Local reactive boundary scheme for lattice Boltzmann method

TL;DR

This paper introduces a local reactive boundary scheme for the lattice Boltzmann method that accurately models heterogeneous surface reactions with simple implementation on complex geometries.

Contribution

It presents a physically intuitive, locally based boundary scheme for the D2Q5 lattice Boltzmann method that improves accuracy and applicability for reactive flow simulations.

Findings

Achieves second-order accuracy on straight walls

Attains 1.5 to 2.0 order accuracy on inclined walls

Results agree well with analytical solutions and previous studies

Abstract

In this paper, a boundary scheme is proposed for the two-dimensional five-velocity (D2Q5) lattice Boltzmann method with heterogeneous surface reaction, in which the unknown distribution function is determined locally based on the kinetic flux of the incident particles. Compared with previous boundary schemes, the proposed scheme has a clear physical picture that reflects the consumption and production in the reaction. Furthermore, the scheme only involves local information of boundary nodes such that it can be easily applied to complex geometric structures. In order to validate the accuracy of the scheme, some benchmark tests, including the convection-diffusion problems in straight and inclined channels are conducted. Numerical results are in excellent agreement with the analytical solutions, and the convergence tests demonstrate that second-order spatial accuracy is achieved for straight walls, and the order of accuracy is between 1.5 and 2.0 for general inclined walls. Finally, we simulated the density driving flow with dissolution reactions in a two-dimensional cylindrical array, and the results agree well with those in previous studies