Collaborative Research: Models, Algorithms, Simulations, and Applications for Three-Phase Systems with Solidification and Moving Contact Lines

该项目将开发数学模型和数值算法，以应对模拟液体，固体和冰等多相流体的挑战。具有多个流体相的现象在许多自然现象和工业应用中起着重要作用，例如大气结冰、增材制造和热喷涂。 例如，当雨滴撞击到冷的固体表面时，它会在固体上扩散，同时由于低温而冻结。物理问题涉及三相（液体，相同材料的固体和空气），界面由不同的物理学决定。待开发的数值模型将促进对基础物理学的理解，并为飞机，3D打印机和热喷涂设备的疏冰表面的设计提供指导。学生将参与并接受计算数学和跨学科方面的培训。该项目的目标如下：（i）推导出一个变分相场模型，以描述凝固前沿以及液-气界面的演变，考虑接触线动力学，非平衡凝固和变密度/粘度;（ii）为建议的模型发展有效率、易于实施和能量稳定的数值计算方法，并采用离散能量定律;及（iii）进行数值模拟，以验证模型和数值计算方法，并进一步研究物理问题。该模型满足物理上一致的能量定律，这是忠实描述真实的物理的必要条件。所开发的数值格式是能量稳定的，具有允许大时间步长的优点，这对于具有不同时间尺度的多物理场问题尤为重要。开发的代码将使我们能够在各种各样的应用中模拟由不同材料制成的流动液滴的固化。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.