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Updated: Dec 17, 2025
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Reviving the local second-order boundary approach within the two-relaxation-time lattice Boltzmann modelling
Goncalo Silva1, Irina Ginzburg2
1LAETA, IDMEC, Mechanical Engineering Department, IST, University of Lisbon, 1049-001 Lisbon, Portugal.
Summary
This study enhances the lattice Boltzmann method (LBM) for fluid flow in complex ducts. A reformulated local second-order boundary (LSOB) scheme achieves high accuracy with simplified implementation for steady-state Stokes flow.
Area of Science:
- Computational Fluid Dynamics
- Numerical Methods for Fluid Flow
- Mesoscopic Fluid Simulation
Background:
- Accurate modeling of steady-state Stokes flow in complex geometries is crucial for applications like porous media flow.
- Existing lattice Boltzmann method (LBM) boundary schemes face challenges in accuracy and implementation complexity for intricate duct shapes.
- The Dirichlet boundary condition for momentum requires robust and efficient numerical treatment within LBM.
Purpose of the Study:
- To reformulate the local second-order boundary (LSOB) scheme within the two-relaxation-time (TRT) LBM framework.
- To develop and assess novel LSOB strategies (Lwall and Lnode) for implementing Dirichlet momentum boundary conditions.
- To evaluate the performance of the reformulated LSOB method against established LBM boundary schemes for 3D duct flows.
Main Methods:
- Reformulation of the LSOB method using the two-relaxation-time (TRT) lattice Boltzmann approach.
- Explicit reconstruction of unknown boundary populations via Chapman-Enskog expansion, extracting momentum derivatives locally.
- Implementation and evaluation of two LSOB strategies (Lwall, Lnode) for plane, curved, and cornered walls in 3D duct flows.
Main Results:
- The reformulated LSOB method, integrated with TRT, provides a standardized and user-friendly algorithm.
- The LSOB scheme accurately captures first- and second-order momentum derivatives locally, avoiding complex finite-difference approximations.
- Numerical tests demonstrate that LSOB schemes achieve accuracy comparable to parabolic multi-reflection schemes, requiring only single-node operations.
Conclusions:
- The TRT-based LSOB method offers a highly accurate and computationally efficient approach for Dirichlet momentum boundary conditions in LBM.
- The LSOB method effectively handles complex duct geometries, including corners, relevant to porous media flow simulations.
- This work presents a significant advancement in LBM boundary condition treatment, enhancing its applicability to challenging fluid dynamics problems.
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