The numerical treatment of fluid-particle systems is a very challenging problem because of the complex coupling phenomena occurring between the two phases. Although accurate mathematical modelling is available to address this kind of application, the computational cost of the numerical simulations is very expensive. The use of the most modern high-performance computing infrastructures could help to mitigate such an issue but not completely fix it. In this work, we develop a non-intrusive data-driven reduced order model (ROM) for Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations. The ROM is built using the proper orthogonal decomposition (POD) for the computation of the reduced basis space and the Long Short-Term Memory (LSTM) network for the computation of the reduced coefficients. We are interested in dealing both with system identification and prediction. The most relevant novelties rely on (i) a filtering procedure of the full-order snapshots to reduce the dimensionality of the reduced problem and (ii) a preliminary treatment of the particle phase. The accuracy of our ROM approach is assessed against the classic Goldschmidt fluidized bed benchmark problem. Finally, we also provide some insights about the efficiency of our ROM approach.

翻译：对流体-颗粒系统进行数值处理是一个极具挑战性的问题，原因在于两相之间复杂的耦合现象。尽管已有精确的数学模型可用于处理此类应用，但数值模拟的计算成本非常高昂。使用最现代的高性能计算基础设施虽有助于缓解这一问题，却无法彻底解决。本研究开发了一种用于计算流体动力学（CFD）-离散元法（DEM）模拟的非侵入式数据驱动降阶模型（ROM）。该ROM采用本征正交分解（POD）计算降阶基空间，并利用长短期记忆（LSTM）网络计算降阶系数。我们重点关注系统辨识与预测两方面问题。最主要的创新点包括：（i）对全阶快照进行滤波处理以降低降阶问题的维度，（ii）对颗粒相进行预处理。我们通过经典的金施密特流化床基准问题评估了ROM方法的准确性，并进一步提供了关于该方法效率的见解。