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A reduced-dimensional explicit discrete element solver for simulating granular mixing problems

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Abstract

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.

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Acknowledgements

Financial support for the first author is provided by the China Scholarship Council (CSC) under Grant Number 201606260177. The first and third author are supported by the Fundamental Research Funds for the Central Universities, the National Water Pollution Control and Treatment Science and Technology Major Project (2017ZX07201001), and the National Basic Research Program of China (973 Program: 2011CB013800). XRZ would like to thank Dr. Kun Wang for his help during his stay at Columbia University. WCS’s research is supported by the Dynamic Materials and Interactions Program from the Air Force Office of Scientific Research under Grant Contract FA9550-17-1-0169, the Earth Materials and Processes program from the US Army Research Office under Grant Contract W911NF-18-2-0306, and the NSF CAREER Grant CMMI-1846875. These supports are gratefully acknowledged. The views and conclusions contained in this document are those of the authors, and should not be interpreted as representing the official policies, either expressed or implied, of the sponsors, including the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for government purposes notwithstanding any copyright notation herein.

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Authors and Affiliations

  1. Chengdu Guimu Robot Co., Ltd, Chengdu, China

    Xinran Zhong

  2. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China

    Xinran Zhong & Ying Dai

  3. Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, USA

    Xinran Zhong & WaiChing Sun

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  1. Xinran Zhong
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Zhong, X., Sun, W. & Dai, Y. A reduced-dimensional explicit discrete element solver for simulating granular mixing problems. Granular Matter 23, 13 (2021). https://doi.org/10.1007/s10035-020-01077-z

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