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    Thermodynamically Consistent Algorithms for the Solution of Phase-Field Models

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    Name:
    Philippe Vignal - Dissertation - Final Draft.pdf
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    22.95Mb
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    Type
    Dissertation
    Authors
    Vignal, Philippe cc
    Advisors
    Calo, Victor M. cc
    Committee members
    Manchon, Aurelien cc
    Nunes, Suzana Pereira cc
    Al-Ghoul, Mazen
    Program
    Material Science and Engineering
    KAUST Department
    Physical Science and Engineering (PSE) Division
    Date
    2016-02-11
    Permanent link to this record
    http://hdl.handle.net/10754/596477
    
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    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.
    Citation
    Vignal, P. (2016). Thermodynamically Consistent Algorithms for the Solution of Phase-Field Models. KAUST Research Repository. https://doi.org/10.25781/KAUST-20W5Z
    DOI
    10.25781/KAUST-20W5Z
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-20W5Z
    Scopus Count
    Collections
    PhD Dissertations; Physical Science and Engineering (PSE) Division; Material Science and Engineering Program

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