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Phase-field Modeling and Simulation in Computational Mechanics

Hector Gomez, Purdue University

Krishna Garikipati, University of Michigan

Shiva Rudraraju, University of Wisconsin

Victor Calo, Curtin University

Harald van Brummelen, TU Eindhoven

Many processes in engineering and natural sciences involve the evolution of interfaces. Prime examples include systems such as two-phase flows, binary alloys, fluid-phase transition, grain growth, solidification, dendritic crystal growth, and even the growth of cancerous tumors. Propagating cracks or domain walls are classical examples of moving interfaces within solids, while biomembranes are soft material interfaces that usually evolve in a fluid. Phase-field modeling refers to a particular mathematical description of a system with evolving interfaces. In phase-field modeling interfaces are described by a smooth function, the so-called phase field, that changes quickly across the interface. The partial differential equation that governs the phase-field evolution defines the motion of the interfaces and encodes the interfacial physics at once. The governing equations are inherently nonlinear often with higher-order spatial derivatives. The higher-order terms are scaled with a small coefficient (usually controlling the interface thickness) that makes the equations singularly perturbed. Phase-field models offer significant new opportunities to model interface dynamics problems, but also bring a new set of challenges for numerical simulations, such as, for example, discretization of higher-order partial differential equations, stiff semi-discretizations, stable time-stepping algorithms, and the treatment of steep internal layers. In this minisymposium, we invite contributions on modeling and discretization techniques, their numerical analysis, but also their application to problems of fluid mechanics, solid mechanics, and the life sciences or related research areas. We expect a multidisciplinary audience with experts from computational mechanics, mathematical modeling, numerical analysis and applied mathematics.