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In this article, we present a numerical iterative method for the solution of internal viscous and incompressible flows in real porous three-dimensional bodies at their pore scale. We use the penalized formulation of the problem involving velocity and vorticity: an operator splitting allows to split apart the diffusion (inherited from Stokes equatio...
This study provides the analysis of the generalized 3D Stokes problem in a time dependent domain, modeling a solid in motion. The fluid viscosity is a non-linear function of the shear-rate and depends on a transported and diffused quantity. This is a natural model of flow at very low Reynolds numbers, typically at the microscale, involving a miscib...
We propose an estimation of the effective viscosity of a random mixture of Newtonian fluids that ignores capillary effects. The local viscosity of the mixture is assumed to be a random function of the position. Using perturbation expansions up to the second order, the resulting formula can be recast under the form of a simple power averaging mixing...
This project objective is to bring new methods and models for the understanding of micro-meter flows arising in geoscience and biomechanics. Concerning the geoscience activity, we are currently focusing our efforts on the elaboration of new numerical methods in order to study behavior of complex fluids in porous rock (non-Newtonian fluids in complex geometry). Concerning the health science, we are investigating the mechanisms involved in the mucociliary clearance breakdown linked to some pathologies such as cystic fibrosis. The scale and the transport of heterogeneous and miscible constituents with non-trivial rheology is a common aspects between these topics. Each of them can benefit from the developments performed to the other, at a numerical analysis, scientific computing, HPC and mathematical analysis level.