High-performance phase-field modeling

Handle URI:
http://hdl.handle.net/10754/581420
Title:
High-performance phase-field modeling
Authors:
Vignal, Philippe ( 0000-0001-5300-6930 ) ; Sarmiento, Adel; Cortes, Adriano Mauricio ( 0000-0002-0141-9706 ) ; Dalcin, L.; Collier, N.; Calo, Victor M. ( 0000-0002-1805-4045 )
Abstract:
Many processes in engineering and sciences involve the evolution of interfaces. Among the mathematical frameworks developed to model these types of problems, the phase-field method has emerged as a possible solution. Phase-fields nonetheless lead to complex nonlinear, high-order partial differential equations, whose solution poses mathematical and computational challenges. Guaranteeing some of the physical properties of the equations has lead to the development of efficient algorithms and discretizations capable of recovering said properties by construction [2, 5]. This work builds-up on these ideas, and proposes novel discretization strategies that guarantee numerical energy dissipation for both conserved and non-conserved phase-field models. The temporal discretization is based on a novel method which relies on Taylor series and ensures strong energy stability. It is second-order accurate, and can also be rendered linear to speed-up the solution process [4]. The spatial discretization relies on Isogeometric Analysis, a finite element method that possesses the k-refinement technology and enables the generation of high-order, high-continuity basis functions. These basis functions are well suited to handle the high-order operators present in phase-field models. Two-dimensional and three dimensional results of the Allen-Cahn, Cahn-Hilliard, Swift-Hohenberg and phase-field crystal equation will be presented, which corroborate the theoretical findings, and illustrate the robustness of the method. Results related to more challenging examples, namely the Navier-Stokes Cahn-Hilliard and a diusion-reaction Cahn-Hilliard system, will also be presented. The implementation was done in PetIGA and PetIGA-MF, high-performance Isogeometric Analysis frameworks [1, 3], designed to handle non-linear, time-dependent problems.
KAUST Department:
Center for Numerical Porous Media (NumPor)
Conference/Event name:
Pan American Congresses on Computational Mechanics (PANACM) 2015
Issue Date:
27-Apr-2015
Type:
Presentation
Additional Links:
http://congress.cimne.com/panacm2015/admin/files/fileabstract/a406.pdf
Appears in Collections:
Presentations

Full metadata record

DC FieldValue Language
dc.contributor.authorVignal, Philippeen
dc.contributor.authorSarmiento, Adelen
dc.contributor.authorCortes, Adriano Mauricioen
dc.contributor.authorDalcin, L.en
dc.contributor.authorCollier, N.en
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2015-10-29T14:02:15Zen
dc.date.available2015-10-29T14:02:15Zen
dc.date.issued2015-04-27en
dc.identifier.urihttp://hdl.handle.net/10754/581420en
dc.description.abstractMany processes in engineering and sciences involve the evolution of interfaces. Among the mathematical frameworks developed to model these types of problems, the phase-field method has emerged as a possible solution. Phase-fields nonetheless lead to complex nonlinear, high-order partial differential equations, whose solution poses mathematical and computational challenges. Guaranteeing some of the physical properties of the equations has lead to the development of efficient algorithms and discretizations capable of recovering said properties by construction [2, 5]. This work builds-up on these ideas, and proposes novel discretization strategies that guarantee numerical energy dissipation for both conserved and non-conserved phase-field models. The temporal discretization is based on a novel method which relies on Taylor series and ensures strong energy stability. It is second-order accurate, and can also be rendered linear to speed-up the solution process [4]. The spatial discretization relies on Isogeometric Analysis, a finite element method that possesses the k-refinement technology and enables the generation of high-order, high-continuity basis functions. These basis functions are well suited to handle the high-order operators present in phase-field models. Two-dimensional and three dimensional results of the Allen-Cahn, Cahn-Hilliard, Swift-Hohenberg and phase-field crystal equation will be presented, which corroborate the theoretical findings, and illustrate the robustness of the method. Results related to more challenging examples, namely the Navier-Stokes Cahn-Hilliard and a diusion-reaction Cahn-Hilliard system, will also be presented. The implementation was done in PetIGA and PetIGA-MF, high-performance Isogeometric Analysis frameworks [1, 3], designed to handle non-linear, time-dependent problems.en
dc.relation.urlhttp://congress.cimne.com/panacm2015/admin/files/fileabstract/a406.pdfen
dc.titleHigh-performance phase-field modelingen
dc.typePresentationen
dc.contributor.departmentCenter for Numerical Porous Media (NumPor)en
dc.conference.date27-29 April, 2015en
dc.conference.namePan American Congresses on Computational Mechanics (PANACM) 2015en
dc.conference.locationBuenos Airesen
dc.contributor.institutionConsejo Nacional de Investigaciones Cientificas y Tecnicas, Santa Fe, Argentinaen
dc.contributor.institutionOak Ridge National Laboratory, Oak Ridge, Tennessee, USAen
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