The Generation and Application of the Quadtree Grid for LABSWE

The lattice Boltzmann method for the shallow water equations (LABSWE) is a novel numerical method to simulate the shallow water. The generation and application of the quadtree grid for LABSWE with a Graphical User Interface (GUI) is implemented by C++ programming language and Qt platform in this study. The smoothed quadtree grid with a minimum width is introduced in this model in order to describe the flexuous solid boundary with as few lattices as possible. The quadtree structure and two-dimensional array is mapped to each other in grid generation process to smooth the grid automatically. As an intermediate outcome, each lattice in the water region is numbered by special rules and the information of the grid is stored in the database. In the LABSWE model, the central moments (CMs) collision scheme is used and optimized of the matrix operator. Based on the multi-block grid, a perfect binary tree and the pre-order traversal are introduced skilfully to ensure the temporal consistency of the different blocks. The advanced spatial interpolation assumes that the gradient of the water surface is lower than the gradient of the water depth, which satisfies the dead water in the N property condition. In addition, the compiler directives of OpenMP annotates the code in which parallelism should occur. In the test cases, the lid-driven plane cavity flow and the wind-driven circulation in a dish-shaped basin are used to verify the present model, and the agreements between predictions and results by LABSWE on uniform grids are satisfactory.