A Boltzmann-based mesoscopic model for contaminant transport in flow systems

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 .