Boundary scheme for linear heterogeneous surface reactions in the lattice Boltzmann method

Area of Science:

• Computational fluid dynamics
• Numerical methods

Background:

• The lattice Boltzmann method (LBM) is a powerful tool for simulating fluid flows.
• Accurate treatment of boundary conditions, especially for heterogeneous surface reactions, remains a challenge in LBM.

Purpose of the Study:

• To propose a novel boundary scheme for implementing general Robin boundary conditions in LBM.
• To accurately model linear heterogeneous surface reactions at fluid-solid interfaces.

Main Methods:

• The scheme computes scalar variable gradients using moments of non-equilibrium distribution functions.
• For straight walls, a local scheme is derived.
• For curved walls, linear extrapolation is used to determine the exact boundary position.

Main Results:

• The proposed scheme achieves second-order accuracy for flat walls.
• For curved walls, the accuracy is between 1.0 and 1.5 orders.
• The method simplifies the treatment of heterogeneous reactions compared to existing techniques.

Conclusions:

• The developed boundary scheme is effective for simulating heterogeneous surface reactions in LBM.
• The scheme offers a straightforward and accurate approach for both planar and curved boundaries.
• This work contributes to advancing LBM applications in complex flow scenarios with surface reactions.