Permeability Prediction Using a Multigrid Method

A finite difference based Stokes solver is developed to predict the mesoscopic permeability of textile reinforcements. In general, a high grid resolution is employed (either globally or locally) to capture the geometrical details of the reinforcement. Local grid refinements often result in poor aspect ratios of the elements, resulting in inaccurate results, whereas the computational cost of complete fine grid models is extremely high, if not too high for practical use. A Multigrid method is implemented to combine computational efficiency with accuracy. The fine grid levels allow a sufficiently accurate description of the internal geometry of the fabric, whereas the coarse grid levels ensure a sufficiently fast convergence for practical use of the solver. The Multigrid Stokes solver is validated on experimental and numerical results found in literature. It can be concluded that the performance of the solver is excellent, for both high and low fibre contents. The solver is currently being used to investigate the transverse permeability of fabric used for CETEX fabric reinforced thermoplastic plates.