A viscosity counteracting approach in the lattice Boltzmann BGK model for low viscosity flow: Preliminary verification

Abstract

Due to numerical instability, the lattice Boltzmann model (LBM) with the Bhatnagar–Gross–Krook (BGK) collision operator has some limitations in the simulation of low viscosity flows. In this paper, we propose a viscosity counteracting approach for simulating a moderate viscosity flow. An extra negative viscosity term is introduced to counteract part of the moderate viscosity by using the lattice Boltzmann equation with a source term. The counteracting viscosity term is treated as a non-uniform unsteady source. The stability is enhanced; thus small viscosity flows can be simulated. Model verification consists of benchmark cases such as those of Poiseuille flow, Couette flow, waterhammer waves, Taylor–Green vortex flow, and lid-driven cavity flow. The flow patterns, error characteristics, and representative parameters are carefully analyzed. It is shown that this approach can simulate flows with lower viscosities than may be simulated using the normal LBGK model; the second-order accuracy of the LBGK model is definitely retained, although a little dissipation is added. These preliminary studies prove the effectiveness and accuracy of the model. Sophisticated analysis and further verification of the stability mechanism will be done in the near future.