Shock Structure Simulation Using Hyperbolic Moment Models in Partially-Conservative Form

The Boltzmann equation is often used to model rarefied gas flow in the transition or kinetic regime for moderate to large Knudsen numbers. However, standard moment methods like Grad's approach lack hyperbolicity of the equations. We point out the failure of Grad's method and overcome the deficiencies with the help of the new hyperbolic moment models called QBME and HME, derived by an operator projection framework. The new model equations are in partially-conservative form meaning that a subset of the equations cannot be written in conservative form due to some changes in these equations. This leads to additional numerical difficulties. The influence of the partially-conservative terms on the solution is analyzed and we present a numerical scheme for the solution of the partially-conservative PDE systems, namely the PRICE-C scheme by Canestrelli. Furthermore, a shock structure test case is used to compare the accuracy of the different hyperbolic moment models to a discrete velocity reference solution. The results show that the new hyperbolic models achieve higher accuracy than the standard Grad model despite the fact that the model equations cannot be fully written in conservative form.