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Updated: Jul 3, 2026
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Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Straight velocity boundaries in the lattice Boltzmann method.
Jonas Latt1, Bastien Chopard, Orestis Malaspinas
1University of Geneva, Geneva, Switzerland.
Summary
This study compares five boundary conditions for lattice Boltzmann methods solving Navier-Stokes equations. Results show accuracy and stability depend on flow type, classifying methods for low or high Reynolds numbers.
Area of Science:
- Computational Fluid Dynamics
- Numerical Analysis
- Fluid Mechanics
Background:
- The Navier-Stokes equations govern fluid motion, and their numerical solutions are crucial in many scientific and engineering fields.
- The lattice Boltzmann method (LBM) is a powerful computational fluid dynamics (CFD) technique.
- Accurate implementation of boundary conditions is essential for the reliability of LBM simulations.
Purpose of the Study:
- To review, analyze, and compare five common boundary condition implementations for LBM.
- To evaluate the analytical and numerical performance of these methods for velocity Dirichlet conditions on straight lattice-aligned boundaries.
- To provide guidance on selecting appropriate boundary conditions based on flow characteristics.
Main Methods:
- Analytical inspection using multiscale analysis applied to boundary nodes.
- Numerical benchmarking of two- and three-dimensional flows to assess accuracy and stability.
- Classification of boundary conditions into two groups based on their behavior and performance.
Main Results:
- All five reviewed boundary conditions demonstrate second-order accuracy, consistent with LBM's inherent accuracy.
- No single boundary condition method is universally superior; performance varies with flow geometry and Reynolds number.
- Boundary conditions preserving bulk information excel in low Reynolds number flows.
- Boundary conditions replacing boundary values offer superior stability for high Reynolds number flows.
Conclusions:
- The choice of boundary condition in LBM for Navier-Stokes equations is application-dependent.
- A trade-off exists between accuracy and stability, guiding the selection process.
- Two distinct groups of boundary conditions emerge, suited for different flow regimes (low vs. high Reynolds numbers).
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