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 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.