Convergence of a vortex in cell method for the two-dimensional Euler equations

Cottet, G.-H.

doi:10.1090/S0025-5718-1987-0906179-9

Convergence of a vortex in cell method for the two-dimensional Euler equations
HTML articles powered by AMS MathViewer

by G.-H. Cottet PDF

Math. Comp. 49 (1987), 407-425 Request permission

Abstract:

We describe a Vortex In Cell method in which the assignment function used to compute vorticity values at the grid points from particles is twice differentiable, while the velocity need only be continuous. We prove an error estimate for the velocity in terms of the meshsize, the interparticle distance and the size of the computational domain.

References

J. Thomas Beale and Andrew Majda, Vortex methods. I. Convergence in three dimensions, Math. Comp. 39 (1982), no. 159, 1–27. MR 658212, DOI 10.1090/S0025-5718-1982-0658212-5
P. G. Ciarlet and P.-A. Raviart, Maximum principle and uniform convergence for the finite element method, Comput. Methods Appl. Mech. Engrg. 2 (1973), 17–31. MR 375802, DOI 10.1016/0045-7825(73)90019-4

Ann. Inst. H. Poincarè

G.-H. Cottet and P.-A. Raviart, On particle-in-cell methods for the Vlasov-Poisson equations, Transport Theory Statist. Phys. 15 (1986), no. 1-2, 1–31. MR 831210, DOI 10.1080/00411458608210442
Ole Hald and Vincenza Mauceri del Prete, Convergence of vortex methods for Euler’s equations, Math. Comp. 32 (1978), no. 143, 791–809. MR 492039, DOI 10.1090/S0025-5718-1978-0492039-1

Computer Simulation Using Particles

A. Leonard, Vortex methods for flow simulation, J. Comput. Phys. 37 (1980), no. 3, 289–335. MR 588256, DOI 10.1016/0021-9991(80)90040-6
Rolf Rannacher and Ridgway Scott, Some optimal error estimates for piecewise linear finite element approximations, Math. Comp. 38 (1982), no. 158, 437–445. MR 645661, DOI 10.1090/S0025-5718-1982-0645661-4

An Analysis of Particle Methods

Vidar Thomée, Discrete interior Schauder estimates for elliptic difference operators, SIAM J. Numer. Anal. 5 (1968), 626–645. MR 238505, DOI 10.1137/0705050