Numerical simulation of rarefied supersonic flows using a fourth-order maximum-entropy moment method with interpolative closure

Maximum-entropy moment methods allow for the modeling of gases from the continuum regime to strongly rarefied conditions. The development of approximated solutions to the entropy maximization problem has made these methods computationally affordable. In this work, we apply a fourth-order maximum-entropy moment method to the study of supersonic rarefied flows. For such conditions, we compare the maximum-entropy solutions to results obtained from the kinetic theory of gases at different Knudsen numbers. The analysis is performed for both a simplified model of a gas with a single translational degree of freedom (5-moment system) and for a typical gas with three degrees of freedom (14-moment system). The maximum-entropy method is applied to the study of the Sod shock-tube problem at various rarefaction levels, and to the simulation of two-dimensional low-collisional crossed supersonic jets. We show that, in rarefied supersonic conditions, it is important to employ accurate estimates of the wave speeds. Since analytical expressions are not presently available, we propose an approximation, valid for the 14-moment system. In these conditions, the solution of the maximum-entropy system is shown to realize large degrees of non-equilibrium and to approach the Junk subspace, yet provides a good overall accuracy and agreement with the kinetic theory. Numerical procedures for reaching second-order accurate discretizations are discussed, as well as the implementation of the 14-moment solver on Graphics Processing Units (GPUs).

Automated summary

Max-entropy moment methods are used to model gases from continuum to rarefied conditions. This study applies a fourth-order maximum-entropy moment method to supersonic rarefied flows. It compares the maximum-entropy solutions to results obtained from the kinetic theory of gases and proposes an approximation for accurate estimates of wave speeds. The results show that the maximum-entropy method provides good accuracy and agreement with the kinetic theory in rarefied supersonic conditions.