For the manufacturing of composite materials with textile reinforcement, the permeability of the textile is a key characteristic. Using the law of Darcy, permeability can be derived from a numerical simulation of the fluid flow, i.e. by solving the Navier-Stokes or Brinkman equations. In this report we present the results of simulations with two different flow solvers: a finite difference Navie...

This article analyses the convergence of the Vertex Approximate Gradient (VAG) scheme recently introduced in Eymard et al. 2012 for the discretization of multiphase Darcy flows on general polyhedral meshes. The convergence of the scheme to a weak solution is shown in the particular case of an incompressible immiscible two-phase Darcy flow model with capillary diffusion using a global pressure f...

This report analyzes a partitioned time stepping algorithm, meaning a non-iterative, domain decomposition method, which allows different time steps in the fluid region and the porous region for the fully evolutionary Stokes-Darcy problem. The method presented requires only one, uncoupled Stokes and Darcy sub-physics and sub-domain solve per time step. Under a time step restriction of the form 4...

In this article we investigate the numerical approximation of coupled Stokes and Darcy fluid flow equations in an axisymmetric domain. The fluid flow is assumed to be axisymmetric. Rewriting the problem in cylindrical coordinates reduces the 3-D problem to a problem in 2-D. This reduction to 2-D requires the numerical analysis to be studied in suitably weighted Hilbert spaces. In this setting w...