Riemann-Hilbert Problems for the Shapes Formed by Bodies Dissolving, Melting, and Eroding in Fluid Flows

作者：Moore M Nicholas J^*

来源：Communications on Pure and Applied Mathematics, 2017, 70(9): 1810-1831.

DOI：10.1002/cpa.21689

The classical Stefan problem involves the motion of boundaries during phase transition, but this process can be greatly complicated by the presence of a fluid flow. Here we consider a body undergoing material loss due to either dissolution (from molecular diffusion), melting (from thermodynamic phase change), or erosion (from fluid-mechanical stresses) in a fast-flowing fluid. In each case, the task of finding the shape formed by the shrinking body can be posed as a singular Riemann-Hilbert problem. A class of exact solutions captures the rounded surfaces formed during dissolution/melting, as well as the angular features formed during erosion, thus unifying these different physical processes under a common framework. This study, which merges boundary-layer theory, separated-flow theory, and Riemann-Hilbert analysis, represents a rare instance of an exactly solvable model for high-speed fluid flows with free boundaries.

• 出版日期2017-9