Collaborative Research: Models, algorithms, simulations and applications for dendritic solidifications of two-phase multi-component alloys in the mushy zone

合金通常由多种金属和非金属成分的熔融混合物固化而成，在各个领域都有广泛的应用，对我们的经济至关重要。与纯金属不同，合金的凝固发生在糊状区，其中相变、溶液扩散、热扩散、体积变化和熔体对流相互作用，强烈影响凝固合金的机械、物理和化学性能。本项目旨在开发糊状区凝固过程的数学模型和数值算法。数值结果将促进对糊化区复杂物理过程的认识，并为设计具有理想性能的合金提供指导。pi团队由来自三个不同机构的三名研究人员组成，预计将在这些机构就项目主题对研究生进行培训。本课题主要研究两相多组分合金在糊状区枝晶凝固的数学建模、算法开发与分析、数值模拟及工程应用。研究人员将在数值上解决这些具有挑战性的问题，目标如下：(i)考虑热扩散、溶质扩散、对流、密度变化和能量定律，为合金在糊状区凝固建立一个通用的两相多分量相场模型；（ii）开发和分析高效、易于实施和能量稳定的数值方案，以准确捕捉凝固动力学；（iii）进行数值模拟以验证模型和数值方案，并进一步研究物理动机问题。由于模型和算法的广泛适用性，所获得的建模和数值工具允许研究人员模拟各种应用中实际感兴趣的相关物理问题。该奖项反映了美国国家科学基金会的法定使命，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。

Alloys, typically formed by solidifying a molten mixture of multiple metal and non-metal components, find extensive applications in various fields and are vital to our economy. Unlike pure metals, solidification of alloys occurs in a mushy zone where phase change, solution diffusion, thermal diffusion, volume change, and melt convection interact and strongly influence the mechanical, physical, and chemical properties of the solidified alloy. This project aims to develop mathematical models and numerical algorithms for the solidification process in the mushy zone. The numerical results will advance the understanding on the complex physical processes in the mushy zone and provide guidance to the design of alloys with desirable properties. The team of PIs consists of the three researchers from three different institutions, where training of graduate students on the topics of the project is expected. This research project focuses on mathematical modeling, algorithm development and analysis, numerical simulations, and engineering applications of dendritic solidification of two-phase multi-component alloys in the mushy zone. The investigators will address these challenging problems numerically with the following goals: (i) to develop a general two-phase multi-component phase-field model for the solidification of alloys in the mushy zone, with the consideration of thermal diffusion, solute diffusion, convection, density variation, and energy law; (ii) to develop and analyze efficient, easy-to-implement, and energy-stable numerical schemes to accurately capture the solidification dynamics; and (iii) to perform numerical simulations to validate the models and numerical schemes, and further study physically motivated problems. The obtained modeling and numerical tools allow the investigators to simulate relevant physical problems of practical interest in a variety of applications due to the wide applicability of the models and algorithms.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.