Particle approximation of convection–diffusion equations

Christian Lécot and Wolfgang Ch. Schmid

Mathematics and Computers in Simulation (MATCOM), 2001, vol. 55, issue 1, 123-130

Abstract: We present a particle method for solving initial-value problems for convection–diffusion equations with constant diffusion coefficients. We sample N particles at locations xj(0) from the initial data. We discretize time into intervals of length Δt. We represent the solution at time tn=nΔt by N particles at locations xj(n). In each time interval the evolution of the system 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 position. In the third step the diffusive process is modeled by a random walk. We study the convergence of the scheme when quasi-random numbers are used. We compare several constructions of quasi-random point sets based on the theory of (t,s)-sequences. We show that an improvement in both magnitude of error and convergence rate can be achieved when quasi-random numbers are used in place of pseudo-random numbers.

Keywords: Random walk; Convection–diffusion equations; Discrepancy (search for similar items in EconPapers)
Date: 2001
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475400002524
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:55:y:2001:i:1:p:123-130

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().