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arXiv · 2611.07137

Improving the accuracy of the momentum-exchange method in lattice Boltzmann methods

Abbas Fakhari
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Abstract

In the lattice Boltzmann method (LBM), the momentum-exchange method (MEM) is widely used to evaluate hydrodynamic forces at fluid-solid interfaces due to its computational efficiency and geometric flexibility. However, when mapping complex geometries onto structured Cartesian grids, the physical boundary rarely intersects the lattice links exactly at their midpoints. This discrepancy violates an implicit assumption inherent to the conventional momentum-exchange (CME) formulation. In this study, we systematically analyze this geometric deficiency and demonstrate that it induces significant force inaccuracies, even in elementary flows where the solid boundary deviates from the midway position. To resolve this, we propose a modified momentum-exchange (MME) method that explicitly accounts for the exact boundary location along the lattice links, demonstrating enhanced accuracy for both flat and curved geometries. Furthermore, we address another critical issue with the interpolation-supplemented bounce-back (ISBB) schemes, and that is their inherent violation of local mass conservation. This mass leakage induces unphysical pressure buildup in the system, which compromises the accuracy and stability of the LBM. We propose a mass-conservative remedy for ISBB schemes that eliminates this leakage. Through a series of benchmark simulations of increasing complexity, we demonstrate that combining the proposed MME with the mass-corrected ISBB scheme drastically improves the fidelity of hydrodynamic force evaluations, establishing a robust framework essential for moving boundary problems and fluid-structure interactions.

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Abbas Fakhari. 2026-11-04. Improving the accuracy of the momentum-exchange method in lattice Boltzmann methods. https://arxiv.org/abs/2611.07137

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