School of Mathematical Sciences, Shenzhen University  

Liyuan Scholar Colloquium No. 145  

Lecture Title: How to Efficiently Simulate the Microstructural Evolution of Superalloys? — An Energy-Stable Phase-Field Numerical Method  

Lecturer: Professor Wang Xiaoping [The Chinese University of Hong Kong, Shenzhen (CUHK-Shenzhen)]  

Lecture Time: October 15, 2025, 10:00-11:00 (morning)  

Venue: Classroom 4, Huixing Building, Yuehai Campus, Shenzhen University  

Abstract:  

Superalloys are structural materials with excellent properties at high temperatures, widely used in key equipment such as aero-engines and gas turbines. Their performance largely depends on the morphology and distribution of "γ′ phase" precipitates in the microstructure. To predict and control the evolution of these microstructures, scientists often use "phase-field models" for numerical simulation. However, traditional numerical methods face problems of low computational efficiency and numerical instability when solving such phase-field models involving elastic energy. In this study, we propose a numerical scheme with second-order temporal accuracy and unconditional energy stability. By introducing a constant scalar auxiliary variable, we transform the time derivative of the nonlinear term into an easily manageable conservative form, thereby significantly improving numerical stability while ensuring computational accuracy. We prove the energy decay property of this scheme through rigorous mathematical analysis, and conduct extensive numerical experiments to verify its effectiveness and accuracy. In addition, we systematically study the influence of elastic parameters (such as misfit strain and elastic modulus) on the morphology of precipitates, and find that the formation of microstructures is the result of the combined action of multiple elastic parameters, rather than being determined by a single factor.  

Lecturer’s Biography:  

Professor Wang Xiaoping obtained his Bachelor of Mathematics degree from Peking University in 1984 and his doctoral degree from the Courant Institute of Mathematical Sciences, New York University (NYU) in 1990. He has served successively as Assistant Professor, Associate Professor, Professor, and Chair Professor in the Department of Mathematics at the Hong Kong University of Science and Technology (HKUST), and once held the position of Head of the Department of Mathematics at HKUST. He is the founding President of the Hong Kong Society for Industrial and Applied Mathematics (HKSIAM). Currently, Professor Wang is Executive Deputy Director of the Shenzhen International Center for Industrial and Applied Mathematics, University President's Chair Professor at the School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, and Fellow of the Chinese Society for Industrial and Applied Mathematics (CSIAM).  

For many years, Professor Wang has engaged in research on various complex problems in the field of engineering and scientific computing, and has made internationally influential achievements in the research of mathematical physics models, algorithm construction, and theoretical analysis in engineering and scientific computing. In particular, his research results on algorithms for micromagnetic computing, the theory and simulation of moving contact line models for multiphase flows, and efficient algorithms for topology optimization in intelligent manufacturing have been highly recognized by peers at home and abroad. He was awarded the Feng Kang Prize in Scientific Computing in 2007, delivered a plenary lecture at the SIAM Conference on Mathematics of Materials Science (USA) in 2016, and gave a plenary lecture at the International Congress on Industrial and Applied Mathematics (ICIAM) in 2019. He is also a Changjiang Scholar Professor appointed by the Ministry of Education and a Pearl River Distinguished Talent of Guangdong Province.  

Faculty and students are welcome to attend!  

School of Mathematical Sciences  

October 13, 2025