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A free-energy stable nodal discontinuous Galerkin approximation with summation-by-parts property for the Cahn-Hilliard equation
Cita
Manzanero Torrico, Juan 
ORCID: https://orcid.org/0000-0003-3252-7061, Rubio Calzado, Gonzalo ORCID: https://orcid.org/0000-0002-6231-4801, Kopriva, David A., Ferrer Vaccarezza, Esteban ORCID: https://orcid.org/0000-0003-1519-0444 and Valero Sánchez, Eusebio ORCID: https://orcid.org/0000-0002-1627-6883
(2019).
A free-energy stable nodal discontinuous Galerkin approximation with summation-by-parts property for the Cahn-Hilliard equation.
"Journal of Computational Physics"
;
ISSN 0021-9991.
https://doi.org/10.1016/j.jcp.2019.109072.
ORCID: https://orcid.org/0000-0003-3252-7061, Rubio Calzado, Gonzalo ORCID: https://orcid.org/0000-0002-6231-4801, Kopriva, David A., Ferrer Vaccarezza, Esteban ORCID: https://orcid.org/0000-0003-1519-0444 and Valero Sánchez, Eusebio ORCID: https://orcid.org/0000-0002-1627-6883
(2019).
A free-energy stable nodal discontinuous Galerkin approximation with summation-by-parts property for the Cahn-Hilliard equation.
"Journal of Computational Physics"
;
ISSN 0021-9991.
https://doi.org/10.1016/j.jcp.2019.109072.
Descripción
| Título: | A free-energy stable nodal discontinuous Galerkin approximation with summation-by-parts property for the Cahn-Hilliard equation |
|---|---|
| Autor/es: |
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| Tipo de Documento: | Artículo |
| Título del Evento: | VII European workshop on high order numerical methods for evolutionary PDEs (HONOM 2019) |
| Lugar del Evento: | Madrid |
| Título de Revista/Publicación: | Journal of Computational Physics |
| Fecha: | Febrero 2019 |
| ISSN: | 0021-9991 |
| Materias: | |
| ODS: | |
| Palabras Clave Informales: | Cahn–Hilliard; Summation–by–parts property; High-order methods; Discontinuous Galerkin |
| Escuela: | E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM) |
| Departamento: | Matemática Aplicada a la Ingeniería Aeroespacial |
| Licencias Creative Commons: | Reconocimiento - Sin obra derivada - No comercial |
Resumen
We present a nodal Discontinuous Galerkin (DG) scheme for the Cahn–Hilliard equation that satisfies the summation–by–parts simultaneous–approximation–term (SBP–SAT) property. The latter permits us to show that the discrete free–energy is bounded, and as a result, the scheme is provably stable. The scheme and the stability proof are presented for general curvilinear three–dimensional hexahedral meshes. We use the Bassi–Rebay 1 (BR1) scheme to compute interface fluxes, and a first order IMplicit–EXplicit (IMEX) scheme to integrate in time. We provide a semi–discrete stability study, and a fully–discrete proof subject to a positivity condition on the solution. Lastly, we test the theoretical findings using numerical cases that include two and three–dimensional problems.
Proyectos asociados
Tipo
Código
Acrónimo
Responsable
Título
Gobierno de España
TRA2015-67679-C2-2-R
Sin especificar
Sin especificar
Estudio de la interacción chorro- pared en condiciones realistas de motor
Más información
| ID de Registro: | 67195 |
|---|---|
| Identificador DC: | https://oa.upm.es/67195/ |
| Identificador OAI: | oai:oa.upm.es:67195 |
| URL Portal Científico: | https://portalcientifico.upm.es/es/ipublic/item/5998759 |
| Identificador DOI: | 10.1016/j.jcp.2019.109072 |
| URL Oficial: | https://www.sciencedirect.com/science/article/pii/... |
| Depositado por: | Memoria Investigacion |
| Depositado el: | 20 Dic 2021 10:16 |
| Ultima Modificación: | 12 Nov 2025 00:00 |
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