Large-time behavior of deterministic particle approximations to the Navier-Stokes equations

Cottet, Georges-Henri

doi:10.1090/S0025-5718-1991-1052089-X

Large-time behavior of deterministic particle approximations to the Navier-Stokes equations
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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

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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

Convergence of deterministic vortex methods for the Navier-Stokes equations

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Thèse d’Etat

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