Numerical methods for multiphase flows
Abstract
Multiphase flows are ubiquitous in both nature and engineering. Over the past two to three decades, substantial progress has been made in developing numerical methods for simulating these complex flows. Yet, significant challenges persist in accurately capturing intricate interfacial dynamics and the multi-scale interactions inherent to multiphase systems. This review focuses on several key numerical approaches that have proven particularly relevant from both practical and theoretical perspectives. In particular, we discuss Volume-Of-Fluid techniques, level set methods, diffuse interface models, and front tracking methods, along with immersed boundary strategies designed for particle-laden flows. We also examine multi-fluid Eulerian frameworks, population balance models for reactive processes, and sub-grid scale techniques for handling unresolved dynamics. Furthermore, emerging hybrid strategies that integrate conventional numerical methods with data-driven machine learning techniques are highlighted as promising directions. In conclusion, while current methodologies offer valuable insights into multiphase flow behavior, continued interdisciplinary efforts are essential to enhance predictive accuracy, computational efficiency, and the overall applicability of these simulations to real-world challenges.
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BibTeX
@article{garciavillalba2026numerical,
title = {{Numerical methods for multiphase flows}},
author = {Manuel García-Villalba and Tim Colonius and Olivier Desjardins and Dirk Lucas and Ali Mani and Daniele Marchisio and Omar K. Matar and Francesco Picano and Stéphane Zaleski},
journal = {International Journal of Multiphase Flow},
year = {2026},
month = oct,
doi = {10.1016/j.ijmultiphaseflow.2025.105285},
url = {https://hal.science/hal-05781404v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Numerical methods for multiphase flows
AU - Manuel García-Villalba
AU - Tim Colonius
AU - Olivier Desjardins
AU - Dirk Lucas
AU - Ali Mani
AU - Daniele Marchisio
AU - Omar K. Matar
AU - Francesco Picano
AU - Stéphane Zaleski
PY - 2026
DA - 2026/10/06
JO - International Journal of Multiphase Flow
DO - 10.1016/j.ijmultiphaseflow.2025.105285
UR - https://hal.science/hal-05781404v1
AB - Multiphase flows are ubiquitous in both nature and engineering. Over the past two to three decades, substantial progress has been made in developing numerical methods for simulating these complex flows. Yet, significant challenges persist in accurately capturing intricate interfacial dynamics and the multi-scale interactions inherent to multiphase systems. This review focuses on several key numerical approaches that have proven particularly relevant from both practical and theoretical perspectives. In particular, we discuss Volume-Of-Fluid techniques, level set methods, diffuse interface models, and front tracking methods, along with immersed boundary strategies designed for particle-laden flows. We also examine multi-fluid Eulerian frameworks, population balance models for reactive processes, and sub-grid scale techniques for handling unresolved dynamics. Furthermore, emerging hybrid strategies that integrate conventional numerical methods with data-driven machine learning techniques are highlighted as promising directions. In conclusion, while current methodologies offer valuable insights into multiphase flow behavior, continued interdisciplinary efforts are essential to enhance predictive accuracy, computational efficiency, and the overall applicability of these simulations to real-world challenges.
SN - 0301-9322
ER -