Dr. Jean-Christophe Nave
The focus of this talk is the numerical solution of the two-phase
incompressible
Navier-Stokes equations. These equations have discontinuous coefficients and
their solutions exhibit jumps in the pressure field and in gradients of the
velocity field. Traditional methods aim at smearing discontinuities.
However,
when considering numerical approximations on a grid of finite resolution,
the
smearing approach leads to inaccurate solutions.
I will give an overview of the issues encountered, and provide some
solutions to
systematically tackle these problems. Specifically, I will first present a
novel
gradient-augmented level set scheme to evolve the interface and second, a
general approach to enforce sub-grid jump conditions to a high order of
accuracy. The presented approach leads to several desirable computational
features: high order, optimally local stencils, minimal modification of
existing linear solvers, and sub-grid accuracy.
Throughout this talk, we will motivate and illustrate the present approach
using
examples such as falling liquid films, partial coalescence, bouncing
droplets on
a soap film, and walking droplets on a parametrically excited bath.
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