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Lattice Boltzmann Simulation of Spatial Fractional Convection-Diffusion Equation
1School of Liberal Arts and Sciences, North China Institute of Aerospace Engineering, Langfang 065000, China.
Entropy (Basel, Switzerland)
|September 27, 2024
Summary
This study introduces a lattice Boltzmann model for the space fractional advection-diffusion equation, offering an effective numerical method for complex natural phenomena simulations. The model
Area of Science:
- Computational Mathematics
- Applied Mathematics
- Physics
Background:
- Fractional partial differential equations (PDEs) are vital for modeling complex natural phenomena.
- The space fractional advection-diffusion equation offers enhanced accuracy in describing these phenomena.
- Analytical solutions for these equations are often complex, necessitating numerical approaches.
Purpose of the Study:
- To develop and investigate a numerical method for the space fractional advection-diffusion equation.
- To perform error analysis on the proposed numerical model.
- To validate the model's effectiveness through comparative studies.
Main Methods:
- Development of a lattice Boltzmann model tailored for the spatial fractional convection-diffusion equation.
- Conducting rigorous error analysis to assess model accuracy.
- Solving the equation for various test cases and comparing results with established methods.
Main Results:
- A lattice Boltzmann model was successfully developed for the space fractional advection-diffusion equation.
- Error analysis confirmed the model's stability and convergence properties.
- Numerical solutions obtained from the lattice Boltzmann method showed strong agreement with existing solutions.
Conclusions:
- The lattice Boltzmann method is a powerful and effective tool for solving the space fractional advection-diffusion equation.
- This numerical approach provides a viable alternative for investigating complex physical processes described by fractional PDEs.
- The study validates the lattice Boltzmann method's applicability in computational physics and applied mathematics.
Keywords:
Riemann–Liouville fractional derivativelattice Boltzmann methodnumerical simulationspatial fractional convection–diffusion equationMore Related Videos
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