@Article{CiCP-8-995,
author = {J. W. Banks},
title = {On Exact Conservation for the Euler Equations with Complex Equations of State},
journal = {Communications in Computational Physics},
year = {2010},
volume = {8},
number = {5},
pages = {995--1015},
abstract = {<p style="text-align: justify;">Conservative numerical methods are often used for simulations of fluid
flows involving shocks and other jumps with the understanding that conservation
guarantees reasonable treatment near discontinuities. This is true in that convergent
conservative approximations converge to weak solutions and thus have the correct
shock locations. However, correct shock location results from any discretization whose
violation of conservation approaches zero as the mesh is refined. Here we investigate
the case of the Euler equations for a single gas using the Jones-Wilkins-Lee (JWL) equation
of state. We show that a quasi-conservative method can lead to physically realistic
solutions which are devoid of spurious pressure oscillations. Furthermore, we demonstrate
that under certain conditions, a quasi-conservative method can exhibit higher
rates of convergence near shocks than a strictly conservative counterpart of the same
formal order.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.090909.100310a},
url = {http://global-sci.org/intro/article_detail/cicp/7606.html}
}