Aljohani, MA, Jimack, PK orcid.org/0000-0001-9463-7595 and Walkley, MA orcid.org/0000-0003-2541-4173 (2023) A Faster Optimal Solver for Thin Film Flows. Applied Numerical Mathematics, 184. pp. 357-370. ISSN 0168-9274
Abstract
A new, multigrid-based, algorithm is proposed for the solution of the discretized lubrication equations which are widely used to model a broad class of thin film flow phenomena. The approach is based upon the use of a Newton-Krylov solver for the nonlinear algebraic systems of equations that arise following mesh-based spatial discretizations and implicit time discretizations. The novel contribution is to propose a block-based preconditioner that includes two applications of algebraic multigrid (AMG) as a key component: thus allowing AMG techniques to be applied in the solution of thin film flow problems for the first time. An implementation of this preconditioned solver is demonstrated for a typical thin film scenario of free-surface flow down a non-smooth inclined plane, considering both steady state and time-dependent configurations. Systematic computational testing is undertaken in comparison with two other state-of-the-art multigrid methods in order to demonstrate the substantial computational advantages of the proposed algorithm.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 The Author(s). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Thin film flow, Nonlinear systems, Multigrid, Preconditioned Newton-Krylov |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Oct 2022 12:04 |
Last Modified: | 25 Jun 2023 23:08 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.apnum.2022.10.012 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:192522 |
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