A lattice-BGK model for the Navier–Stokes equations based on a rectangular grid. (15th August 2019) - Peng, Cheng; Guo, Zhaoli; Wang, Lian-Ping
Abstract: In this paper, starting from the standard lattice BGK (LBGK) equation with an extended equilibrium distribution and applying the multiscale Chapman–Enskog (CE) analysis, we show theoretically that the correct Navier–Stokes (N–S) equations can be reproduced on a non-standard rectangular grid, using only the BGK collision model. The parameters in the extended equilibrium distribution are determined through an inverse design process. This new LBGK model is then validated using two benchmark cases, i.e., the 2D decaying Taylor–Green vortex flow and the lid-driven cavity flow. The accuracy and stability of the new model are discussed. The new model clearly extends the standard LBGK model as it was previously thought to be impossible to construct an LBGK model for the N–S equations on a rectangular grid.