Variational bound finite element methods for three-dimensional creeping porous media and sedimentation flows
✍ Scribed by Matteo Pedercini; Anthony T. Patera; Manuel E. Cruz
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 538 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0271-2091
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✦ Synopsis
We present an analytico-computational methodology for the prediction of the effective properties of two types of three-dimensional particulate Stokes ¯ows: porous media and sedimentation ¯ows. In particular, we determine the permeability and average settling rate of media that consist of non-colloidal monodisperse solid spherical particles immersed in a highly viscous Newtonian ¯uid. Our methodology recasts the original problem into three scale-decoupled subproblems: the macro-, meso-and microscale subproblems. In the macroscale analysis the appropriate effective property is used to calculate the bulk quantity of interest. The mesoscale problem provides this effective property through the ®nite element solution of the transport equations in a periodic cell containing many particles distributed according to a prescribed joint probability density function. Finally, the microscale analysis allows us to accommodate mesoscale realizations in which two or more inclusions are in very close proximity; this geometrical stiffness is alleviated by introducing simple domain modi®cations that relax the mesh generation requirements while simultaneously yielding rigorous bounds for the effective property. Our methodology can treat random particle distributions as well as regular arrays; in the current paper we analyse only the latter.