{rfName}
En

Indexed in

License and use

Citations

27

Altmetrics

Grant support

This work has received funding from the European Research Council through the ERC Starting Grant "An Exascale aware and Un-crashable Space-Time-Adaptive Discontinuous Spectral Element Solver for Non-Linear Conservation Laws" (Extreme), ERC grant agreement no. 714487 (Gregor J. Gassner and Andres Rueda-Ramirez). Gregor Gassner and Andres M. Rueda-Ramirez acknowledge funding through the Klaus-Tschira Stiftung via the project "HiFiLab" (00.014.2021). Jesse Chan gratefully acknowledges support from the National Science Foundation under award DMS-CAREER-1943186. We furthermore thank the Regional Computing Center of the University of Cologne (RRZK) for providing computing time on the High Performance Computing (HPC) system ODIN as well as support.

Analysis of institutional authors

Rueda-Ramirez, Andres MCorresponding Author

Share

Publications
>
Article

Entropy-stable Gauss collocation methods for ideal magneto-hydrodynamics

Publicated to:Journal Of Computational Physics. 475 111851- - 2023-01-03 475(), DOI: 10.1016/j.jcp.2022.111851

Authors: Rueda-Ramirez, Andres M; Hindenlang, Florian J; Chan, Jesse; Gassner, Gregor J

Affiliations

Abstract

In this paper, we present an entropy-stable Gauss collocation discontinuous Galerkin (DG) method on 3D curvilinear meshes for the GLM-MHD equations: the single-fluid magnetohydrodynamics (MHD) equations with a generalized Lagrange multiplier (GLM) divergence cleaning mechanism. For the continuous entropy analysis to hold and to ensure Galilean invariance in the divergence cleaning technique, the GLM-MHD system requires the use of non-conservative terms.Traditionally, entropy-stable DG discretizations have used a collocated nodal variant of the DG method, also known as the discontinuous Galerkin spectral element method (DGSEM) on Legendre-Gauss-Lobatto (LGL) points. Recently, Chan et al. [1, "Efficient Entropy Stable Gauss Collocation Methods". SIAM (2019)] presented an entropy-stable DGSEM scheme that uses Legendre-Gauss points (instead of LGL points) for conservation laws. Our main contribution is to extend the discretization technique of Chan et al. to the non-conservative GLM-MHD system.We provide a numerical verification of the entropy behavior and convergence properties of our novel scheme on 3D curvilinear meshes. Moreover, we test the robustness and accuracy of our scheme with a magneto-hydrodynamic Kelvin-Helmholtz instability problem. The numerical experiments suggest that the entropy-stable DGSEM on Gauss points for the GLM-MHD system is more accurate than the LGL counterpart.(c) 2022 Elsevier Inc. All rights reserved.

Keywords

ApproximationBy-parts operatorsCompressible magnetohydrodynamicsDg schemeDiscontinuous galerkin methodsDiscontinuous galerkin spectral elementEntropy stabilityGauss nodeMagnetohydrodynamicsMethodsMhdNonlinear conservation-lawsPropertShallow-water equationsSplit-form

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Journal Of Computational Physics due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2023, it was in position 3/60, thus managing to position itself as a Q1 (Primer Cuartil), in the category Physics, Mathematical. Notably, the journal is positioned above the 90th percentile.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2025-06-06:

  • Google Scholar: 15
  • WoS: 5
  • Scopus: 7
  • OpenCitations: 5

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-06-06:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 8.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 8 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 0.25.
  • The number of mentions on the social network X (formerly Twitter): 1 (Altmetric).

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Germany; United States of America.

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (RUEDA RAMIREZ, ANDRES MAURICIO) .

the author responsible for correspondence tasks has been RUEDA RAMIREZ, ANDRES MAURICIO.