基于扩展多面体单元的DEM-SPH耦合算法及应用

Dilated polyhedron-based DEM-SPH coupling algorithm and a pplications

对于颗粒材料与流体介质的动力作用可分别通过离散元方法(Discrete Element Method, DEM)和光滑粒子流体动力学方法(Smoothed Particle Hydrodynamics, SPH)模拟颗粒和流体,并采用DEM-SPH算法计算两种介质间的耦合作用。当颗粒材料采用多面体单元进行模拟时,颗粒单元与流体之间会形成几何形状复杂的流固耦合界面,不宜采用计算效率较低的传统边界粒子方法。为此,该文基于Minkowski Sum方法构造扩展多面体单元,并通过Hertz接触模型计算单元间的接触力,进而建立基于扩展多面体单元的DEM方法;流体介质采用弱可压缩格式的SPH方法。将几何复杂的流固界面耦合作用近似为排斥力模型,从而只对SPH粒子与固体界面进行几何判断即可确定两者的相互作用力。该方法避免了对大量边界粒子进行的相关计算,具有计算简便且适用于复杂固体边界的优点。该文进一步采用基于GPU的并行算法从而实现DEM和SPH的高性能计算以提高DEM-SPH耦合的计算效率。采用以上方法对方柱绕流和溃坝冲击块体过程进行了数值计算,并与相关试验数值和计算结果进行了对比验证,一致性很好,进而说明了该文建立的DEM-SPH耦合方法对颗粒材料与流体介质相互作用数值模拟的合理性和准确性。

In the study of coupling problems between granular materials and fluid dynamics, the discrete element method(DEM) and the smoothed particle hydrodynamics(SPH) can be adopted to simulate the granular materials and fluid, respectively,and the coupled DEM-SPH algorithm can be established to calculate their interaction. When the discrete elements are constructed with polyhedron blocks, the complex geometric boundary shape between fluid and polyhedron shaped granular media is inefficient to use the traditional particle boundary. In this study, the dilated polyhedron-based elements are constructed with the Minkowski sum theory, while the Hertzian contact force model is employed to determine the impact load between the polyhedron elements.Meanwhile, the weakly compressible SPH is adopted to simulate the hydrodynamics. The repulsive force model is employed for the complex geometric boundary shape between fluid and solid, which only demands the geometric detection in the calculation of the repulsive force. This approach avoids the huge amount of boundary particles in the boundary formation, and thus it is efficient for the complex boundary shape. Accordingly, the DEM-SPH coupling method is developed to simulate the interaction between granular materials and fluid. Furthermore, the GPU-based parallel algorithm is utilized to improve the computational efficiency.The dam break flow against a rectangular cylinder and the dynamic process of discrete blocks in dam breaking flow are simulated with the present DEM-SPH coupling model. The simulated results are compared well with the physical experiment and numerical simulation from the published literatures. The results show that the DEM-SPH method proposed in this study is an effective approach to simulate the coupling process of granular materials and fluid flow.