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Filter-matrix lattice Boltzmann model for incompressible thermal flows
Congshan Zhuo1, Chengwen Zhong, Jun Cao
1National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China.
Summary
A new filter-matrix lattice Boltzmann (FMLB) model enhances accuracy and stability for fluid flow simulations. This improved model effectively simulates incompressible thermal flows without velocity-dependent pressure issues.
Area of Science:
- Computational Fluid Dynamics
- Numerical Analysis
- Thermal Engineering
Background:
- Existing filter-matrix lattice Boltzmann (FMLB) models possess inherent defects, such as velocity-dependent pressure.
- Simulating incompressible thermal flows requires robust numerical methods.
Purpose of the Study:
- To propose and validate an improved filter-matrix lattice Boltzmann (FMLB) model.
- To extend the FMLB model for simulating incompressible thermal flows.
- To address limitations of existing FMLB models, including velocity-dependent pressure.
Main Methods:
- Developed a novel equilibrium solution using Hermite expansion for the FMLB model.
- Introduced temperature-distribution functions to incorporate thermal flow capabilities.
- Coupled the improved FMLB model with temperature-evaluation equations.
- Performed numerical simulations on 2D lid-driven cavity and natural convection flows.
Main Results:
- The improved FMLB model eliminates velocity-dependent pressure, a defect in Somers's model.
- Numerical results demonstrate superior accuracy and stability compared to the lattice Bhatnagar-Gross-Krook (LBGK) model.
- The improved model shows comparable accuracy and enhanced stability versus the multi-relaxation-time (MRT) model, without complex parameter tuning.
- Coupled models achieved excellent agreement with benchmark solutions for natural convection flows.
Conclusions:
- The enhanced FMLB model provides a more accurate and stable approach for fluid dynamics simulations.
- The model's extension to thermal flows is effective and validated through numerical experiments.
- This work offers a robust alternative to existing lattice Boltzmann methods for complex flow problems.
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