordinary differentia equations. The unknown functions of those equations defined as , wxmyn dxdy allow to find the vorticity field and next the velocity. We also show a number of 2-D numerical examples.
References
[1] M.V. Melander, A. Styczek, N.J. Zabusky. Elliptically desingularized vortex model for the two-dimensional Euler equations. Physical Review Letters. 53: 1222-1225, 1984.
[2] M.V. Melander, A. Styczek, N.J. Zabusky. A moment model for vortex interactions of the two-dimensional Euler equation. Part l. Computational validation of a Hamiltonian elliptical representation. Journal of Fluid Mechanics 167: 95-115, 1986.
[3] A. Styczek, N.J. Zabusky. The evolution of a plane, viscous vortex field. Archives of Mechanics 41: 343-350, 1989.
[4] H. Bateman. Higher Transcendental Functions. McGraw-Hill, New York, 1953.
[5] D.S. Mitronovic. Elementary Inequalities, PWN, Warsaw, 1972 (in Polish)
[2] M.V. Melander, A. Styczek, N.J. Zabusky. A moment model for vortex interactions of the two-dimensional Euler equation. Part l. Computational validation of a Hamiltonian elliptical representation. Journal of Fluid Mechanics 167: 95-115, 1986.
[3] A. Styczek, N.J. Zabusky. The evolution of a plane, viscous vortex field. Archives of Mechanics 41: 343-350, 1989.
[4] H. Bateman. Higher Transcendental Functions. McGraw-Hill, New York, 1953.
[5] D.S. Mitronovic. Elementary Inequalities, PWN, Warsaw, 1972 (in Polish)
Published
2023-07-18
Issue
pp. 149-160
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Bresiński, R., & Styczek, A. (2023). The algebraic moments of vorticity. Theory and numerical tests. Computer Assisted Methods in Engineering and Science, 2(2), 149-160. https://cames3.ippt.pan.pl/index.php/cames/article/view/1483
