@Article{CiCP-7-138,
author = {A. van Dam and P. A. Zegeling},
title = {Balanced Monitoring of Flow Phenomena in Moving Mesh Methods},
journal = {Communications in Computational Physics},
year = {2010},
volume = {7},
number = {1},
pages = {138--170},
abstract = {<p style="text-align: justify;">Adaptive moving mesh research usually focuses either on analytical derivations
for prescribed solutions or on pragmatic solvers with challenging physical applications.
In the latter case, the monitor functions that steer mesh adaptation are often
defined in an ad-hoc way. In this paper we generalize our previously used monitor
function to a balanced sum of any number of monitor components. This avoids
the trial-and-error parameter fine-tuning that is often used in monitor functions. The
key reason for the new balancing method is that the ratio between the maximum and
average value of a monitor component should ideally be equal for all components.
Vorticity as a monitor component is a good motivating example for this. Entropy also
turns out to be a very informative monitor component. We incorporate the monitor
function in an adaptive moving mesh higher-order finite volume solver with HLLC
fluxes, which is suitable for nonlinear hyperbolic systems of conservation laws. When
applied to compressible gas flow it produces very sharp results for shocks and other
discontinuities. Moreover, it captures small instabilities (Richtmyer-Meshkov, Kelvin-Helmholtz).
Thus showing the rich nature of the example problems and the effectiveness
of the new monitor balancing.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.2009.09.033},
url = {http://global-sci.org/intro/article_detail/cicp/7622.html}
}