Development of a multigrid finite difference solver for benchmark permeability analysis

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Abstract

A finite difference solver, dedicated to flow around fibre architectures is currently being developed. The complexity of the internal geometry of textile reinforcements results in extreme computation times, or inaccurate solutions. A compromise between the two is found by implementing a multigrid algorithm and analytical solutions at the coarsest level of discretisation. Hence, the computational load of the solver is drastically reduced. This paper discusses the main features of the 3D multigrid algorithm implemented as well as the implementation of the analytical solution in the finite difference scheme. The first tests of the solver on the permeability benchmark lithographic reference geometry are discussed. Several tests were performed to assess the accuracy and the reduction in calculation time. The methods prove to be both accurate and efficient. However, the code is developed in Matlab© and hence is relatively slow. A C++ code is currently under development to achieve acceptable calculation times.
Original languageUndefined
Title of host publicationProceedings of the 10th International Conference on Flow Processes in Composite Materials
EditorsV. Michaud
Place of PublicationAscona, Switserland
PublisherEPFL-ETH
Pages1-5
Number of pages5
Publication statusPublished - 11 Jul 2010
Event10th International Conference on Flow Processes in Composite Materials, FPCM-10 2010 - Monte Verita, Ascona, Switzerland
Duration: 11 Jul 201015 Jul 2010
Conference number: 10

Publication series

Name
PublisherEPFL-ETH

Conference

Conference10th International Conference on Flow Processes in Composite Materials, FPCM-10 2010
Abbreviated titleFPCM
CountrySwitzerland
CityAscona
Period11/07/1015/07/10

Keywords

  • Benchmark
  • IR-73135
  • METIS-266990
  • Permeability
  • Multigrid

Cite this

Loendersloot, R., Grouve, W. J. B., Akkerman, R., & de Boer, A. (2010). Development of a multigrid finite difference solver for benchmark permeability analysis. In V. Michaud (Ed.), Proceedings of the 10th International Conference on Flow Processes in Composite Materials (pp. 1-5). Ascona, Switserland: EPFL-ETH.
Loendersloot, Richard ; Grouve, Wouter Johannes Bernardus ; Akkerman, Remko ; de Boer, Andries. / Development of a multigrid finite difference solver for benchmark permeability analysis. Proceedings of the 10th International Conference on Flow Processes in Composite Materials. editor / V. Michaud. Ascona, Switserland : EPFL-ETH, 2010. pp. 1-5
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abstract = "A finite difference solver, dedicated to flow around fibre architectures is currently being developed. The complexity of the internal geometry of textile reinforcements results in extreme computation times, or inaccurate solutions. A compromise between the two is found by implementing a multigrid algorithm and analytical solutions at the coarsest level of discretisation. Hence, the computational load of the solver is drastically reduced. This paper discusses the main features of the 3D multigrid algorithm implemented as well as the implementation of the analytical solution in the finite difference scheme. The first tests of the solver on the permeability benchmark lithographic reference geometry are discussed. Several tests were performed to assess the accuracy and the reduction in calculation time. The methods prove to be both accurate and efficient. However, the code is developed in Matlab{\circledC} and hence is relatively slow. A C++ code is currently under development to achieve acceptable calculation times.",
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Loendersloot, R, Grouve, WJB, Akkerman, R & de Boer, A 2010, Development of a multigrid finite difference solver for benchmark permeability analysis. in V Michaud (ed.), Proceedings of the 10th International Conference on Flow Processes in Composite Materials. EPFL-ETH, Ascona, Switserland, pp. 1-5, 10th International Conference on Flow Processes in Composite Materials, FPCM-10 2010, Ascona, Switzerland, 11/07/10.

Development of a multigrid finite difference solver for benchmark permeability analysis. / Loendersloot, Richard; Grouve, Wouter Johannes Bernardus; Akkerman, Remko; de Boer, Andries.

Proceedings of the 10th International Conference on Flow Processes in Composite Materials. ed. / V. Michaud. Ascona, Switserland : EPFL-ETH, 2010. p. 1-5.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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AB - A finite difference solver, dedicated to flow around fibre architectures is currently being developed. The complexity of the internal geometry of textile reinforcements results in extreme computation times, or inaccurate solutions. A compromise between the two is found by implementing a multigrid algorithm and analytical solutions at the coarsest level of discretisation. Hence, the computational load of the solver is drastically reduced. This paper discusses the main features of the 3D multigrid algorithm implemented as well as the implementation of the analytical solution in the finite difference scheme. The first tests of the solver on the permeability benchmark lithographic reference geometry are discussed. Several tests were performed to assess the accuracy and the reduction in calculation time. The methods prove to be both accurate and efficient. However, the code is developed in Matlab© and hence is relatively slow. A C++ code is currently under development to achieve acceptable calculation times.

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Loendersloot R, Grouve WJB, Akkerman R, de Boer A. Development of a multigrid finite difference solver for benchmark permeability analysis. In Michaud V, editor, Proceedings of the 10th International Conference on Flow Processes in Composite Materials. Ascona, Switserland: EPFL-ETH. 2010. p. 1-5