Lattice Boltzmann method and channel flow

Abstract

Lattice Boltzmann methods are presented at an introductory level with a focus on fairly simple simulations that can be used to test and illustrate the model’s capabilities. Two scenarios are presented. The first is a simple laminar flow in a straight channel driven by a pressure gradient (Poiseuille flow). The second is a more complex, including a wedge where Moffatt vortices may be induced if the wedge is deep enough. Simulations of the Poiseuille flow scenario accurately capture the theoretical velocity profile. The experiment shows the location of the fluid-wall boundary and the effects viscosity has on the velocity and convergence time. The numerical capabilities of the lattice Boltzmann model are tested further by simulating the more complex Moffatt vortex scenario. The method reproduces with high accuracy the theoretical predction that Moffat vortices will not form in a wedge if the vertex angle exceeds 146°. Practical issues limitations of the lattice Boltzmann method are discussed. In particular the accuracy of the bounce-back boundary condition is first order dependent on the grid resolution.

Simulation of fluid dynamics through complicated networks of channels with cellular automata

“…There are different options or tools available when modeling fluid dynamics: solving the analytic equations, or, if that is not possible, considering a numeric solution (finite difference, finite volume, or finite element methods) [1]. In general these methods work with noncomplex borders.…”

“…With complex structures, fluid dynamics numeric simulation takes a heavy burden on computation time to find solutions to solve Navier-Stokes equations. Another option is to solve multiple border problems in statistical terms or with lattice Boltzmann models to simplify the dynamics at a macroscopic level [1][2][3]. Another approach is to handle a mixture of particles and a continuous medium [4][5][6].…”