Stochastic Particle Method for Nonlinear Hyperbolic Problems

In this paper, we present a new method based on stochastic particles, which allows us to compute solutions of a system of nonlinear transport equations arising in the modeling of immiscible displacement in porous pedia. In this approach, we use different particles for different phases and move them according to the stochastic rules for which the probability density function depends on the spatial distribution of the particles. Our motivation for such a method is a Lagrangian modeling framework in which one can describe certain physical phenomena more naturally than in an Eulerian framework. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)