Regularized lattice Boltzmann model for a class of convection-diffusion equations
Lei Wang1, Baochang Shi1,2, Zhenhua Chai1,2
1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 14, 2015
Summary
A new regularized lattice Boltzmann model accurately solves nonlinear convection-diffusion equations. This model enhances stability and precision compared to existing methods for complex fluid dynamics simulations.
Area of Science:
- Computational fluid dynamics
- Numerical analysis
- Mathematical physics
Background:
- Nonlinear convection-diffusion equations are crucial in modeling various physical phenomena.
- Existing lattice Boltzmann models face challenges with accuracy and stability for these equations.
- Variable coefficients and anisotropic diffusion complicate numerical solutions.
Purpose of the Study:
- To propose a novel regularized lattice Boltzmann model for nonlinear convection-diffusion equations with variable coefficients.
- To enhance the accuracy and stability of lattice Boltzmann methods for these complex equations.
- To validate the model's performance against established numerical tests.
Main Methods:
- Introduction of precollision distribution functions based on macroscopic moments.
- Chapman-Enskog analysis to verify recovery of the target equations.
- Numerical simulations including Fokker-Planck, Buckley-Leverett, and anisotropic diffusion equations.
Main Results:
- The proposed model correctly recovers the nonlinear convection-diffusion equations.
- Numerical tests demonstrate superior accuracy compared to existing lattice Boltzmann models.
- The model exhibits enhanced stability over traditional single-relaxation-time models.
Conclusions:
- The regularized lattice Boltzmann model provides an accurate and stable numerical solution for nonlinear convection-diffusion equations.
- The method is effective for problems with discontinuous initial conditions and anisotropic diffusion.
- This advancement offers a more robust tool for simulating complex fluid dynamics.
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