Lattice Boltzmann equation for convection-diffusion flows with Neumann boundary condition

Area of Science:

• Computational Fluid Dynamics
• Numerical Analysis
• Heat Transfer

Background:

• Convection-diffusion flows are crucial in many engineering applications.
• Accurately modeling Neumann boundary conditions in complex geometries remains challenging.
• Existing methods often require complex treatments for boundary conditions.

Purpose of the Study:

• To develop a lattice Boltzmann equation (LBE) solver for convection-diffusion flows.
• To incorporate Neumann boundary conditions naturally within a complex geometry framework.
• To validate the proposed LBE method through benchmark simulations.

Main Methods:

• Extended the physical fluid domain to a larger fictitious domain.
• Reformulated the convection-diffusion equation (CDE) for the extended domain.
• Designed an LBE solver based on the extended CDE, naturally incorporating Neumann conditions.
• Conducted simulations for thermal diffusion, natural convection, and mixed convection.

Main Results:

• The developed LBE method successfully handles Neumann boundary conditions in complex geometries.
• Simulations of various convection-diffusion scenarios showed excellent agreement with theoretical and existing results.
• The fictitious domain approach simplified the treatment of boundary conditions.

Conclusions:

• The proposed LBE method provides an efficient and accurate approach for convection-diffusion problems with Neumann boundary conditions.
• This method offers a robust alternative for simulating fluid dynamics in complex geometries.
• Further applications in diverse engineering fields are anticipated.