基于CUDA-GPU架构的超二次曲面离散单元并行算法

大规模离散元的并行计算通常基于理想的球体单元,然而自然界或工业生产中普遍存在的是由非球形颗粒组成的复杂体系,其在不同空间尺度下的动力学行为及力学性质与球形颗粒具有显著差异.基于连续函数包络的超二次曲面单元能有效地构造非球形颗粒的几何形态,并通过非线性Newton迭代算法准确计算单元间的作用力.针对非球形颗粒间接触判断的复杂性及其大规模离散元计算的需求,该文发展了基于CUDA-GPU构架下超二次曲面单元并行算法.该方法在球形颗粒并行计算的基础上,通过核函数建立单元包围盒的粗判断列表及Newton迭代的细判断列表,并优化了并行算法和内存访问模式以提高算法的计算效率.为检验超二次曲面并行算法的可靠性,对非球形颗粒的流动过程进行离散元模拟,并与试验结果进行对比验证.在此基础上,进一步分析了颗粒单元不同长宽比和表面尖锐度对颗粒材料流动特性的影响,为非球形颗粒材料的大规模离散元模拟提供了一种有效的数值方法.

A Parallel Algorithm for Super-Quadric Discrete Elements Based on the CUDA-GPU Architecture

The traditional parallel computing of large-scale discrete elements was suitable for spherical particles. However, in natural fields or industrial applications, the granular systems commonly comprise non-spherical particles. Meanwhile, the dynamic behaviors and mechanical properties of non-spherical particles are strongly different from those of spherical particles at different spatial scales. Super-quadric elements based on the continuous function envelope were used to effectively describe the geometric shapes of irregular particles, and accurately calculate the contact forces between elements with the non-linear Newtonian method. In view of the complexity of the contact detection between non-spherical particles and the large-scale computational requirements of the discrete element method, a CUDA-GPU parallel algorithm was developed for super-quadric elements. Based on the parallel calculation of spherical particles, the rough contact list of the element envelope and the accurate contact list of the Newtonian method were established with the kernel function. Meanwhile, the parallel algorithm and the memory access mode were optimized to improve the computation efficiency. To examine the reliability of the parallel algorithm, the flow process of non-spherical particles was simulated with the discrete element method and compared with the experimental results. Furthermore, the influences of the aspect ratio and the sharpness parameter of elements on the flow characteristics of non-spherical particles were analyzed. This study provides an effective numerical method for large-scale simulation of non-spherical granular materials.