We present a reduced-dimensional proper orthogonal decomposition (POD) solver to accelerate discrete element method (DEM) simulations of the granular mixing problem. We employ the method of snapshots to create a low-dimensional solution space from previous DEM simulations. By reducing the dimensionality of the problem, we accelerate the calculations of the incremental solution with fewer degrees of freedom (DOF), while enabling a larger stable time step due to the filtering of low-energy mode. We analyze two feasible strategies to generate the reduced-dimensional basis, one generating by finding the orthogonal basis from the global snapshots captured at the same location in the parametric domains; another one employing the known POD bases from the closest known cases. Our results show that, when POD bases are generated via the local strategy, the reduced-order model is a more efficient alternative to the full-scale simulations for extrapolating behaviors in the parametric domain. Numerical examples of granular mixing problems are presented to demonstrate the efficiency and accuracy of the proposed approach.

我们提出了一种降维固有正交分解（POD）求解器，以加快颗粒混合问题的离散元方法（DEM）模拟。我们采用快照方法从以前的DEM仿真创建低维解决方案空间。通过减小问题的维数，我们以较少的自由度（DOF）加速了增量解的计算，同时由于低能量模式的过滤而使较大的稳定时间步长成为可能。我们分析了两种可行的策略来生成降维基础，一种是通过从在参数域中相同位置捕获的全局快照中找到正交基础来生成的。另一种采用最接近的已知案例中的已知POD库。我们的结果表明，通过本地策略生成POD基地时，降阶模型是用于在参数域中外推行为的全面模拟的更有效替代方法。给出了颗粒混合问题的数值例子，以证明所提方法的效率和准确性。