A faster optimal solver for thin film flows

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 steadystate 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. (c) 2022 The Author(s). Published by Elsevier B.V. on behalf of IMACS. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Automated summary

A new multigrid-based algorithm is proposed for solving the discretized lubrication equations commonly used to model thin film flow phenomena. The algorithm utilizes a Newton-Krylov solver for solving the resulting nonlinear algebraic systems of equations. The key innovation is the introduction of a block-based preconditioner incorporating algebraic multigrid (AMG) techniques, enabling their application in thin film flow problems for the first time. Computational testing shows that the proposed algorithm offers substantial advantages over other state-of-the-art multigrid methods.