@Article{CiCP-21-981,
author = {Julian Koellermeier and Manuel Torrilhon},
title = {Numerical Study of Partially Conservative Moment Equations in Kinetic Theory},
journal = {Communications in Computational Physics},
year = {2018},
volume = {21},
number = {4},
pages = {981--1011},
abstract = {<p style="text-align: justify;">Moment models are often used for the solution of kinetic equations such
as the Boltzmann equation. Unfortunately, standard models like Grad&#39;s equations are
not hyperbolic and can lead to nonphysical solutions. Newly derived moment models
like the Hyperbolic Moment Equations and the Quadrature-Based Moment Equations
yield globally hyperbolic equations but are given in partially conservative form that
cannot be written as a conservative system.<br/>In this paper we investigate the applicability of different dedicated numerical
schemes to solve the partially conservative model equations. Caused by the non-conservative
type of equation we obtain differences in the numerical solutions, but
due to the structure of the moment systems we show that these effects are very small
for standard simulation cases. After successful identification of useful numerical settings
we show a convergence study for a shock tube problem and compare the results
to a discrete velocity solution. The results are in good agreement with the reference
solution and we see convergence considering an increasing number of moments.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0053},
url = {http://global-sci.org/intro/article_detail/cicp/11268.html}
}