A free-energy stable nodal discontinuous Galerkin approximation with summation-by-parts property for the Cahn-Hilliard equation

Manzanero Torrico, Juan and Rubio Calzado, Gonzalo and Kopriva, David A. and Ferrer Vaccarezza, Esteban and Valero Sanchez, Eusebio (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.

Description

Title: A free-energy stable nodal discontinuous Galerkin approximation with summation-by-parts property for the Cahn-Hilliard equation
Author/s:
  • Manzanero Torrico, Juan
  • Rubio Calzado, Gonzalo
  • Kopriva, David A.
  • Ferrer Vaccarezza, Esteban
  • Valero Sanchez, Eusebio
Item Type: Article
Event Title: VII European workshop on high order numerical methods for evolutionary PDEs (HONOM 2019)
Event Location: Madrid
Título de Revista/Publicación: Journal of Computational Physics
Date: February 2019
ISSN: 0021-9991
Subjects:
Freetext Keywords: Cahn–Hilliard; Summation–by–parts property; High-order methods; Discontinuous Galerkin
Faculty: E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM)
Department: Matemática Aplicada a la Ingeniería Aeroespacial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

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.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainTRA2015-67679-C2-2-RUnspecifiedUnspecifiedEstudio de la interacción chorro- pared en condiciones realistas de motor

More information

Item ID: 67195
DC Identifier: https://oa.upm.es/67195/
OAI Identifier: oai:oa.upm.es:67195
DOI: 10.1016/j.jcp.2019.109072
Official URL: https://www.sciencedirect.com/science/article/pii/S0021999119307776
Deposited by: Memoria Investigacion
Deposited on: 20 Dec 2021 10:16
Last Modified: 20 Dec 2021 10:16
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