"High-performance phase-field modeling for engineering applications"
Mathematical Soft Matter Unit (Fried Unit) would like to invite you to a Seminar by Prof. Victor Calo from Western Australian School of Mines, Science & Eng, Curtin University.
Date: Thursday, March 30, 2017
Venue: C016, Level C, Lab1
Professor Victor Calo
Western Australian School of Mines,
Faculty of Science & Eng, Curtin University
High-performance phase-field modeling for engineering applications
Victor Calo, Nathan Collier, Adriano Cortes, Lisandro Dalcin, Luis Espath, Adel Sarmiento, Philippe Vignal
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. Phase-fields nonetheless lead to complex nonlinear, high-order partial differential equations, whose solution poses mathematical and computational challenges.
Guaranteeing relevant physical properties of the equations required the development of efficient algorithms and discretizations capable of recovering said properties by construction. This work builds upon these provably stable algorithms and proposes novel discretization strategies that guarantee numerical energy dissipation for both conserved and non-conserved phase-field models. The temporal discretization uses a novel method which relies on Taylor series and ensures strong energy
stability. The discrete method is second-order accurate, and can also be rendered linear to speed up the solution process. The spatial discretization relies on Isogeometric Analysis, a finite element method that possesses a high-continuity refinement methodology that enables the generation of high-order, high-continuity basis functions (k refinement). These basis functions handle with ease the high-order operators present in phase-field models.
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 high-performance Isogeometric Analysis frameworks, we designed to handle non-linear, time-dependent problems.