Small Darcy Number Limit Of The Navier-Stokes-Darcy System

Author

Wenqi Lyu
Xiaoming Wang, Missouri University of Science and TechnologyFollow

Abstract

We study the small Darcy number behavior of the Navier-Stokes-Darcy system with the conservation of mass, Beavers-Joseph-Saffman-Jones condition, and the Lions balance of the normal-force interface boundary conditions imposed on the interface separating the Navier-Stokes flow and Darcy flow. We show that the asymptotic behavior of the coupled system, at small Darcy number, can be captured by two semi-decoupled Darcy number independent sequences: a sequence of (linearized) Navier-Stokes equations, and a sequence of Darcy equations with appropriate initial and boundary data. Approximate solutions to any order of the small parameter (Darcy number) can be constructed via the two sequences. The local in time validity of the asymptotic expansion up to second order is presented. And the global in time convergence is derived under the assumption that the Reynolds number is below a threshold value.

Recommended Citation

W. Lyu and X. Wang, "Small Darcy Number Limit Of The Navier-Stokes-Darcy System," Nonlinearity, vol. 37, no. 2, article no. 025016, IOP Publishing; London Mathematical Society, Feb 2024.

The definitive version is available at https://doi.org/10.1088/1361-6544/ad1a4b

Department(s)

Mathematics and Statistics

Comments

National Natural Science Foundation of China, Grant 11871159

Keywords and Phrases

asymptotic expansion; Darcy number; Navier-Stokes; porous media

International Standard Serial Number (ISSN)

1361-6544; 0951-7715

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 IOP Publishing; London Mathematical Society, All rights reserved.

Publication Date

01 Feb 2024