Numerical Study of Partially Conservative Moment Equations in Kinetic Theory (Communications in Computational Physics, 2018)
Moment models are often used for the solution of kinetic equations suchas the Boltzmann equation. Unfortunately, standard models like Grad's equations arenot hyperbolic and can lead to nonphysical solutions. Newly derived moment modelslike the Hyperbolic Moment Equations and the Quadrature-Based Moment Equationsyield globally hyperbolic equations but are given in partially conservative form thatcannot be written as a conservative system.In this paper we investigate the applicability of different dedicated numericalschemes to solve the partially conservative model equations. Caused by the non-conservativetype of equation we obtain differences in the numerical solutions, butdue to the structure of the moment systems we show that these effects are very smallfor standard simulation cases. After successful identification of useful numerical settingswe show a convergence study for a shock tube problem and compare the resultsto a discrete velocity solution. The results are in good agreement with the referencesolution and we see convergence considering an increasing number of moments.