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Rectangular lattice Boltzmann model for nonlinear convection-diffusion equations
Jianhua Lu1, Zhenhua Chai, Baochang Shi
1School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China.
Summary
A new rectangular lattice Boltzmann model accurately solves nonlinear convection-diffusion equations (NCDEs). This advanced model demonstrates superior numerical accuracy compared to existing methods, offering a robust solution for complex problems.
Area of Science:
- Computational fluid dynamics
- Numerical analysis
- Partial differential equations
Background:
- Nonlinear convection-diffusion equations (NCDEs) are crucial in modeling various physical phenomena.
- Existing numerical methods often face challenges in accuracy and generality for NCDEs.
- The lattice Boltzmann method (LBM) offers a promising alternative for solving such equations.
Purpose of the Study:
- To propose a novel rectangular lattice Boltzmann model for solving nonlinear convection-diffusion equations.
- To enhance the accuracy and applicability of LBM for general NCDEs.
- To validate the proposed model through detailed numerical simulations.
Main Methods:
- Development of a rectangular lattice Boltzmann model.
- Incorporation of a real/complex-valued quadric equilibrium distribution function.
- Utilization of a suitable relaxation time parameter.
- Validation using benchmark nonlinear convection-diffusion problems.
Main Results:
- The proposed model effectively solves NCDEs of a very general form.
- Numerical simulations show excellent agreement between computed and analytical solutions.
- The model exhibits significantly improved numerical accuracy over methods using linear equilibrium functions.
Conclusions:
- The developed rectangular lattice Boltzmann model provides an accurate and efficient approach for solving NCDEs.
- The use of a quadric equilibrium distribution function is key to the model's enhanced performance.
- This work offers a valuable tool for researchers and engineers dealing with convection-diffusion phenomena.
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