On the consistency of pseudo-potential lattice Boltzmann methods
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910915498082304 |
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| author | Czelusniak, Luiz Eduardo Bingert, Tim Niklas Krause, Mathias J. Simonis, Stephan |
| author_facet | Czelusniak, Luiz Eduardo Bingert, Tim Niklas Krause, Mathias J. Simonis, Stephan |
| contents | We derive the partial differential equation (PDE) to which the pseudo-potential lattice Boltzmann method (P-LBM) converges under diffusive scaling, providing a rigorous basis for its consistency analysis. By establishing a direct link between the method's parameters and physical properties-such as phase densities, interface thickness, and surface tension-we develop a framework that enables users to specify fluid properties directly in SI units, eliminating the need for empirical parameter tuning. This allows the simulation of problems with predefined physical properties, ensuring a direct and physically meaningful parametrization. The proposed approach is implemented in OpenLB, featuring a dedicated unit converter for multiphase problems. To validate the method, we perform benchmark tests-including planar interface, static droplet, Galilean invariance, and two-phase flow between parallel plates-using R134a as the working fluid, with all properties specified in physical units. The results demonstrate that the method achieves second-order convergence to the identified PDE, confirming its numerical consistency. These findings highlight the robustness and practicality of the P-LBM, paving the way for accurate and user-friendly simulations of complex multiphase systems with well-defined physical properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15018 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the consistency of pseudo-potential lattice Boltzmann methods Czelusniak, Luiz Eduardo Bingert, Tim Niklas Krause, Mathias J. Simonis, Stephan Fluid Dynamics We derive the partial differential equation (PDE) to which the pseudo-potential lattice Boltzmann method (P-LBM) converges under diffusive scaling, providing a rigorous basis for its consistency analysis. By establishing a direct link between the method's parameters and physical properties-such as phase densities, interface thickness, and surface tension-we develop a framework that enables users to specify fluid properties directly in SI units, eliminating the need for empirical parameter tuning. This allows the simulation of problems with predefined physical properties, ensuring a direct and physically meaningful parametrization. The proposed approach is implemented in OpenLB, featuring a dedicated unit converter for multiphase problems. To validate the method, we perform benchmark tests-including planar interface, static droplet, Galilean invariance, and two-phase flow between parallel plates-using R134a as the working fluid, with all properties specified in physical units. The results demonstrate that the method achieves second-order convergence to the identified PDE, confirming its numerical consistency. These findings highlight the robustness and practicality of the P-LBM, paving the way for accurate and user-friendly simulations of complex multiphase systems with well-defined physical properties. |
| title | On the consistency of pseudo-potential lattice Boltzmann methods |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2504.15018 |