The Onsager Regularized LBM

The traditional single relaxation time (SRT) lattice Boltzmann method (LBM), namely the Lattice-BGK method (LBGK), demonstrates crippling physical and numerical defects that manifest as numerical instabilities in extreme flow conditions characterized by large Reynolds and Mach numbers. Although well established improvements to the LBGK models such as the Entropic LBM and Regularized LBM schemes address these issues, these methods are still characterized by subtle limitations such as the retention of spurious hydrodynamic moments in the case of the Entropic LBM and, an inherent inability to filter all non-hydrodynamic moments for every admissible lattice structure in the case of the state-of-the-art scheme among the Regularized LBMs. Here, we present a novel Regularized LBM scheme, named the Onsager-Regularized LBM (ORegularized LBM for brevity) which is derived from a phenomenological non-equilibrium thermodynamics perspective that is consistent with the Onsager Reciprocity Principle. The proposed method is extensively characterized for several canonical one- and two-dimensional benchmark flow problems and is found to significantly improve the stability regime over existing Regularized LBM schemes while also overcoming the limitations of the Entropic LBM methods.