In this papcr we analyze and compare the lattice Boltzmann equation with the beam scheme in details. We notice the similarity and differences between the lattice Boltzmann equation and the beam scheme. We show that the accuracy of the lattice Boltzmann equation is indeed second order in space. We discuss the advantages and limitations of lattice Boltzmann equation and the beam scheme. Based on ...

Owing to its efficiency and aptitude for a massive parallelization, the lattice Boltzmann method generally outperforms conventional solvers in terms of execution time weakly-compressible flows. However, authorized time-step (being inversely proportional speed sound) becomes prohibitively small incompressible limit, so that performance advantage over continuum-based vanishes. A remedy increase i...

A boundary condition for lattice Boltzmann methods, based on the movement of information through Euler characteristic directions, is developed. With respect to the similar conditions used in finite-difference or finite-volume implementations, some corrections are needed to compensate the isothermal compressible nature of standard lattice Boltzmann methods for fluid flow. The results show that t...

The lattice Boltzmann method (LBM) has two key steps: collision and streaming. In a conventional LBM, the streaming is exact, where each distribution function perfectly shifted to neighbor node on uniform mesh arrangement. This advantage may curtail applicability of problems with complex geometries. To overcome this issue, high-order meshless interpolation-based approach proposed handle step. O...