Wed 4th October @ noon, Rm 312.222
Abstract:
Many processes in engineering and sciences involve the evolution of interfaces. Among the mathematical models for these types of problems, the phase-field method has emerged as a possible solution. Cahn and Hilliard initially proposed one of the most popular phase-field descriptions to model phenomena associated with spontaneous phase separation of immiscible fluids. This process occurs below a critical temperature, where the phase separation allows for the formation of spatial domains rich in each component. Phase-fields nonetheless lead to complex nonlinear, high-order partial differential equations, whose solution poses mathematical and computational challenges.
We describe two- and three-dimensional simulations of the Allen-Cahn, Cahn-Hilliard, Swift Hohenberg and phase-field crystal equations, which corroborate the theoretical findings, and illustrate the robustness of the method. We also discuss a challenging example, namely the Navier-Stokes Cahn-Hilliard in the context of droplet dynamics. The implementations use PetIGA and PetIGA-MF, which are high-performance isogeometric analysis frameworks, we designed to handle non-linear, time-dependent problems.
Ultimately, this simulation framework will allow us to model thermo-chemo-mechanical processes that are relevant to many geological systems. Following the work of Cahn and Hilliard, we propose a generalised Cahn-Hilliard system coupled with the law of mass action which reproduces the kinetics of multicomponent systems as a chemical reaction between the species takes place. The understanding of reaction-diffusion systems requires a comprehensive treatment of both the diffusion and reaction parameters that rule the evolution of the interaction. For instance, when considering a diffusion process driven by gradients in the chemical potential, the interfacial energy parameter between the species plays a key role. We will provide a brief description of this thermodynamically consistent model for multiphase chemical reactions that can reproduce dissolution and reprecipitation processes.
Bio:
Dr Calo holds a professional engineering degree in Civil Engineering from the University of Buenos Aires. He received a master‘s in Geomechanics and a doctorate in Civil and Environmental Engineering from Stanford University. In 2009, Dr Calo became a founding Assistant Professor at the King Abdullah University of Science and Technology. In 2012, Prof Calo and Prof Efendiev developed the Center for Numerical Porous Media with the support of the King Abdullah University of Science and Technology (KAUST). In 2013, Dr Calo was promoted to Associate Professor and later in that year he was listed as a Highly Cited Researcher in the List of the Academic Ranking of World Universities by the Shanghai Jiao Tong University and Thomson Reuters. In 2016, he moved to Perth to become the CSIRO Professorial Chair in Computational Geoscience.
