Force-driven compressible plane Poiseuille flow by Onsager-Burnett equations

Abstract

The purpose of this work is to evaluate the recently derived Onsager-Burnett (OBurnett) equations [N. Singh, R. S. Jadhav, and A. Agrawal, “Derivation of stable Burnett equations for rarefied gas flows,” Phys. Rev. E 96, 013106 (2017)] for force-driven compressible plane Poiseuille flow. This classical internal flow problem depicts several non-equilibrium phenomena, for instance, non-constant pressure profile in the transverse direction and tangential heat flux, which are not captured by the classical Navier-Stokes-Fourier equations. The results of OBurnett equations for conserved and non-conserved variables are validated against the existing direct simulation Monte Carlo (DSMC) and molecular dynamics (MD) simulation results. These results suggest that the OBurnett equations are able to predict most of the variables well with respect to DSMC and MD simulation results. We find that the OBurnett equations predict a strictly monotonic pressure profile, in contrast to the bimodal profile predicted by the DSMC results and the conventional Burnett equations, but in agreement with the molecular dynamics simulation results. The equations also recover the non-zero tangential heat flux but fail to capture the peculiar temperature dip at the center, owing to its second order accuracy. These results suggest that the evaluated equations are accurate in predicting the non-equilibrium phenomena observed in the rarefied gas flows for the case considered.