Thermodynamically Consistent Algorithms for the Solution of Phase-Field Models

Handle URI:
http://hdl.handle.net/10754/596477
Title:
Thermodynamically Consistent Algorithms for the Solution of Phase-Field Models
Authors:
Vignal, Philippe ( 0000-0001-5300-6930 )
Abstract:
Phase-field models are emerging as a promising strategy to simulate interfacial phenomena. Rather than tracking interfaces explicitly as done in sharp interface descriptions, these models use a diffuse order parameter to monitor interfaces implicitly. This implicit description, as well as solid physical and mathematical footings, allow phase-field models to overcome problems found by predecessors. Nonetheless, the method has significant drawbacks. The phase-field framework relies on the solution of high-order, nonlinear partial differential equations. Solving these equations entails a considerable computational cost, so finding efficient strategies to handle them is important. Also, standard discretization strategies can many times lead to incorrect solutions. This happens because, for numerical solutions to phase-field equations to be valid, physical conditions such as mass conservation and free energy monotonicity need to be guaranteed. In this work, we focus on the development of thermodynamically consistent algorithms for time integration of phase-field models. The first part of this thesis focuses on an energy-stable numerical strategy developed for the phase-field crystal equation. This model was put forward to model microstructure evolution. The algorithm developed conserves, guarantees energy stability and is second order accurate in time. The second part of the thesis presents two numerical schemes that generalize literature regarding energy-stable methods for conserved and non-conserved phase-field models. The time discretization strategies can conserve mass if needed, are energy-stable, and second order accurate in time. We also develop an adaptive time-stepping strategy, which can be applied to any second-order accurate scheme. This time-adaptive strategy relies on a backward approximation to give an accurate error estimator. The spatial discretization, in both parts, relies on a mixed finite element formulation and isogeometric analysis. The codes are available online and implemented in PetIGA, a high-performance isogeometric analysis framework.
Advisors:
Calo, Victor M. ( 0000-0002-1805-4045 )
Committee Member:
Manchon, Aurelien ( 0000-0002-4768-293X ) ; Nunes, Suzana Pereira ( 0000-0002-3669-138X ) ; Al-Ghoul, Mazen
KAUST Department:
Physical Sciences and Engineering (PSE) Division; Materials Science and Engineering Program
Program:
Materials Science and Engineering
Issue Date:
11-Feb-2016
Type:
Dissertation
Appears in Collections:
Dissertations; Physical Sciences and Engineering (PSE) Division; Materials Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.advisorCalo, Victor M.en
dc.contributor.authorVignal, Philippeen
dc.date.accessioned2016-02-17T08:47:30Zen
dc.date.available2016-02-17T08:47:30Zen
dc.date.issued2016-02-11en
dc.identifier.urihttp://hdl.handle.net/10754/596477en
dc.description.abstractPhase-field models are emerging as a promising strategy to simulate interfacial phenomena. Rather than tracking interfaces explicitly as done in sharp interface descriptions, these models use a diffuse order parameter to monitor interfaces implicitly. This implicit description, as well as solid physical and mathematical footings, allow phase-field models to overcome problems found by predecessors. Nonetheless, the method has significant drawbacks. The phase-field framework relies on the solution of high-order, nonlinear partial differential equations. Solving these equations entails a considerable computational cost, so finding efficient strategies to handle them is important. Also, standard discretization strategies can many times lead to incorrect solutions. This happens because, for numerical solutions to phase-field equations to be valid, physical conditions such as mass conservation and free energy monotonicity need to be guaranteed. In this work, we focus on the development of thermodynamically consistent algorithms for time integration of phase-field models. The first part of this thesis focuses on an energy-stable numerical strategy developed for the phase-field crystal equation. This model was put forward to model microstructure evolution. The algorithm developed conserves, guarantees energy stability and is second order accurate in time. The second part of the thesis presents two numerical schemes that generalize literature regarding energy-stable methods for conserved and non-conserved phase-field models. The time discretization strategies can conserve mass if needed, are energy-stable, and second order accurate in time. We also develop an adaptive time-stepping strategy, which can be applied to any second-order accurate scheme. This time-adaptive strategy relies on a backward approximation to give an accurate error estimator. The spatial discretization, in both parts, relies on a mixed finite element formulation and isogeometric analysis. The codes are available online and implemented in PetIGA, a high-performance isogeometric analysis framework.en
dc.language.isoenen
dc.subjectPhase-fielden
dc.subjectTime Integrationen
dc.subjectNonlinear Stabilityen
dc.titleThermodynamically Consistent Algorithms for the Solution of Phase-Field Modelsen
dc.typeDissertationen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentMaterials Science and Engineering Programen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberManchon, Aurelienen
dc.contributor.committeememberNunes, Suzana Pereiraen
dc.contributor.committeememberAl-Ghoul, Mazenen
thesis.degree.disciplineMaterials Science and Engineeringen
thesis.degree.nameDoctor of Philosophyen
dc.person.id101769en
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