Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10357849 | Journal of Computational Physics | 2005 | 13 Pages |
Abstract
Monte Carlo (MC) simulation of diffusion processes has proved to be a powerful and valuable adjunct to deterministic solutions of the diffusion equation. In its simplest one-dimensional implementation, a particle is stepped to left or right, with equal probability, a distance 2DÎt where D is the diffusion coefficient and Ît is the timestep. This gives accurate results if D is constant, but in the case where D is spatially dependent a systematic error occurs, as shown by comparing MC averages with deterministic solutions. Furthermore, this error does not reduce when the timestep Ît is reduced. We show that the results can be reconciled by altering both the MC stepsize and stepping probability, and give simple formulas for the correction terms that are also applicable in higher dimensions. This supplements our previous work on corrections to the Gaussian-step MC method [J. Comput. Phys. 198 (2004) 65].
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
L. Farnell, W.G. Gibson,