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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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The weighted particle method for convection-diffusion equations. I. The case of an isotropic viscosity
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by P. Degond and S. Mas-Gallic PDF
Math. Comp. 53 (1989), 485-507 Request permission


The aim of this paper is to present and study a particle method for convection-diffusion equations based on the approximation of diffusion operators by integral operators and the use of a particle method to solve integro-differential equations described previously by the second author. The first part of the paper is concerned with isotropic diffusion operators, whereas the second part will consider the general case of a nonconstant matrix of diffusion. In the former case, the approximation of the diffusion operator is much simpler than in the general case. Furthermore, we get two possibilities of approximations, depending on whether or not the integral operator is positive.
  • Sylvie Mas-Gallic, A deterministic particle method for the linearized Boltzmann equation, Proceedings of the conference on mathematical methods applied to kinetic equations (Paris, 1985), 1987, pp. 855–887. MR 906929, DOI 10.1080/00411458708204318
  • 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
  • Alexandre Joel Chorin, Numerical study of slightly viscous flow, J. Fluid Mech. 57 (1973), no. 4, 785–796. MR 395483, DOI 10.1017/S0022112073002016
  • Stephen Roberts, Accuracy of the random vortex method for a problem with nonsmooth initial conditions, J. Comput. Phys. 58 (1985), no. 1, 29–43. MR 789554, DOI 10.1016/0021-9991(85)90154-8
  • P. R. Spalart, Numerical Simulation of Separated Flows, NASA technical memorandum 84328, 1984.
  • James J. Duderstadt and William R. Martin, Transport theory, A Wiley-Interscience Publication, John Wiley & Sons, New York-Chichester-Brisbane, 1979. MR 551868
  • G. H. Cottet & S. Gallic, "A particle method to solve transport-diffusion equations— Part 1: The linear case," Numer. Math. (To appear.) G. H. Cottet & S. Mas-Gallic, "A particle method to solve transport-diffusion equations —Part II: The Navier-Stokes equation," submitted to Numer. Math. S. Huberson, Modélisation Asymptotique et Numérique de Noyaux Tourbillonaires Enroulés, Thèse d’état, Université Pierre et Marie Curie, 1986.
  • J. Thomas Beale and Andrew Majda, Rates of convergence for viscous splitting of the Navier-Stokes equations, Math. Comp. 37 (1981), no. 156, 243–259. MR 628693, DOI 10.1090/S0025-5718-1981-0628693-0
  • R. A. Gingold & J. J. Monaghan, "Shock simulation by the particle method S.P.H.," J. Comput. Phys., v. 52, 1983, pp. 374-389. S. Mas-Gallic & P. A. Raviart, Particle Approximation of Convection-Diffusion Problems, Pub. Labo. Anal. Num., Univ. Pierre et Marie Curie, 1985.
  • Sylvie Mas-Gallic, Méthode particulaire pour une équation de convection-diffusion, C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), no. 10, 431–434 (French, with English summary). MR 916346
  • J. P. Choquin & B. Lucquin-Desreux, "Accuracy of a deterministic particle method for Navier-Stokes equations," submitted to Internat. J. Numer. Methods Fluids. J. T. Beale, On the Accuracy of Vortex Methods at Large Times, Proceedings of the Workshop on Computational Fluid Dynamics and Reacting Gas Flows, Institute of Applied Mathematics, Minneapolis, MN, 1986. J. P. Choquin & S. Huberson, Application de la Méthode Particulaire aux Écoulements à Grand Nombre de Reynolds, 18è Congrès National d’Analyse Numérique, Puy St Vincent, 1985. B. Lucquin-Desreux, "Approximation particulaire des équations de Navier-Stokes bidimensionnelles," Rech. Aérospat., v. 4, 1987, pp. 1-12.
  • G. Winckelmans and A. Leonard, Improved vortex methods for three-dimensional flows, Mathematical aspects of vortex dynamics (Leesburg, VA, 1988) SIAM, Philadelphia, PA, 1989, pp. 25–35. MR 1001786
  • S. Mas-Gallic and P.-A. Raviart, A particle method for first-order symmetric systems, Numer. Math. 51 (1987), no. 3, 323–352. MR 895090, DOI 10.1007/BF01400118
  • P.-A. Raviart, An analysis of particle methods, Numerical methods in fluid dynamics (Como, 1983) Lecture Notes in Math., vol. 1127, Springer, Berlin, 1985, pp. 243–324. MR 802214, DOI 10.1007/BFb0074532
  • Pierre Degond and Francisco-José Mustieles, A deterministic approximation of diffusion equations using particles, SIAM J. Sci. Statist. Comput. 11 (1990), no. 2, 293–310. MR 1037516, DOI 10.1137/0911018
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 485-507
  • MSC: Primary 65M99
  • DOI:
  • MathSciNet review: 983559