zbMATH — the first resource for mathematics

A convergent 3-D vortex method with grid-free stretching. (English) Zbl 0602.76024
A. Maida and the author [ibid. 39, 1-27 (1982; Zbl 0488.76024) and 39, 29-52 (1982; Zbl 0488.76025)], following the proof of O. Hald and V. Prete for second-order convergence of vortex methods for two-dimensional flow [ibid. 32, 791-809 (1978; Zbl 0387.76021) and SIAM J. Numer. Anal. 16, 726-755 (1979; Zbl 0427.76024)] showed that a three- dimensional version also converges and that high-order accuracy can be achieved. Here, a new convergence proof version of a vortex method for 3- D, incompressible, inviscid flow without boundaries is given.
It is also shown that the previous estimates for the velocity approximation can be improved by taking into account that the integral kernel has average value zero. Implications for the design of the method are discussed.
Reviewer: V.A.Kostova

76B47 Vortex flows for incompressible inviscid fluids
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
Full Text: DOI