Shear stress in lattice Boltzmann simulations
Timm Krüger1, Fathollah Varnik, Dierk Raabe
1Max-Planck-Institut für Eisenforschung, 40237 Düsseldorf, Germany. t.krueger@mpie.de
Summary
The lattice Boltzmann method (LBM) achieves second-order accuracy for shear stress, but boundary conditions can affect this. Researchers derived an analytic expression for fluid density, showing excellent agreement with LBM simulations.
Area of Science:
- Computational fluid dynamics
- Numerical methods
- Fluid mechanics
Background:
- The lattice Boltzmann method (LBM) is a powerful numerical technique for simulating fluid flow.
- Accurate computation of shear stress is crucial in many fluid dynamics applications.
- LBM's accuracy can be influenced by grid resolution and boundary conditions.
Purpose of the Study:
- To thoroughly investigate shear stress accuracy in LBM.
- To analyze the impact of grid resolution and relaxation parameters on shear stress error.
- To understand and analytically describe artificial mass increase in LBM simulations with velocity boundary conditions.
Main Methods:
- Multiscale Chapman-Enskog expansion for error analysis.
- Systematic variation of grid resolution and relaxation parameters.
- Derivation of an analytic expression for fluid density in 3D Poiseuille flow.
- Comparison between analytic results and LBM simulation data.
Main Results:
- LBM achieves second-order accuracy for shear stress, dependent on grid resolution.
- Boundary conditions often degrade the convergence of shear stress accuracy.
- An analytic expression for fluid density was derived, accurately predicting LBM simulation results for Poiseuille flow.
Conclusions:
- LBM offers a robust framework for shear stress computation, with accuracy contingent on boundary condition implementation.
- The derived analytic expression provides valuable insight into compressibility effects and artificial mass increase in LBM.
- This work enhances the understanding and application of LBM in complex fluid flow scenarios.
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The average shearing stress can be calculated by dividing the shear by the area of the cross-section.
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