Fluctuating lattice Boltzmann 论文

摘要

Abstract. – The lattice Boltzmann algorithm efficiently simulates the Navier Stokes equation of isothermal fluid flow, but ignores thermal fluctuations of the fluid, important in mesoscopic flows. We show how to adapt the algorithm to include noise, satisfying a fluctuation-dissipation theorem (FDT) directly at lattice level: this gives correct fluctuations for mass and momentum densities, and for stresses, at all wavevectors k. Unlike previous work, which recovers FDT only as k → 0, our algorithm offers full statistical mechanical consistency in mesoscale simulations of, e.g., fluctuating colloidal hydrodynamics. The lattice Boltzmann equation (LBE) is a widely used lattice formulation of fluid mechanics [1]. It offers a faithful discretization of the Navier Stokes equation of isothermal, incompressible fluid flow, and is very well adapted to parallel computation [2]. While used for large-scale fluid dynamics simulations such as flows around aircraft [3], the LBE approach is particularly adapted to simulating mesoscopic problems [4]. These include, e.g., porous medium flows and flows of complex and multicomponent fluids with microstructure [5–8]. The latter can be modelled using various extensions of the basic algorithm for a single component fluid as considered here [8–10].