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Volume 116
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A source-term-based unresolved LBM–DEM method for fluid–particle flow simulations
Chao Xu a 1, Xiang Li a 1, JiaBao Zhang a, Du Zhou b, Zihan Liu a, Jian Yang a, Lianyong Zhou c, Yongzhi Zhao a *
a College of Energy Engineering, Zhejiang University, Hangzhou, 310027, China
b China Nuclear Power Operations Co., Ltd, Shenzhen, 518000, China
c College of Smart Energy, Shanghai Jiao Tong University, Shanghai, 200240, China
10.1016/j.partic.2026.06.010
Volume 116, September 2026, Pages 17-33
Received 1 April 2026, Revised 18 May 2026, Accepted 8 June 2026, Available online 15 June 2026, Version of Record 20 June 2026.
E-mail: yzzhao@zju.edu.cn
Highlights

• Proposes a novel unresolved LBM-DEM method that strictly recovers the volume-averaged Navier-Stokes equations.

• The proposed method eliminates spurious velocities inherently and achieves fully explicit computation.

• Robustly simulates highly dynamic fluid-particle flows with temporally and spatially varying solid volume fractions.

• The method is validated by the results of benchmark cases and the fluidized bed experiments.


Abstract

This study presents a new source-term-based unresolved LBM–DEM coupling method for fluid–particle flow simulations. The method extends the lattice Boltzmann equation by introducing mass and momentum source terms to recover the volume-averaged governing equations required in unresolved formulations, while preserving the standard equilibrium distribution function and explicit macroscopic update procedure. This treatment avoids spurious velocities and does not introduce additional implicit coupling during the fluid update. To improve numerical robustness, the method is implemented with a multiple-relaxation-time collision model and a WALE-based large-eddy simulation model. The proposed framework is assessed using several benchmark problems, including a variable-porosity no-spurious-velocity test, Couette flow in porous media, and fixed-bed flow. Good agreement is obtained with the corresponding benchmark or analytical results. The method is further applied to a quasi-two-dimensional fluidized-bed case, where the predicted transient particle behavior, bed height, pressure drop, and dominant fluctuation frequency are in reasonable agreement with experimental observations. In addition, a benchmark-specific performance study is conducted against an unresolved CFD–DEM baseline for the same fluidized-bed problem. The results show that the present unresolved LBM–DEM implementation requires less wall-clock time to advance the tested case under the reported hardware and time-step settings. These results indicate that the proposed method provides a theoretically consistent, numerically robust, and computationally promising framework for unresolved fluid–particle flow simulations.

Graphical abstract
Keywords
Lattice Boltzmann method; Discrete element method; LBM-DEM coupling method; Unresolved fluid-particle flow; Multiphase flows
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