APPLICATION EXAMPLES

Lattice Boltzmann Method and coupling with Discrete Element Method

1. Introduction

The Lattice Boltzmann Method is a method using the distribution function of virtual particles to find the solution instead of solving the Navier-Stokes equations. By coupling the two-dimensional Lattice Boltzmann Method with the Discrete Element Method using the Immersed Boundary Scheme, for example, a simulation of fine sand particles movement with flowing fluid inside a geo-material becomes possible. Here, a two-dimensional nine speed model (2D9Q) is used (Figure 1).

Figure1 Two-dimensional nine speed model.

2. Fluid dynamics

A result of cavity flow is shown to verify the scheme. It was found that the accuracy depends on parameters and the relaxation factor, as well as boundary conditions used in calculation. The calculated result is in good agreement with a numerical result from Ghia et al.,1982.

Figure2 Calculated result (left: velocity contour, right: Ghia et al., 1982).

3. Coupling with the Discrete Element Method.

As an example of the two-dimensional Lattice Boltzmann Method using the coupling scheme with the Discrete Element Method, a simulation of fine-grained sand particles movement with flowing fluid inside a geo-material was conducted. The fine-grained sand (yellow color) were added from the left side in keeping a same porosity and changing the condition of each geo-material’s structure, i.e., layout of fixed particle (gray color). The Figure 3 and 4 show results of pressure and velocity contour of fluid in two-typed fixed particle layout, respectively as well as movement of fine-grained sand particles inside geo-material. The scheme enables one to find out the difference of permeability in the case of different layout of particles even when having the same porosity.

Figure 3 Pressure (left) and velocity (right) contour, (fixed particle layout: pattern-0, 30% concentration of fine-grained sand particles).

Figure4 Pressure (left) and velocity (right) contour, (fixed particle layout: pattern-1, 30% concentration of fine-grained sand particles).

References

1) Karasawa, S., Application of Two-dimensinal Lattice Boltzmann Method and coupling schme with Discrete Element Method, Master degree thesis, Tokai University (2013).
2) Ghia, U., Ghia, K.N. and Shin, C.T., High-Re solutions for incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method?Journal of computational physics, 48, 387-411 (1982)?