A Dynamically Adaptive Cell-Centred Lattice Boltzmann Framework for Shallow-Water Flows with Wetting and Drying

Solving the shallow-water equations (SWEs) using the lattice Boltzmann method (LBM) can be computationally expensive on uniform grids. Here we develop a quadtree-based adaptive mesh refinement framework that preserves the Cartesian grid structure while enabling local refinement. A cell-centred data layout is used at coarse–fine interfaces, and hash-table indexing enables efficient neighbour lookup. We evaluate the model using six benchmarks: steady flow over a bed hump, a one-dimensional dam-break wave, rectangular and circular dam-break flows, long-wave resonance in a parabolic basin, and dam-break flow over a triangular sill. We further assess its performance on a natural reach of the lower Minjiang River in Leshan, China, with complex topography. The adaptive model achieves accuracy comparable to that of a uniformly fine grid while substantially reducing the lattice-node count and runtime. This framework provides a practical approach for applying LBM-SWE to moderate-scale real-world problems.