Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction
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The modeling of an incompressible fluid through a porous medium requires to deal with two systems of partial differential equations (PDEs) for the two types of media (fluid and porous). A possible way to couple theses two equations is by using the penaliza ...
We present a new model reduction technique for steady fluid-structure interaction problems. When the fluid domain deformation is suitably parametrized, the coupling conditions between the fluid and structure can be formulated in the low-dimensional space o ...
Society for Industrial and Applied Mathematics2012
We seek to study numerically two-phase flow phenomena with phase change through the finite-element method (FEM) and the arbitrary Lagrangian-Eulerian (ALE) framework. This method is based on the so-called one-fluid formulation; thus, only one set of equati ...
We present a Petrov-Galerkin reduced basis (RB) approximation for the parameterized Stokes equation. Our method, which relies on a reduced solution space and a parameter-dependent test space, is shown to be stable (in the sense of Babuska) and algebraicall ...
We present a new conservative multiscale method for Stokes flow in heterogeneous porous media. The method couples a discontinuous Galerkin finite element method(DG-FEM) at the macroscopic scale for the solution of an effective Darcy equation with a Stokes ...
When modelling the cardiovascular system, the effect of the vessel wall on the blood flow has great relevance. Arterial vessels are complex living tissues and three-dimensional specific models have been proposed to represent their behaviour. The numerical ...
Gravity-driven flows can erode the bed along which they descend and increase their mass by a factor of 10 or more. This process is called "basal entrainment." Although documented by field observations and laboratory experiments, it remains poorly understoo ...
Being able to accurately reproduce the physiological phenomena which take place in blood vessels requires understanding the impact physical parameters have on the fluid’s flow. Modeling blood flow implies choosing, or defining, at least one model with the ...
A model of sedimentation-consolidation processes in so-called clarifier-thickener units is given by a parabolic equation describing the evolution of the local solids concentration coupled with a version of the Stokes system for an incompressible fluid desc ...
In this work we are interested in the numerical solution of the steady incompressible Navier-Stokes equations for fluid flow in pipes with varying curvatures and cross-sections. We intend to compute a reduced basis approximation of the solution, employing ...