FILMPAR: A parallel algorithm designed for the efficient and accurate computation of thin film flow on functional surfaces containing micro-structure

FILMPAR is a highly efficient and portable-,'Parallel multigrid algorithm for solving a discretised form of the lubrication approximation to three. Aimensional, gravity-driven, continuous thin film free-surface flow over substrates containing micro-scale topography. While generally applicable to problems involving heterogeneous and distributed features, for illustrative purposes the algorithm is benchmarked on a distributed memory IBM BlueGene/P computing platform for the case of flow over a single trench topography. enabling direct comparison with complementary experimental data and existing serial multigrid solutions. Parallel performance is assessed as a function of the number of processors employed and shown to lead to super-linear behaviour for the production of mesh-independent solutions. In addition, the approach is used to solve for the case of flow over a complex inter-connected topographical feature and a description provided of how FILMPAR could be adapted relatively simply to solve for a wider class of related thin film flow problems.

Program summary

Program title: FILMPAR

Catalogue identifier: AEEL_v1_0

Program summary URL: http://cpc.cs.qub.ac.tik/summaries/AEEL-vl-O.html

Program obtainablefrom: CPC Program Library, Queen's University, Belfast, N. Ireland

Licensing provisions: Standard CPC licence. http://cpc.cs.qub.ac.uk/licence/licence.html

No. of lines in distributed program, including test data, etc.: 530421

No. ofbytes in distributed program, including test data, etc.: 1960 313

Distribution format: tar.gz

Programming language: C++ and MPI

Computer: Desktop, server

Operating system: Unix/Linux Mac OS X

Has the code been vectorised or parallelised?: Yes. Tested with up to 128 processors

RAM: 512 MBytes

Classification: 12 External routines: GNU C/C++, MPI

Nature of problem: Thin film flows over functional substrates containing well-defined single and complex topographical features are of enormous significance, having a wide variety of engineering, industrial and physical applications. However, despite recent modelling advances, the accurate numerical solution of the equations governing such problems is still at a relatively early stage. Indeed, recent studies employing a simplifying long-wave approximation have shown that highly efficient numerical methods are necessary to solve the resulting lubrication equations in order to achieve the level of grid resolution required to accurately capture the effects of micro- and nano-scale topographical features.

Solution method: A portable parallel multigrid algorithm has been developed for the above purpose, for the particular case of flow over Submerged topographical features. Within the multigrid framework adopted. a W-cycle is used to accelerate convergence in respect of the time dependent nature of the problem, with relaxation sweeps performed using a fixed number of pre- and post-Red-Black Gauss-Seidel Newton iterations. In addition, the algorithm incorporates automatic adaptive time-stepping to avoid the computational expense associated with repeated tinle-step failure.

Running time: 1.31 minutes using 128 processors on BlueGene/P with a problem size of over 16.7 million mesh points. (C) 2009 Elsevier B.V. All rights reserved.