Sharp Material Interface Ace Limit of the Darcy-Boussinesq System
Abstract
We investigate the sharp material interface limit of the Darcy-Boussinesq model for convection in layered porous media with diffused material interfaces, which allow a gradual transition of material parameters between different layers. We demonstrate that as the thickness of these transition layers approaches zero, the conventional sharp interface model with interfacial boundary conditions, commonly adopted by the fluids community, is recovered under the assumption of constant porosity. Our results validate the widely used sharp interface model by bridging it with the more physically realistic case of diffused material interfaces. This limiting process is singular and involves a boundary layer in the velocity field. Our analysis requires delicate estimates for elliptic and parabolic equations with discontinuous coefficients and the subtle validation of the boundary layer.
Recommended Citation
H. Dong and X. Wang, "Sharp Material Interface Ace Limit of the Darcy-Boussinesq System," SIAM Journal on Applied Mathematics, vol. 85, no. 4, pp. 1621 - 1642, Society for Industrial and Applied Mathematics, Jan 2025.
The definitive version is available at https://doi.org/10.1137/25M1740310
Department(s)
Mathematics and Statistics
Keywords and Phrases
convection; Darcy-Boussinesq system; interface boundary conditions; layered porous media; sharp material interface limit
International Standard Serial Number (ISSN)
0036-1399
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2025 Society for Industrial and Applied Mathematics, All rights reserved.
Publication Date
01 Jan 2025
Comments
National Science Foundation, Grant DMS2350129