Convergence of a boundary integral method for 3D interfacial Darcy flow with surface tension
Document Type
Article
Publication Date
1-1-2017
Abstract
We study convergence of a boundary integral method for 3D interfacial flow with surface tension when the fluid velocity is given by Darcy's Law. The method is closely related to a previous method developed and implemented by Ambrose, Siegel, and Tlupova, in which one of the main ideas is the use of an isothermal parameterization of the free surface. We prove convergence by proving consistency and stability, and the main challenge is to demonstrate energy estimates for the growth of errors. These estimates follow the general lines of estimates for continuous problems made by Ambrose and Masmoudi, in which there are good estimates available for the curvature of the free surface. To use this framework, we consider the curvature and the position of the free surface each to be evolving, rather than attempting to determine one of these from the other. We introduce a novel substitution which allows the needed estimates to close.
Identifier
85021841045 (Scopus)
Publication Title
Mathematics of Computation
External Full Text Location
https://doi.org/10.1090/mcom/3196
ISSN
00255718
First Page
2745
Last Page
2775
Issue
308
Volume
86
Grant
DMS-1016267
Fund Ref
National Science Foundation
Recommended Citation
Ambrose, David M.; Liu, Yang; and Siegel, Michael, "Convergence of a boundary integral method for 3D interfacial Darcy flow with surface tension" (2017). Faculty Publications. 9889.
https://digitalcommons.njit.edu/fac_pubs/9889