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Online ISSN 1552-4485; Print ISSN 0033-569X
Error estimates for pressure-driven Hele-Shaw flow
Authors:
John Fabricius, Salvador Manjate and Peter Wall
Journal:
Quart. Appl. Math. 80 (2022), 575-595
MSC (2020):
Primary 76A20, 76D27, 76D07, 76D08
DOI:
https://doi.org/10.1090/qam/1619
Published electronically:
March 30, 2022
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We consider Stokes flow past cylindrical obstacles in a generalized Hele-Shaw cell, i.e. a thin three-dimensional domain confined between two surfaces. The flow is assumed to be driven by an external pressure gradient, which is modeled as a normal stress condition on the lateral boundary of the cell. On the remaining part of the boundary we assume that the velocity is zero. We derive a divergence-free (volume preserving) approximation of the flow by studying its asymptotic behavior as the thickness of the domain tends to zero. The approximation is verified by error estimates for both the velocity and pressure in $H^1$- and $L^2$-norms, respectively.
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Additional Information
John Fabricius
Affiliation:
Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden
MR Author ID:
843760
ORCID:
0000-0003-1993-8229
Email:
john.fabricius@ltu.se
Salvador Manjate
Affiliation:
Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden, and Department of Mathematics and Informatics, Eduardo Mondlane University, Av. Julius Nyerere, 3453 Maputo, Mozambique
ORCID:
0000-0002-6378-3781
Email:
salvador.manjate@ltu.se
Peter Wall
Affiliation:
Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden
MR Author ID:
605963
ORCID:
0000-0001-8211-3671
Email:
peter.wall@ltu.se
Keywords:
Hele-Shaw flow,
asymptotic expansions,
pressure boundary condition,
thin film flow,
error estimates
Received by editor(s):
November 10, 2021
Received by editor(s) in revised form:
January 25, 2022
Published electronically:
March 30, 2022
Article copyright:
© Copyright 2022
Brown University