@Article{CiCP-26-1,
author = {Maria Han Veiga, David A. Velasco-Romero, Rémi Abgrall and Romain Teyssier},
title = {Capturing Near-Equilibrium Solutions: A Comparison Between High-Order Discontinuous Galerkin Methods and Well-Balanced Schemes},
journal = {Communications in Computational Physics},
year = {2019},
volume = {26},
number = {1},
pages = {1--34},
abstract = {<p style="text-align: justify;">Equilibrium or stationary solutions usually proceed through the exact balance between hyperbolic transport terms and source terms. Such equilibrium solutions
are affected by truncation errors that prevent any classical numerical scheme from capturing the evolution of small amplitude waves of physical significance. In order to
overcome this problem, we compare two commonly adopted strategies: going to very
high order and reduce drastically the truncation errors on the equilibrium solution,
or design a specific scheme that preserves by construction the equilibrium exactly, the
so-called well-balanced approach. We present a modern numerical implementation of
these two strategies and compare them in details, using hydrostatic but also dynamical
equilibrium solutions of several simple test cases. Finally, we apply our methodology
to the simulation of a protoplanetary disc in centrifugal equilibrium around its star
and model its interaction with an embedded planet, illustrating in a realistic application the strength of both methods.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2018-0071},
url = {http://global-sci.org/intro/article_detail/cicp/13023.html}
}