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Dimensional formulation for the pseudopotential lattice Boltzmann method

Luiz Eduardo Czelusniak1,*, Ivan Talão Martins1,2, and Luben Cabezas Gómez1

  • *Contact author: luiz.czelusniak@usp.br
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Phys. Rev. E 114, 045302 – Published 7 October, 2026

DOI: https://doi.org/10.1103/l7sd-fx7p

Abstract

The lattice Boltzmann method (LBM) is commonly implemented in lattice units, requiring conversion procedures to relate simulation parameters to physical quantities. In the pseudopotential multiphase model, this conversion becomes particularly restrictive when attempting to reproduce real-fluid properties. In this work, we extend the dimensional lattice Boltzmann framework to the pseudopotential formulation, enabling simulations directly in physical units. A dimensional form of the Shan-Chen interaction force is derived and its continuum limit analyzed, revealing the explicit dependence of the model on the grid parameters Δx and Δt. From the recovered pressure tensor, analytical relations are obtained for the equilibrium interface profile, coexistence densities, and surface tension, establishing a direct connection between pseudopotential parameters and thermophysical properties. Numerical simulations using the Peng-Robinson equation of state for water validate the theory through planar interface test, static droplets, spurious currents, layered flow, pressure-induced bubble dynamics, and thermal droplet evaporation. The results show good agreement with analytical predictions and confirm that the dimensional formulation accurately reproduces bulk densities, surface tension, and viscosity, providing a transparent framework for simulating real multiphase flows with LBM.

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Phys. Rev. E 114, 045302– Published 7 October, 2026
  • Received 10 March 2026
  • Accepted 1 September 2026
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