193 research outputs found
Numerical Simulations of Bouncing Jets
Bouncing jets are fascinating phenomenons occurring under certain conditions
when a jet impinges on a free surface. This effect is observed when the fluid
is Newtonian and the jet falls in a bath undergoing a solid motion. It occurs
also for non-Newtonian fluids when the jets falls in a vessel at rest
containing the same fluid.
We investigate numerically the impact of the experimental setting and the
rheological properties of the fluid on the onset of the bouncing phenomenon.
Our investigations show that the occurrence of a thin lubricating layer of air
separating the jet and the rest of the liquid is a key factor for the bouncing
of the jet to happen.
The numerical technique that is used consists of a projection method for the
Navier-Stokes system coupled with a level set formulation for the
representation of the interface. The space approximation is done with adaptive
finite elements. Adaptive refinement is shown to be very important to capture
the thin layer of air that is responsible for the bouncing
An optimal adaptive Fictitious Domain Method
We consider a Fictitious Domain formulation of an elliptic partial
differential equation and approximate the resulting saddle-point system using
an inexact preconditioned Uzawa iterative algorithm. Each iteration entails the
approximation of an elliptic problems performed using adaptive finite element
methods. We prove that the overall method converges with the best possible rate
and illustrate numerically our theoretical findings
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