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On cubic spline approximations for the vortex patch problem. (English) Zbl 1013.76066
Summary: Based on the contour dynamics equation (CDE), we introduce a numerical method for solving the CDE by means of a global cubic spline interpolation between nodes. This method is shown to be convergent for all time, and is numerically tested against exact solutions for the CDE, the well-known flows of Kirchhoff ellipses. We compare this method with a method obtained by using the building blocks of the method designed by D. G. Dritschel [Comput. Phys. Reports 10, 17-146 (1989)]. Without the use of any node redistribution technique, we find a better performance of our method in several error estimates such as node position, tangent and curvature. This performance improves as the curvature of the contour increases.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76B47 Vortex flows for incompressible inviscid fluids
Full Text: DOI
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