Uniquely Solvable and Energy Stable Decoupled Numerical Schemes for the Cahn-Hilliard-Stokes-Darcy System for Two-Phase Flows in Karstic Geometry
Abstract
We propose and analyze two novel decoupled numerical schemes for solving the Cahn-Hilliard-Stokes-Darcy (CHSD) model for two-phase flows in karstic geometry. In the first numerical scheme, we explore a fractional step method (operator splitting) to decouple the phase-field (Cahn-Hilliard equation) from the velocity field (Stokes-Darcy fluid equations). To further decouple the Stokes-Darcy system, we introduce a first order pressure stabilization term in the Darcy solver in the second numerical scheme so that the Stokes system is decoupled from the Darcy system and hence the CHSD system can be solved in a fully decoupled manner. We show that both decoupled numerical schemes are uniquely solvable, energy stable, and mass conservative. Ample numerical results are presented to demonstrate the accuracy and efficiency of our schemes.
Recommended Citation
W. Chen et al., "Uniquely Solvable and Energy Stable Decoupled Numerical Schemes for the Cahn-Hilliard-Stokes-Darcy System for Two-Phase Flows in Karstic Geometry," Numerische Mathematik, vol. 137, no. 1, pp. 229 - 255, Springer Verlag, Sep 2017.
The definitive version is available at https://doi.org/10.1007/s00211-017-0870-1
Department(s)
Mathematics and Statistics
Research Center/Lab(s)
Center for High Performance Computing Research
Keywords and Phrases
35K61; 76D07; 76S05; 76T99
International Standard Serial Number (ISSN)
0029-599X; 0945-3245
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2017 Springer Verlag, All rights reserved.
Publication Date
01 Sep 2017