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Higher-order Galilean-invariant lattice Boltzmann model for microflows: single-component gas
Wahyu Perdana Yudistiawan1, Sang Kyu Kwak, D V Patil
1Division of Chemical and Biomolecular Engineering, School of Chemical and Biomedical Engineering, Nanyang Technological University, 637459 Singapore, Singapore.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
We developed an off-lattice D3Q27 model for lattice Boltzmann methods, enhancing degrees of freedom. This new model accurately captures microflow phenomena like the Knudsen boundary layer and Knudsen Paradox.
Area of Science:
- Computational fluid dynamics
- Numerical analysis
- Statistical physics
Background:
- The lattice Boltzmann method (LBM) is a powerful numerical technique for simulating fluid dynamics.
- Existing LBM models often face limitations in accurately capturing rarefied gas dynamics and ensuring Galilean invariance.
- The D3Q27 model, while widely used, can exhibit errors in certain flow regimes.
Purpose of the Study:
- To introduce a novel off-lattice D3Q27 model for the lattice Boltzmann method.
- To demonstrate that this model recovers the Galilean-invariant Navier-Stokes equation without cubic errors.
- To validate the model's capability in simulating microflow phenomena, specifically the Knudsen boundary layer and Knudsen Paradox.
Main Methods:
- Development of an off-lattice D3Q27 discrete velocity model.
- Theoretical analysis to ensure recovery of the Navier-Stokes equation with correct equilibrium states.
- Numerical simulations of Couette flow for various Knudsen numbers.
- Comparison with existing on-lattice D3Q19 and D3Q27 models.
Main Results:
- The proposed off-lattice D3Q27 model provides an additional degree of freedom for the same number of discrete velocities.
- The model successfully recovers the Galilean-invariant Navier-Stokes equation, free from cubic errors.
- The model accurately captures the Knudsen boundary layer and the Knudsen Paradox in single-component gas microflows.
- Numerical results for Couette flow show superior accuracy compared to standard on-lattice D3Q19 and D3Q27 models.
- Demonstration of consistency between entropic and quadrature-based construction methods for discrete velocity models.
Conclusions:
- The novel off-lattice D3Q27 lattice Boltzmann model offers enhanced accuracy and capabilities for microflow simulations.
- This model provides a more robust framework for studying rarefied gas dynamics and associated phenomena.
- The findings confirm the compatibility of different discrete velocity model construction approaches.
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