In this paper, we present the surface of revolution discrete element method (SR-DEM) to simulate systems of particles with closed surfaces of revolution. Due to the cylindrical symmetry of a surface of revolution, the geometry of any cross-section about the axis of rotation remains the same. Taking advantage of this geometric feature, a node-to-cross-section contact algorithm is proposed for efficient contact detection between particles with a surface of revolution. In our SR-DEM framework, the contact algorithm is realized in a master-slave fashion: the master particle is approximated by its surface nodes, while the slave particle is represented by a signed distance field (SDF) of the cross-section about the axis of rotation. This hybrid formulation in both 2D and 3D space allows a very efficient contact calculation yet relatively simple code implementation. We then apply SR-DEM to simulate particle-particle, particle-wall impact, granular packing in a cylindrical container, and tablets in a rotating drum, to demonstrate SR-DEM's ability to predict the post-impact velocities, packing porosity, and dynamic angle of repose, respectively. Finally, we suggest a simple approach to find an optimal surface resolution, by increasing the number of surface nodes until some of the bulk properties that could characterize the system converge.

翻译：本文提出了回转曲面离散单元法（SR-DEM），用于模拟具有封闭回转曲面的粒子系统。由于回转曲面具有柱面对称性，其绕旋转轴任意截面的几何形状保持不变。利用这一几何特征，我们提出了一种节点-截面接触算法，以实现回转曲面粒子间的高效接触检测。在SR-DEM框架中，接触算法采用主从模式实现：主粒子通过其表面节点进行近似，而从粒子则由绕旋转轴截面的符号距离场（SDF）表示。这种二维与三维空间的混合公式既可实现高效的接触计算，又能保证相对简单的代码实现。随后，我们将SR-DEM应用于粒子-粒子碰撞、粒子-壁面冲击、柱形容器内的颗粒堆积以及转鼓中的片剂运动等场景，分别验证了SR-DEM在预测碰撞后速度、堆积孔隙率以及动态休止角方面的能力。最后，我们提出了一种确定最优表面分辨率的简单方法：通过增加表面节点数量，直到某些能够表征系统的宏观特性趋于收敛。