The Simplified Lattice Boltzmann Method on Non-Uniform Meshes (Communications in Computational Physics, 2020)
In this paper, we present an improved version of the simplified lattice Boltzmannmethod on non-uniform meshes. This method is based on the recently-proposedsimplified lattice Boltzmann method (SLBM) without evolution of the distributionfunctions. In SLBM, the macroscopic variables, rather than the distribution functions,are directly updated. Therefore, SLBM calls for lower cost in virtual memories and candirectly implement physical boundary conditions. However, one big issue in SLBM isthe lattice uniformity, which is inherited from the standard LBM and this makes SLBMonly applicable on uniform meshes. To further extend SLBM to non-uniform meshes,Lagrange interpolation algorithm is introduced in this paper to determine quantitiesat positions where the streaming process is initiated. The theoretical foundation of theinterpolation process is that both the equilibrium part and the non-equilibrium part ofthe distribution functions are continuous in physical space. In practical implementation,the Lagrange interpolation polynomials can be computed and stored in advance,due to which little extra efforts are brought into the computation. Three numerical testsare conducted with good agreements to reference data, which validates the robustnessof the present method and shows its potential for applications to non-uniform mesheswith curved boundaries.
Keywords: Simplified lattice Boltzmann method; lattice uniformity; Lagrange interpolation; non-uniform meshes; distribution functions.