The dissolution of solids creates spectacular geomorphologies ranging from the tiny centimeter-scale scallops found in caves to the enormous kilometer-scale “stone forests” of China and Madagascar. But how are these different geologic features formed? For millennia, the underlying physical processes have remained a mystery.
In a new research project, NYU Shanghai Assistant Professor of Mathematics Jinzi Mac Huang studied a dissolving candy to better understand the physical formation process of geological patterns found in nature, and develop a numerical approach that can simulate the ever-changing surface of a melting or dissolving body. The results of this research appeared in a recent issue of the Journal of Computational Physics.
“Mathematically, the heat or mass transfer problem involving a moving interface is called the Stefan problem. The study of the Stefan problem appeared as early as the 1830s, and has recently become a hot topic,” explained Professor Huang.
Inspired by a dissolving candy, Huang and his collaborators designed a numerical scheme that can simulate liquid convection and solid-solid phrase transitions to solve this ancient problem. The scheme uses the Immersed Boundary Smooth Extension method to solve the bulk advection-diffusion and fluid equations in the complex, evolving geometry, coupled to a θ-L scheme that provides stable evolution of the boundary. Compared with other existing approaches, this scheme proved to be more accurate in solving dissolution, melting and other complex variable boundary evolution problems.
“We hope our method can shed light onto future studies in geoscience, and find future applications in fields like the pharmaceutical industry,” Huang added.
This research was conducted in collaboration with Professor Michael Shelley from the Courant Institute of Mathematical Sciences at NYU and Dr. David Stein from the Flatiron Institute.
About Professor Jinzi Mac Huang:
Jinzi Mac Huang is an Assistant Professor of Mathematics at NYU Shanghai, and a member of the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai and the NYU-ECNU Institute of Physics at NYU Shanghai. Professor Huang is generally interested in experimental fluid dynamics and applied mathematics. He collaborates closely with scholars from the Courant Institute of Mathematical Sciences at NYU and has published a series of high-profile research papers on natural sculpting processes such as erosion and dissolution. His research results have appeared in internationally renowned journals such as PNAS and Physical Review Fluids.
Huang JM, Shelley MJ, Stein DB. A stable and accurate scheme for solving the Stefan problem coupled with natural convection using the Immersed Boundary Smooth Extension method. Journal of Computational Physics. 2021 May 1;432:110162.