Gravity in a lattice Boltzmann model

Abstract

In this paper we consider the introduction of a body force, in the incompressible limit, into the lattice Boltzmann model. A number of methods are considered and their suitability to our objectives determined. When there is no density variation across the fluid, gravity can be introduced in the form of an altered pressure gradient. This method correctly satisfies the Navier-Stokes equation; however, if there is a non-negligible density variation present (produced by the body force or otherwise) this method becomes less accurate as the density variation increases and the constant density approximation becomes less valid. Three other methods are also considered for application when there is a non-negligible density variation. The equations of motion satisfied by these models are found up to second order in the Knudsen number and it is seen that only one of these methods satisfies the true Navier-Stokes equation. Numerical simulations are performed to compare the different models and to assess the range of application of each.

Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media

“…However, general velocity and pressure boundaries are still under development for the lattice-Boltzmann method [32,33,34]. So far in most of the practical simulations a body force has been implemented [23,27,35] instead of pressure or velocity boundaries.…”

Boundary conditions for free interfaces with the lattice Boltzmann method

“…The shift in the fluid momentum by F/2 is necessary if external forces such as gravitation are included in simulations (cf. Buick and Greated, 2000;Ginzburg et al, 2008). For the latter, one can either make use of additional force terms F q as in Buick and Greated (2000); Guo et al (2002) and set u eq = U, or equivalently work without the source term F q and use u eq = U − F/λ − instead.…”

“…Buick and Greated, 2000;Ginzburg et al, 2008). For the latter, one can either make use of additional force terms F q as in Buick and Greated (2000); Guo et al (2002) and set u eq = U, or equivalently work without the source term F q and use u eq = U − F/λ − instead. The latter simplifies the analysis (Ginzburg et al, 2008) and is adopted in the following.…”

Numerical investigation of pool nucleate boiling in nanofluid with lattice Boltzmann method

“…In the case that forces and potentials act on the particles, there are some methods to incorporate the force term in the LBM model (Shan and Chen, 1993;Guo et al, 2002;Buick and Greated, 2000). Kupershtokh (2004) showed that the Exact Difference Method (EDM) has better accuracy compared with other methods.…”