4 research outputs found
On the Homogenization of Geological Fissured Systems With Curved non-periodic Cracks
We analyze the steady fluid flow in a porous medium containing a network of
thin fissures i.e. width , where all the cracks are
generated by the rigid translation of a continuous piecewise functions
in a fixed direction. The phenomenon is modeled in mixed variational
formulation, using the stationary Darcy's law and setting coefficients of low
resistance on the network. The singularities are
removed performing asymptotic analysis as which yields
an analogous system hosting only tangential flow in the fissures. Finally the
fissures are collapsed into two dimensional manifolds.Comment: 24 pages, 4 figure
On the Navier–Stokes system with the Coulomb friction law boundary condition
International audienceWe propose a new model for the motion of a viscous incompressible fluid. More precisely, we consider the Navier–Stokes system with a boundary condition governed by the Coulomb friction law. With this boundary condition, the fluid can slip on the boundary if the tangential component of the stress tensor is too large. We prove the existence and uniqueness of weak solution in the two–dimensional problem and the existence of at least one solution in the three–dimensional case, together with regularity properties and an energy estimate. We also propose a fully discrete scheme of our problem using the characteristic method and we present numerical simulations in two physical examples
A modified Lagrange-Galerkin method for a fluid-rigid system with discontinuous density
International audienceIn this paper, we propose a new characteristics method for the discretization of the two dimensional fluid-rigid body problem in the case where the densities of the fluid and the solid are different. The method is based on a global weak formulation involving only terms defined on the whole fluid-rigid domain. To take into account the material derivative, we construct a special characteristic function which maps the approximate rigid body at the discrete time level into the approximate rigid body at time . Convergence results are proved for both semi-discrete and fully-discrete schemes