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Modeling of barotropic fluid dynamics on the sphere based on the contour dynamics. (English) Zbl 1045.76035
To study numerically the barotropic fluid motion on a sphere, the author uses the method of contour dynamics which was introduced as a technique for solving nonlinear two-dimensional Euler equations. The main advantage of this method is that it is possible to reduce the dimensions of the problem under consideration and, in addition, to solve problems with non-smooth initial data. In the article under review, it is shown how this concept may be applied to study the motion and interaction of some vortex structures on a sphere. With the help of the so-called contour surgery suggested by D. Dritschel in [J. Comput. Phys. 77, No. 1, 240–266 (1988; Zbl 0642.76025)], the author constructs a numerical algorithm for solving the problem, and the rest of the article is devoted to numerical experiments.
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76B47 Vortex flows for incompressible inviscid fluids
contour surgery
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