Thermodynamically Consistent Algorithms for the Solution of Phase-Field Models
Type
DissertationAuthors
Vignal, Philippe
Advisors
Calo, Victor M.
Committee members
Manchon, Aurelien
Nunes, Suzana Pereira

Al-Ghoul, Mazen
Program
Material Science and EngineeringKAUST Department
Physical Science and Engineering (PSE) DivisionDate
2016-02-11Permanent link to this record
http://hdl.handle.net/10754/596477
Metadata
Show full item recordAbstract
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-20W5Zae974a485f413a2113503eed53cd6c53
10.25781/KAUST-20W5Z