This project will develop mathematical models and numerical algorithms to address challenges in modeling fluids with multiple phases such as liquid, solid and ice. Phenomena with multiple fluid phases play an important role in many natural phenomena and industrial applications, such as atmospheric icing, additive manufacturing, and thermal spraying. For example, when a rain drop impacts onto a cold solid surface, it spreads on the solid and at the same time freezes due to the low temperature. The physical problem involves three phases (liquid, solid of the same material, and air) and the interfaces are governed by different physics. The numerical models to be developed will advance the understanding of the underlying physics and provide guidance to the design of icephobic surfaces for aircrafts, 3D printers, and thermal spraying devices. Students will be involved and trained in the computational mathematics and interdisciplinary aspects of this project.
This project has the following goals: (i) to derive a variational phase-field model to describe the evolution of the solidification front as well as the liquid-air interface, with the consideration of contact line dynamics, non-equilibrium solidification, and variable density/viscosity; (ii) to develop efficient, easy-to-implement, and energy-stable numerical schemes with discrete energy laws for the proposed models; and (iii) to perform numerical simulations to validate the models and numerical schemes, and further study physically motivated problems. The model satisfies a physically consistent energy law, which is a necessary condition for a faithful description of real physics. The developed numerical schemes are energy-stable with the advantage of allowing large time steps, which is particularly important to this multi-physics problem with disparate time scales. The developed codes will allow us to simulate the solidification of flowing drops made of different materials in a wide variety of applications.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
