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)
