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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 1/2019

28.09.2018

A Global Divergence Conforming DG Method for Hyperbolic Conservation Laws with Divergence Constraint

verfasst von: Praveen Chandrashekar

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2019

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Abstract

We propose a globally divergence conforming discontinuous Galerkin (DG) method on Cartesian meshes for curl-type hyperbolic conservation laws based on directly evolving the face and cell moments of the Raviart–Thomas approximation polynomials. The face moments are evolved using a 1-D discontinuous Gakerkin method that uses 1-D and multi-dimensional Riemann solvers while the cell moments are evolved using a standard 2-D DG scheme that uses 1-D Riemann solvers. The scheme can be implemented in a local manner without the need to solve a global mass matrix which makes it a truly DG method and hence useful for explicit time stepping schemes for hyperbolic problems. The scheme is also shown to exactly preserve the divergence of the vector field at the discrete level. Numerical results using second and third order schemes for induction equation are presented to demonstrate the stability, accuracy and divergence preservation property of the scheme.
Vorheriger Artikel A High Order Mixed-FEM for Diffusion Problems on Curved Domains
Nächster Artikel Numerical Methods for Cauchy Bisingular Integral Equations of the First Kind on the Square

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Metadaten
Titel
A Global Divergence Conforming DG Method for Hyperbolic Conservation Laws with Divergence Constraint
verfasst von
Praveen Chandrashekar
Publikationsdatum
28.09.2018
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 1/2019
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-018-0841-4

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