An Improved Regularization Scheme for an Extended Lattice Boltzmann Model

For an extended lattice Boltzmann model based on a product-form equilibrium distribution function, an improved regularization model with enhanced numerical stability is proposed. In this paper’s regularized collision model, coefficients are calculated using two distinct methods during the reconstruction of the non-equilibrium distribution. The first method stems from the direct projection of the non-equilibrium distribution, while the second method relies on the regularization step, which is refined through the recursive calculation of the coefficients of non-equilibrium Hermite polynomials. Compared to the original lattice Boltzmann model, the recursive regularization method significantly enhances the stability of the numerical scheme by appropriately filtering out second-order and/or higher-order non-hydrodynamic contributions. Initially, under isothermal conditions, the periodic double-shear layer simulations are conducted at Reynolds numbers ranging from 104 to 106, testing the enhanced effect of the regularized model in broadening its available speed range. Subsequently, with a fixed Reynolds number, simulations are performed at various temperature values to assess the model’s performance when deviating from the lattice reference temperature. The results demonstrate that, compared to the original model, the recursive regularization model exhibits improved stability and widens the model’s usable speed and temperature ranges.