Numerical method for interaction between multiparticle and complex structures

We propose a numerical method for dealing with interactions between multiple particles and complex structures. In the method, the structures are represented on a grid by using the level set method. The interactions of particles and structures are calculated by a method based on the discrete element method. The method can treat the interaction between multiparticle and complex structures robustly.

Figure 1

Schematic figure of the discrete element method. $K$, $\eta$, and $\mu$ refer to the linear spring, the dashpot, and the slider, respectively.

Figure 2

Schematic figure of a level set function in the one-dimensional case.

Figure 3

(Color online) An example of a level set function in the two-dimensional case. (a) shows the shape of structures. (b) shows the contour lines of the level set function for the structure. The thick and thin lines represent the zero level set and the contour lines of the level set function. A $70\times 70$ Cartesian grid is used.

Figure 4

Configuration to compare computation times.

Figure 5

Schematic figure of a test problem.

Figure 6

Time evolution of the height of the particle from the slope. The solid line and the dotted line represent the numerical result and exact solution, respectively. Five cycles are plotted. $k_n=5\times {10}^7$ is used.

Figure 7

Trajectory of the particle in the case of resolution study II. The configuration is the same as in Fig. 5 except for the gravity direction. The gravity direction is just straight down.

Figure 8

(Color online) Snapshots of interaction between five particles and the structures at $t=0$, 1, 2, 3 s. The movie is available from [15].

Figure 9

(Color online) Snapshots of interaction between 65 particles and the structures at $t=0$, 1, 2, 3 s. The movie is available from [15].