Global random walk algorithm for diffusion processes
AbstractThe Global Random Walk algorithm (GRW) performs the simultaneous tracking on a fixed grid of large collections of particles, while…
global random walk
Numerical modelling of the one-dimensional diffusion by random walkers
AbstractIn this paper we describe a numerical method of cellular automaton type to study the diffusion processes. The macroscopic diffusive…
Evaluation of overshooting errors in particle methods for diffusion by biased global random walk
AbstractThe adjustment of grid steps which guarantees that particles methods yield no numerical diffusion inevitably induces overshooting errors in the…
Generalized random walk algorithm for the numerical modeling of complex diffusion processes
AbstractA generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a…
Numerical Modeling of Large Scale Transport of Contaminant Solutes Using the Global Random Walk Algorithm
AbstractThe methods which track particles to simulate concentrations are successfully used in problems for large scale transport in groundwater, mainly…
Numerical investigations on ergodicity of solute transport in heterogeneous aquifers
AbstractDarcy velocities for lognormal hydraulic conductivity with small variance and finite correlation length were approximated by periodic random fields. Accurate…
Accuracy of numerical simulations of contaminant transport in heterogeneous aquifers: A comparative study
AbstractThis work deals with a comparison of different numerical schemes for the simulation of contaminant transport in heterogeneous porous media.…
Consistency issues in PDF methods
AbstractConcentrations of chemical species transported in random environments need to be statistically characterized by probability density functions (PDF). Solutions to evolution equations…
A Fokker-Planck approach for probability distributions of species concentrations transported in heterogeneous media
AbstractWe identify sufficient conditions under which evolution equations for probability density functions (PDF) of random concentrations are equivalent to Fokker–Planck…
Towards a filtered density function approach for reactive transport in groundwater
AbstractEvolution equations for probability density functions (PDFs) and filtered density functions (FDFs) of random species concentrations weighted by conserved scalars…