Linearized lattice Boltzmann method for micro- and nanoscale flow and heat transfer

Area of Science:

• Computational physics
• Fluid dynamics
• Heat transfer

Background:

• Characterizing heat transfer in micro/nanoscale devices is crucial.
• Simulating gas flows beyond the continuum limit using the Boltzmann equation is computationally challenging.
• Efficient and accurate numerical methods are needed for non-continuum gas dynamics.

Purpose of the Study:

• To develop a hierarchy of thermal lattice Boltzmann (LB) models for simulating non-continuum gas flows.
• To enhance the accuracy and computational efficiency of heat transfer simulations at small length scales.
• To investigate the impact of quadrature schemes and continuum-limit simplifications on model performance.

Main Methods:

• Utilized the linearized Boltzmann Bhatnagar-Gross-Krook equation.
• Developed a hierarchy of thermal LB models using half-space Gaussian-Hermite (GH) quadrature.
• Employed double distribution functions for model construction.
• Derived simplified LB models for the continuum limit.
• Assessed model accuracy by simulating thermal Couette flows across various Knudsen numbers.

Main Results:

• The proposed LB models demonstrate improved computational capability for non-continuum flows.
• Accuracy was validated against simulations of thermal Couette flows.
• The study elaborates on the effects of quadrature schemes (half-space GH vs. full-space GH) and continuum-limit simplifications.
• Consistency was shown between simplified LB models and existing thermal LB models.

Conclusions:

• The developed hierarchy of thermal LB models provides an accurate and efficient approach for heat transfer analysis in non-continuum gas flows.
• These models are suitable for applications involving micro- and nanoscale devices.
• The findings highlight the importance of quadrature schemes and model simplifications for computational accuracy in rarefied gas dynamics.