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Lattice Boltzmann approaches to the Euler-Euler equations for two-phase flows

Githin Tom Zachariah* and Harry E. A. Van den Akker

  • *Contact author: githintz@gmail.com
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Phys. Rev. Fluids 11, 044904 – Published 6 April, 2026

DOI: https://doi.org/10.1103/b4mq-2hm6

Abstract

This paper reports on the development of a lattice Boltzmann (LB) code for the Euler-Euler, or two-fluid, large eddy simulation (LES) of turbulent dispersed two-phase flow. To correct for the inbuilt pressure handling inherent to the standard LB method, we develop two LB approaches to the Euler-Euler equations. In the first approach, we naturally remove the inbuilt pressure component by invoking the well-balanced LB method proposed by Guo et al. [Phys. Fluids 33, 031709 (2021)]. Subsequently, the correct pressure term is added as an external force in a Poisson equation. The second approach utilizes a mixture model to generate the required pressure field, assuming an incompressible dilute mixture. This is then coupled to an LB equation for the dispersed phase flow. The two proposed models are validated against two test cases: a falling cloud of particles and a Rayleigh-Taylor instability. The results demonstrate the accuracy of the proposed models while identifying their differences. Subsequently, both models are used to simulate a homogeneous isotropic turbulent two-phase emulsion in a LES supported by the static Smagorinsky subgridscale model. The results of these LESs are compared with a full-scale direct numerical simulation solution. The new models reproduce the larger scales of turbulence accurately, demonstrating the robustness and accuracy of the two proposed models in complex and chaotic scenarios.

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Phys. Rev. Fluids 11, 044904– Published 6 April, 2026
  • Received 9 January 2025
  • Accepted 22 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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