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Kinetic boundary conditions in the lattice Boltzmann method
Santosh Ansumali1, Iliya V Karlin
1ETH-Zürich, Department of Materials, Institute of Polymers, ETH-Zentrum, Sonneggstrasse 3, ML J 19, CH-8092 Zürich, Switzerland.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
Summary
This study extends the lattice Boltzmann method (LBM) from kinetic theory to derive boundary conditions for fluid dynamics simulations. It accurately reproduces the Knudsen layer, crucial for understanding fluid behavior at small scales.
Area of Science:
- Computational fluid dynamics
- Kinetic theory
- Numerical methods
Background:
- The lattice Boltzmann method (LBM) is a powerful computational fluid dynamics tool.
- Extending LBM with accurate boundary conditions is essential for simulating complex fluid phenomena.
- Existing LBM implementations often struggle with realistic boundary conditions.
Purpose of the Study:
- To derive accurate boundary conditions for the lattice Boltzmann method from continuous kinetic theory.
- To develop and validate a new boundary condition model for diffusively reflecting moving solid walls.
- To analyze the discretization error and convergence properties of the derived boundary conditions.
Main Methods:
- Extended the derivation of the lattice Boltzmann method from continuous kinetic theory.
- Developed a boundary condition for a diffusively reflecting moving solid wall model.
- Estimated the discretization error associated with the new boundary condition.
- Performed numerical simulations to validate the method.
Main Results:
- Successfully derived boundary conditions for the lattice Boltzmann method.
- The derived boundary conditions demonstrate convergence to the hydrodynamic limit.
- Accurately reproduced the Knudsen layer in Kramers' problem for small Knudsen numbers.
- Quantified the discretization error of the developed boundary condition.
Conclusions:
- The extended lattice Boltzmann method provides accurate boundary conditions for fluid dynamics simulations.
- The new boundary condition model is effective for diffusively reflecting moving solid walls.
- This work advances the applicability of LBM for simulating rarefied gas dynamics and near-wall phenomena.
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