Abstract:
The role of the boundary condition is critical to a simulation. A simulation with its boundary improperly applied will result in significantly different results. Conventionally, a rigid or membrane-based boundary is applied for the discrete element method (DEM) simulation. This paper describes a 2D fast and flexible boundary detection algorithm for DEM simulation. This algorithm is localized so the speed is fast. Once the first element on boundary is searched and found globally, all the other elements on the boundary are searched locally. This algorithm is flexible, suitable for closed boundary (where the beginning element and the ending element share the same element, such as the inner boundary of a tunnel), or open boundary (where the beginning element and the ending element are not the same element) provided that the criteria for the beginning element and ending element are given. It is also powerful because it has the capability of handling any boundary shape, whether it is a regular circular or rectangular boundary or an irregular shape boundary.
With this algorithm, the boundary elements could be easily identified and updated periodically. Because of the fast performance of this algorithm, the boundary actually could be updated in each iteration. Once the boundary elements are identified, the forces applied on the boundary in a DEM simulation can realistically act on each real boundary element, rather than a rigid “wall” boundary or membrane-based boundary.
Numerical experiments further demonstrate the power of this algorithm. Even in a transient simulation where the boundary shape is changing dynamically in various irregular shapes, the boundary could still be captured easily to apply the realistic boundary forces. The algorithm discussed in this paper is for 2D simulation; however, it is expandable to 3D, which will be reported later.
Introduction
The role of the boundary condition is critical to a simulation. A simulation with its boundary improperly applied will result in significantly different results. Conventionally, a rigid or membrane-based boundary is applied for the discrete element method (DEM) simulation (Wang and Tonon, 2008; Tannant and Wang, 2007). A rigid boundary is valid and proper in a simulation if the actual boundary is a rigid boundary where the relative locations of the elements on the boundary and the shape of the boundary do not change during the simulation, so as to simulate a uniaxial compression testing experiment in two parallel plates where these two plates are the boundary, as illustrated in Fig. 1 (Tannant and Wang, 2007). A membrane-based boundary (Wang and Tonon, 2008) is applied when a solid-liquid hydraulic boundary is met in the simulation where the boundary does not have a big change and the shape of the boundary is not complex.
