A modified lattice Boltzmann approach based on radial basis function approximation for the non-uniform rectangular mesh

We have presented a novel lattice Boltzmann approach for the non-uniform rectangular mesh based on the radial basis function approximation (RBF-LBM). The non-uniform rectangular mesh is a good option for local grid refinement, especially for the wall boundaries and flow areas with intensive change of flow quantities. Which allows, the total number of grid cells to be reduced and so the computational cost, therefore improving the computational efficiency. But the grid structure of the non-uniform rectangular mesh is no longer applicable to the classic lattice Boltzmann method (CLBM), which is based on the famous BGK collision-streaming evolution. This is why the present study is inspired by the idea of the interpolation-supplemented LBM (ISLBM) methodology. The ISLBM algorithm is improved in the present manuscript and developed into a novel LBM approach through the radial basis function approximation instead of the Lagrangian interpolation scheme. The new approach is validated for both steady states and unsteady periodic solutions. The comparison between the radial basis function approximation and the Lagrangian interpolation is discussed. It is found that the novel approach has a good performance on computational accuracy and efficiency. Proving that the non-uniform rectangular mesh allows grid refinement while obtaining precise flow predictions. When compared with the classic lattice Boltzmann method, the convergence speed of the present RBF-LBM is highly accelerated. The modified algorithm is trustable for both steady and unsteady solutions. Numerical results have a good agreement with that of the classic LBM and are more accurate than that of the Lagrangian interpolation schemes. image