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Grid-Free Simulation of Convection-Diffusion

  • Christian Lécot
  • Abdoul Koudiraty
Conference paper

Abstract

This paper examines a particle numerical method for time-dependent convection-diffusion equations ins-dimensions. The solution is approximated as a linear combination of Dirac measures (particles). Particles are sampled from the initial data. The evolution of the system in a time interval Δt is obtained in three steps. In the first step the particles are transported under the action of the convec­tive field. In the second step, the particles are relabeled according to their positions. In the third step the diffusion is simulated using a quasi-Monte Carlo approximation in the 2s-dimensional unit cube. We prove a convergence theorem in the context of the diffusion equation. Pseudorandom and quasirandom sequences are compared in computational experiments, for some simple model problems whose solutions can be found analytically. The results show that quasirandom points can produce more accurate results than pseudorandom points.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Christian Lécot
    • 1
  • Abdoul Koudiraty
    • 1
  1. 1.Laboratoire de MathématiquesUniversité de Savoie, Campus scientifiqueLe Bourget-du-Lac cedexFrance

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