A discontinuous Galerkin method with artificial viscosity geared toward numerical relativity applications
Abstract
Artificial viscosity can be used to deal with shocks and other discontinuities such as star surfaces, that can arise in matter. We explain in detail how a local discontinuous Galerkin method can be used to add artificial viscosity terms to hyperbolic evolution equations. These artificial terms are multiplied by a viscosity that is non-zero only in elements that are flagged as non-smooth by a newly developed smoothness indicator. Our artificial viscosity method works well in several simple shock test cases such as with Burgers' equation and blast wave tests. For the first time, we are also able to evolve single neutron star in full general relativistic hydrodynamics. To achieve this, we use different viscosities for the momentum density than for the rest of the matter variables.
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BibTeX
@misc{tichy2026discontinuous,
title = {{A discontinuous Galerkin method with artificial viscosity geared toward numerical relativity applications}},
author = {Wolfgang Tichy and Ananya Adhikari and Faezeh Faghihnia Torshizi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07536},
eprint = {2610.07536},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07536},
}
RIS
TY - UNPB
TI - A discontinuous Galerkin method with artificial viscosity geared toward numerical relativity applications
AU - Wolfgang Tichy
AU - Ananya Adhikari
AU - Faezeh Faghihnia Torshizi
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.07536
UR - https://arxiv.org/abs/2610.07536
AB - Artificial viscosity can be used to deal with shocks and other discontinuities such as star surfaces, that can arise in matter. We explain in detail how a local discontinuous Galerkin method can be used to add artificial viscosity terms to hyperbolic evolution equations. These artificial terms are multiplied by a viscosity that is non-zero only in elements that are flagged as non-smooth by a newly developed smoothness indicator. Our artificial viscosity method works well in several simple shock test cases such as with Burgers' equation and blast wave tests. For the first time, we are also able to evolve single neutron star in full general relativistic hydrodynamics. To achieve this, we use different viscosities for the momentum density than for the rest of the matter variables.
ER -