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Published on: February 22, 2018
Slip velocity and Knudsen layer in the lattice Boltzmann method for microscale flows
Seung Hyun Kim1, Heinz Pitsch, Iain D Boyd
1Department of Mechanical Engineering, Stanford University, California 94305-3035, USA. shkcomb@stanford.edu
Summary
We developed mesoscopic fluid-wall interaction models for lattice Boltzmann (LB) simulations. Modifications improve LB accuracy for microscale flows with slip velocity, especially at higher Knudsen numbers.
Area of Science:
- Computational fluid dynamics
- Mesoscopic fluid dynamics
- Non-equilibrium statistical mechanics
Background:
- Lattice Boltzmann (LB) methods are widely used for microscale flow simulations.
- Accurate modeling of fluid-wall interactions, particularly slip velocity, is crucial at the microscale.
- Standard LB models exhibit limitations in quantitative accuracy for higher Knudsen numbers.
Purpose of the Study:
- To develop and validate mesoscopic fluid-wall interaction models for LB simulations.
- To analyze the slip velocity and Knudsen layer phenomena in microscale flows.
- To enhance the quantitative accuracy of LB methods for finite Knudsen numbers.
Main Methods:
- Obtained exact solutions for slip velocity in LB equations with Bhatnagar-Gross-Krook collision operator for Poiseuille flow.
- Consistently defined the Knudsen number for LB simulations.
- Modified LB models by altering nonequilibrium energy flux or introducing effective relaxation time.
Main Results:
- Standard LB models with D2Q9 scheme show slightly larger slip coefficients than Boltzmann equation, limiting accuracy to small Knudsen numbers.
- Modified LB methods analytically reproduce slip phenomena up to second order in Knudsen number.
- The Knudsen layer is captured in standard LB methods only with modifications to relaxation dynamics, such as effective relaxation time.
Conclusions:
- Mesoscopic fluid-wall interaction models enhance LB simulation accuracy for microscale flows.
- Modifications to LB models are necessary to accurately capture slip phenomena at higher Knudsen numbers.
- Effective relaxation time models are crucial for resolving the Knudsen layer in LB simulations.
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