Lattice Boltzmann method for simulating transport phenomena avoiding the use of lattice units

In this paper, we propose a dimensional lattice Boltzmann method (LBM) that numerically solves the discrete lattice Boltzmann equation directly in physical units. This procedure facilitates the LBM application for simulating transport phenomena completely avoiding the use of lattice units and conseq...

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Bibliographic Details
Published inJournal of the Brazilian Society of Mechanical Sciences and Engineering Vol. 46; no. 6
Main Authors Martins, Ivan T., Alvariño, Pablo F., Cabezas-Gómez, Luben
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2024
Springer Nature B.V
Subjects
Boltzmann transport equation
Engineering
Finite difference method
Forced convection
Gas density
Gas-liquid systems
Kinematics
Mechanical Engineering
Simulation
Stability
Technical Paper
Transport phenomena
Viscosity
Viscosity ratio
Modified LBE for physical units
Dimensional LBM
LBM without lattice units
Transport phenomena simulation
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Summary:In this paper, we propose a dimensional lattice Boltzmann method (LBM) that numerically solves the discrete lattice Boltzmann equation directly in physical units. This procedure facilitates the LBM application for simulating transport phenomena completely avoiding the use of lattice units and consequently of any particular unit conversion system. Several test problems related to different physical phenomena are simulated, such as heat diffusion, lid-driven cavity, forced convection in channels (both developed and under development) and two-phase liquid–gas systems, considering stationary and dynamic flows under very high density and viscosity ratios. We compare the numerical results with analytical or finite difference solutions, finding a good agreement between them. Similarly, we performed a stability analyses for three of the test cases. The traditional LBM was also considered for the sake of comparison, showing both the same accuracy and stability, as expected. Furthermore, we present solutions using the Allen–Cahn phase-field LBM model for high liquid/gas density and gas/liquid kinematic viscosity ratios, up to 43,300 and 470, respectively, commonly not found in open literature. The proposed methodology enhances the LBM use as a simulation tool for the wide transport phenomena where it finds application.
ISSN:1678-5878
1806-3691
DOI:10.1007/s40430-024-04905-y