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

卷:432

Article

Mac Huang, Jinzi^1,3,4  Shelley, Michael J.^1,2  Stein, David B.² 

[1] NYU, Courant Inst, Appl Math Lab, New York, NY 10012 USA

[2] Simons Fdn, Flatiron Inst, Ctr Computat Biol, New York, NY 10010 USA

[3] New York Univ Shanghai, NYU ECNU Inst Phys, Shanghai 200122, Peoples R China

[4] New York Univ Shanghai, Inst Math Sci, Shanghai 200122, Peoples R China

关键词: Dissolution;    Melting;    Shape dynamics;    Fluid-structure interaction;    Immersed boundary;    Stefan problem;   

DOI  :  10.1016/j.jcp.2021.110162

来源: Elsevier

【 摘 要 】

The dissolution of solids has created spectacular geomorphologies ranging from centimeterscale cave scallops to the kilometer-scale stone forests of China and Madagascar. Mathematically, dissolution processes are modeled by a Stefan problem, which describes how the motion of a phase-separating interface depends on local concentration gradients, coupled to a fluid flow. Simulating these problems is challenging, requiring the evolution of a free interface whose motion depends on the normal derivatives of an external field in an ever-changing domain. Moreover, density differences created in the fluid domain induce self-generated convecting flows that further complicate the numerical study of dissolution processes. In this contribution, we present a numerical method for the simulation of the Stefan problem coupled to a fluid flow. 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 theta-Lscheme that provides stable evolution of the boundary. We demonstrate 3rd-order temporal and pointwise spatial convergence of the scheme for the classical Stefan problem, and 2nd-order temporal and pointwise spatial convergence when coupled to flow. Examples of dissolution of solids that result in high-Rayleigh number convection are numerically studied, and qualitatively reproduce the complex morphologies observed in recent experiments. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free