zbMATH — the first resource for mathematics

Go-with-the-flow lattice Boltzmann methods for tracer dynamics. (English) Zbl 1037.76046
Nielaba, P. (ed.) et al., Bridging time scales: Molecular simulations for the next decade. Berlin: Springer (ISBN 3-540-44317-7/hbk). Lect. Notes Phys. 605, 267-285 (2002).
Summary: Because of its underlying basis in kinetic theory, we discuss the advantages of using the lattice-Boltzmann equation (LPE) as a component in multi-scale simulations. As an example of upward coupling, we examine how the simple problem of the dynamics of tracers can be studied within the LBF framework. We describe how, by utilizing the kinetic view of the model, very efficient techniques can be developed to study this problem. For the specific example of hydrodynamic dispersion (the extra spreading of the tracer due to fluid flow), we apply the methods to a problem where there is an analytic value to compare with, namely to flow in a tube, and to a more complex system, namely a close packed cubic array of spheres. For the former we show that the method accurately reproduces known results, even with a crude representation of the tube. For the latter we show that the dispersion coefficient asymptotes on a time-scale determined by molecular difflision. This behaviour is not what is expected for a random medium. Our results thus illustrate that a periodic system is too crude approximation, as far as dispersion in random media is concerned. Nonetheless, our values for the dispersion coefficient agree nicely with experimental results on periodic systems.
For the entire collection see [Zbl 1029.00018].

76M28 Particle methods and lattice-gas methods
76S05 Flows in porous media; filtration; seepage
76T99 Multiphase and multicomponent flows
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)