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Fully Lagrangian and lattice Boltzmann methods for the advection-diffusion equation. (English) Zbl 0971.76073
Summary: In the last decade or so, the lattice Boltzmann method (LBM) has achieved great success in computational fluid dynamics. The fully Lagrangian method (FLM) is the generalization of LBM for conservation systems. LBM can also be developed from FLM. In this paper we develop a FL model and a LB model for \(D\)-dimensional advection-diffusion equation. The LB model can be viewed as an improved version of the FL model. We present results of simulation of one-dimensional advection-diffusion equation, which are found to be in good agreement with the analytic solution.

76M28 Particle methods and lattice-gas methods
76R99 Diffusion and convection
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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