Small Moving Rigid Body into a Viscous Incompressible Fluid

Small moving rigid body into a viscous incompressible fluid

We consider a single disk moving under the influence of a 2D viscous fluid and we study the asymptotic as the size of the solid tends to zero. If the density of the solid is independent of ε, the energy equality is not sufficient to obtain a uniform estimate for the solid velocity. This will be achieved thanks to the optimal Lp − Lq decay estimates of the semigroup associated to the fluid-rigid...

Motion of a rigid body in a viscous fluid

We introduce a concept of weak solution for a boundary value problem modelling the motion of a rigid body immersed in a viscous fluid. The time variation of the fluid’s domain (due to the motion of the rigid body) is not known a priori, so we deal with a free boundary value problem. Our main theorem asserts the existence of at least one weak solution for this problem. The result is global in ti...

Convergence Analysis of a Penalization Method for the Three-Dimensional Motion of a Rigid Body in an Incompressible Viscous Fluid

We present and analyze a penalization method which extends the the method of [2] to the case of a rigid body moving freely in an incompressible fluid. The fluid-solid system is viewed as a single variable density flow. The interface is captured by a color function satisfying a transport equation. The solid velocity is computed by averaging at every time the flow velocity in the solid phase. Thi...

Numerical analysis of a penalization method for the three-dimensional motion of a rigid body in an incompressible viscous fluid

We present and analyze a penalization method wich extends the the method of [2] to the case of a rigid body moving freely in an incompressible fluid. The fluid-solid system is viewed as a single variable density flow with an interface captured by a level set method. The solid velocity is computed by averaging at avery time the flow velocity in the solid phase. This velocity is used to penalize ...

Existence of global weak solutions for a phase–field model of a vesicle moving into a viscous incompressible fluid