an:01591303
Zbl 1013.76066
Chac??n Vera, E.; Chac??n Rebollo, T.
On cubic spline approximations for the vortex patch problem
EN
Appl. Numer. Math. 36, No. 4, 359-387 (2001).
00073201
2001
j
76M25 76B47
convergence analysis; curvature of contour; vortex patch problem; contour dynamics equation; global cubic spline interpolation; Kirchhoff ellipses
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 \textit{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.