Recursive finite-difference Lattice Boltzmann schemes

The motivation of this study is twofold. First, a recursive mathematical formulation the discrete-velocity Boltzmann equation (DVBE) under Bhatnagar-Gross-Krook (BGK) approximation introduced. This allows us to formally express solution DVBE as an infinite sum over successive particle derivatives distributions associated with local equilibrium. A Chapman-Enskog multiple-scales expansion shows that can be safely truncated beyond second order if Navier-Stokes level description requested. Therefore, distribution functions depend only on first and second-order related equilibrium distributions. alternative defines basis design kinetic schemes for evolution based solely flow variables are sufficient define Second, family mass-conserving numerical introduced from by discretizing backward finite differences. Interestingly, so-called “simplified Lattice method” Chen et al. in 2017 recast family. Numerical simulations highlight dissipation generally higher than obtained standard scheme, expected approximating Nevertheless, we show using von Neumann analysis it possible parametrize our according relaxation coefficient DVBE, reduce significantly its improve spectral properties. We believe modeling also interest connect macroscopic representations, e.g. when dealing initial boundary conditions or hybrid matching schemes.