objective of this paper is to demonstrate the formulation of a numerical mo
del for mass transport based on the Bhatnagar-Gross-Krook (BGK) Boltzmann e
quation. To this end, the classical chemical transport equation is derived
as the zeroth moment of the BGK Boltzmann differential equation. The relati
onship between the mass transport equation and the BGK Boltzmann equation a
llows an alternative approach to numerical modeling of mass transport, wher
ein mass fluxes are formulated indirectly from the zeroth moment of a diffe
rence model for the BGK Boltzmann equation rather than directly from the tr
ansport equation. In particular, a second-order numerical solution for the
transport equation based on the discrete BGK Boltzmann equation is develope
d. The numerical discretization of the first-order BGK Boltzmann differenti
al equation is straightforward and leads to diffusion effects being account
ed for algebraically rather than through a second-order Fickian term. The r
esultant model satisfies the entropy condition, thus preventing the emergen
ce of non-physically realizable solutions including oscillations in the vic
inity of the front. Integration of the BGK Boltzmann difference equation in
to the particle velocity space provides the mass fluxes from the control vo
lume and thus the difference equation for mass concentration. The differenc
e model is a local approximation and thus may be easily included in a paral
lel model or in accounting for complex geometry. Numerical tests for a rang
e of advection-diffusion transport problems, including one- and two-dimensi
onal pure advection transport and advection-diffusion transport show the ac
curacy of the proposed model in comparison to analytical solutions and solu
tions obtained by other schemes. (C) 2001 Published by Elsevier Science Ltd
.