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• W1995623318 abstract "The simulation of diffusion of a continuum field by the random walk displacement of a set of particles is investigated in detail. Computational particles are used to transport elements of the gradients of the diffusive concentration. One-dimensional and quasi-one-dimensional cases are treated for a generalized diffusion variable. Different types of boundary conditions of the diffusion equation are considered, as well as the extensions to a system of coupled diffusion equations, the reaction-diffusion equations and the convection-diffusion set of equations. It is shown that by using concentration gradients in the random walk process, statistical errors are reduced and each realization of the numerical solution is a representation of the exact solution. Moreover, transport of higher-order derivatives can be utilized to improve the smoothness. The algorithm is grid-free, and the computational elements move to follow the gradients, thus it is self-adaptive and uniform resolution is attained for all times. The method is particularly suitable for the simulation of diffusion in systems which involve more than one transport mechanism, when the diffusivity is small and when Lagrangian elements are used to model the other mechanisms." @default.
• W1995623318 created "2016-06-24" @default.
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• W1995623318 date "1985-10-01" @default.
• W1995623318 modified "2023-10-11" @default.
• W1995623318 title "Grid-free simulation of diffusion using random walk methods" @default.
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• W1995623318 doi "https://doi.org/10.1016/0021-9991(85)90058-0" @default.
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