Lagrangian steady-state discrete Boltzmann model for non-equilibrium flows at micro-nanoscale

In micro- and nanoscale channels, where the characteristic scale approaches or falls below the mean free path between gas molecules, flow characteristics exhibit pronounced discontinuity. In such scenarios, continuum-based models are inadequate, and adopting kinetic models based on statistical mechanics becomes imperative for accurately describing the gas transport phenomenon. This paper presents a novel steady-state discrete Boltzmann model (DBM) that is specifically tailored for non-equilibrium flows at the micro-nanoscale. Unlike the conventional DBM, the new model focuses on the evolution equation of the non-equilibrium component of the molecular velocity distribution function in the Lagrangian coordinate system, which follows the fluid micro-element. Through numerous numerical simulations, we demonstrate the effectiveness of our model in capturing gas flow characteristics across a wide spectrum of rarefaction parameters, ranging from slip flow to free molecular flow. Utilizing this new model, we initially examine the Onsager reciprocal relationship between heat flux generated by pressure gradients and mass flux resulting from temperature gradients in micro/nanochannels. Subsequently, we calculate higher-order non-equilibrium quantities up to the 10th order and make a comparison of their characteristics. Finally, we present and discuss the features of the non-equilibrium component of the molecular velocity distribution function.