Large-time behavior of deterministic particle approximations to the Navier-Stokes equations
HTML articles powered by AMS MathViewer
- by Georges-Henri Cottet PDF
- Math. Comp. 56 (1991), 45-59 Request permission
Abstract:
We prove that for a class of deterministic vortex methods for the Navier-Stokes equations in two dimensions, the numerical solution decays for large time with the same rate as the exact solution. We substantiate our result with numerical experiments and with a remark concerning the problem of reinitialization of a distribution of particles.References
- J. U. Brackbill and H. M. Ruppel, FLIP: a method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions, J. Comput. Phys. 65 (1986), no. 2, 314–343. MR 851901, DOI 10.1016/0021-9991(86)90211-1
- Georges-Henri Cottet, A particle-grid superposition method for the Navier-Stokes equations, J. Comput. Phys. 89 (1990), no. 2, 301–318. MR 1067048, DOI 10.1016/0021-9991(90)90146-R G. H. Cottet and S. Mas-Gallic, Convergence of deterministic vortex methods for the Navier-Stokes equations (in preparation).
- John G. Heywood and Rolf Rannacher, Finite element approximation of the nonstationary Navier-Stokes problem. II. Stability of solutions and error estimates uniform in time, SIAM J. Numer. Anal. 23 (1986), no. 4, 750–777. MR 849281, DOI 10.1137/0723049 S. Mas-Gallic, Thèse d’Etat, Université Paris 6, 1988.
- Maria Elena Schonbek, $L^2$ decay for weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal. 88 (1985), no. 3, 209–222. MR 775190, DOI 10.1007/BF00752111
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Math. Comp. 56 (1991), 45-59
- MSC: Primary 65M99; Secondary 35Q30, 76D05
- DOI: https://doi.org/10.1090/S0025-5718-1991-1052089-X
- MathSciNet review: 1052089