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Volume 107
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Simulation and analysis of bulk particle water entry dynamics using MP-PIC-VOF: A new volume-conservative model
Utkan Çalışkan, Sanja Miskovic *
Norman B. Keevil Institute of Mining Engineering, University of British Columbia, 2329 West Mall, Vancouver, BC, V6T 1Z4, Canada
10.1016/j.partic.2025.10.004
Volume 107, December 2025, Pages 113-133
Received 4 October 2024, Revised 25 September 2025, Accepted 2 October 2025, Available online 16 October 2025, Version of Record 24 October 2025.
E-mail: sanja.miskovic@ubc.ca
Highlights

• New MP-PIC-VOF model is developed for simulation of dense solid-liquid-gas flows.

• Trilinear interpolation technique is implemented to work with unstructured meshes.

• Integration of hydrostatic pressure adaptation in the momentum equation.

• The volume-conservative alpha transport equation ensures mass conservation.

• The model is validated against experimental and CFD-DEM-VOF results.


Abstract

This paper introduces the advanced MP-PIC-VOF model tailored for dense particle-laden flows with free surface, which has been developed and extensively tested across a set of validation cases found in literature and original bulk particle water entry case. A distinctive feature of the MP-PIC method is its demonstrated ability to accurately capture the behavior of closely packed particles in a fluid, even in the absence of direct pairwise particle-particle interactions. At a closed packed limit, the MP-PIC method achieves the accurate representation of the state through the resolved mean particle velocity field and implementation of the velocity limiter in the inter-particle stress force. The new model integrates a trilinear interpolation technique, specifically adapted for unstructured hexahedral meshes, and a weighted least squares method for efficient gradient computation that operates at a sub-cell level, enabling more accurate calculation of inter-particle stress gradients. Other key contributions include the integration of hydrostatic pressure adaptation in the momentum equation and a volume-conservative alpha transport equation that ensures mass conservation during the transfer of the solid phase between distinct fluid phases. The coupling framework includes a range of coupled fluid-particle forces important for particles immersed in liquid, including a dense virtual mass force. The model's validation against experimental data and CFD-DEM-VOF results focuses on key flow parameters, specifically particle velocity, dispersion profile, and cavity evolution during bulk particle water entry. The model is shown to accurately simulate complex solid-liquid-gas interactions, demonstrating its potential for optimizing a wide range of complex industrial processes such as liquid fluidized beds, solid-liquid stirred tanks, and clarifiers.

Graphical abstract
Keywords
MP-PIC-VOF; CFD-DEM-VOF; Particle-laden flow; Free-surface; Water entry; Volume conservation; Solid-liquid impact
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