Published October 2025 | Published
Journal Article Open

Numerical methods for multiphase flows

  • 1. ROR icon TU Wien
  • 2. ROR icon California Institute of Technology
  • 3. ROR icon Cornell University
  • 4. ROR icon Helmholtz-Zentrum Dresden-Rossendorf
  • 5. ROR icon Stanford University
  • 6. ROR icon Polytechnic University of Turin
  • 7. ROR icon Imperial College London
  • 8. ROR icon University of Padua
  • 9. ROR icon Sorbonne University

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.

Copyright and License

© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Acknowledgement

AM gratefully acknowledges Dr. Makrand Khanwale and Mr. Henry Collis for proof editing a draft of Section 3 and offering new additions. SZ has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (TRUFLOW project, grant agreement number 883849).
The authors acknowledge TU Wien Bibliothek for financial support through its Open Access Funding Programme.

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Created:
June 9, 2025
Modified:
June 9, 2025