@Article{CiCP-9-688,
author = {},
title = {Constraint Preserving Schemes Using Potential-Based Fluxes I Multidimensional Transport Equations},
journal = {Communications in Computational Physics},
year = {2011},
volume = {9},
number = {3},
pages = {688--710},
abstract = {<p style="text-align: justify;">We consider constraint preserving multidimensional evolution equations.
A prototypical example is provided by the magnetic induction equation of plasma
physics. The constraint of interest is the divergence of the magnetic field. We design
finite volume schemes which approximate these equations in a stable manner and
preserve a discrete version of the constraint. The schemes are based on reformulating
standard edge centered finite volume fluxes in terms of vertex centered potentials.
The potential-based approach provides a general framework for faithful discretizations
of constraint transport and we apply it to both divergence preserving as well as curl
preserving equations. We present benchmark numerical tests which confirm that our
potential-based schemes achieve high resolution, while being constraint preserving.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.030909.091109s},
url = {http://global-sci.org/intro/article_detail/cicp/7517.html}
}