A Consistent Grid Coupling Method for Lattice-Boltzmann Schemes

Asymptotic analysis of the lattice Boltzmann equation

“…In the modified equation analysis, the same assumption is used and it has been shown, for example in [16,5], that it lacks mathematical justification. Since our goal is to develop a method which will enable us to analyze the lattice Boltzmann method in combination with boundary conditions [25], coupling conditions for different meshes [42] and in the presence of initial layers [4], we circumvent this technical problem and apply an asymptotic expansion directly to the discrete lattice Boltzmann equation itself, in the spirit of finite-difference analysis [45,46,33].…”

An adaptive scheme using hierarchical grids for lattice Boltzmann multi-phase flow simulations

“…An approach where also the Mach number is lowered on finer grid levels to ensure a faster convergence to the incompressible NavierStokes equations can be found in [22]. This approach requires one to do four time steps on the finer grid during one time step on the coarser mesh.…”

Implementation of the compact interpolation within the octree based Lattice Boltzmann solver Musubi

“…Previous studies [12,15,20,21,34,35] have indicated that a quadratic or cubic interpolation is necessary to maintain the second order convergence of the LBM algorithm. However, Eitel et al [7,16] have obtained good results by using linear interpolations in combination with a subgrid-scale model.…”