Automatic boundary geometry classification for discrete Boltzmann method with complex solid–fluid interfaces

To address the persistent bottlenecks in handling complex solid–fluid interfaces on Cartesian grids, including the heavy reliance on explicit geometric descriptions and the difficulty of deploying boundary schemes, this work presents an automatic boundary geometry classification method via 8-neighborhood topological analysis. By building a library of 12 standard geometric templates covering common morphologies, the method enables automatic feature identification of boundary nodes and lookup-table-based indexing of their normal-direction adjacent fluid nodes. Transforming complex geometric processing into local topological mapping yields excellent scalability. First, it is decoupled from specific numerical frameworks, applicable to mainstream fluid dynamics methods including the mesoscopic lattice Boltzmann method and discrete Boltzmann method (DBM), as well as macroscopic finite difference method and finite volume method, and compatible with classic boundary schemes such as non-equilibrium extrapolation and bounce-back. Second, it supports fast local reconstruction of boundary information solely from updated solid–fluid markers, naturally adapting to dynamic interface scenarios including fluid-structure interaction. Third, the first-order neighborhood version is fully compatible with second-order boundary schemes and can be readily extended to multi-order neighborhoods. Using a D2Q16-based DBM for two-dimensional shallow water flows, we validate the method via three typical test cases with the non-equilibrium extrapolation scheme. Results demonstrate that the proposed method preserves the inherent accuracy of the underlying boundary scheme while exhibiting exceptional computational efficiency and robustness, providing a universal boundary pre-processing framework for fluid dynamics simulations involving complex static and moving solid–fluid interfaces.