### 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 language | English |
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Pages | 1-5 |

Number of pages | 5 |

Publication status | Published - 11 Jul 2010 |

Event | 10th International Conference on Flow Processes in Composite Materials, FPCM-10 2010 - Monte Verita, Ascona, Switzerland Duration: 11 Jul 2010 → 15 Jul 2010 Conference number: 10 |

### Conference

Conference | 10th International Conference on Flow Processes in Composite Materials, FPCM-10 2010 |
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Abbreviated title | FPCM |

Country | Switzerland |

City | Ascona |

Period | 11/07/10 → 15/07/10 |

### Keywords

- Benchmark
- Permeability
- Multigrid

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## 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*. 1-5. Paper presented at 10th International Conference on Flow Processes in Composite Materials, FPCM-10 2010, Ascona, Switzerland.