No abstract

In this paper we incorporate a non-equilibrium thermodynamics perspective that is consistent with the Onsager reciprocity principle into the lattice Boltzmann framework to propose a novel regularized lattice Boltzmann formulation for modeling the Navier-Stokes-Fourier equations. The new method is applied to one-dimensional isothermal situations wherein the advantages of incorporating such a non-equilibrium perspective can be explicitly appreciated. In such situations, the non-equilibrium contribution of the lattice populations obtained by the new method completely vanish and the lattice update is reduced to evaluating the equilibrium distribution function only. Such a counter-intuitive one-dimensional mesoscopic description is not obtained in any other existing lattice Boltzmann scheme. We therefore numerically test the proposed formulation on two complex problems namely shockwave and nonlinear wave propagation and compare results with analytical results along with six existing lattice Boltzmann schemes; it is found that the new method indeed yields results that are more stable and accurate. These results highlight the potency of the non-equilibrium thermodynamics based approach for obtaining accurate and stable lattice Boltzmann computations while also providing new insights into established lattice Boltzmann simulation methods.

No abstract

Principal Component Analysis (PCA) is a dimensionality reduction technique widely used to reduce the computational cost associated with numerical simulations of combustion phenomena. However, PCA, which transforms the thermochemical state space based on eigenvectors of co-variance of the data, could fail to capture information regarding important localized chemical dynamics, such as the formation of ignition kernels, appearing as outlier samples in a dataset.