6 research outputs found
Une méthode level set semi-implicite pour les écoulements multiphasiques et l'interaction fluide-structure
International audienceIn this paper we present a novel semi-implicit time-discretization of the level set method introduced in [8] for fluid-structure interaction problems. The idea stems form a linear stability analysis derived on a simplified one-dimensional problem. The semi-implicit scheme relies on a simple filter operating as a post-processing on the level set function. It applies to multiphase flows driven by surface tension as well as to fluid-structure interaction problems. The semi-implicit scheme avoids the stability constraints that explicit scheme need to satisfy and reduces significantly the computational cost. It is validated through comparisons with the original explicit scheme and refinement studies on two and three-dimensional membranes
Semi-implicit Eulerian method for the fluid structure interaction of elastic membranes
In this paper we propose a novel and general approach to design semi-implicit
methods for the simulation of fluid-structure interaction problems in a fully
Eulerian framework. In order to properly present the new method, we focus on
the two-dimensional version of the general model developed to describe full
membrane elasticity. The approach consists in treating the elastic source term
by writing an evolution equation on the structure stress tensor, even if it is
nonlinear. Then, it is possible to show that its semi-implicit discretization
allows us to add to the linear system of the Navier-Stokes equations some
consistent dissipation terms that depend on the local deformation and stiffness
of the membrane. Due to the linearly implicit discretization, the approach does
not need iterative solvers and can be easily applied to any Eulerian framework
for fluid-structure interaction. Its stability properties are studied by
performing a Von Neumann analysis on a simplified one-dimensional model and
proving that, thanks to the additional dissipation, the discretized coupled
system is unconditionally stable. Several numerical experiments are shown for
two-dimensional problems by comparing the new method to the original explicit
scheme and studying the effect of structure stiffness and mesh refinement on
the membrane dynamics. The newly designed scheme is able to relax the time step
restrictions that affect the explicit method and reduce crucially the
computational costs, especially when very stiff membranes are under
consideration
An interface capturing method for liquid-gas flows at low-Mach number
Multiphase, compressible and viscous flows are of crucial importance in a
wide range of scientific and engineering problems. Despite the large effort
paid in the last decades to develop accurate and efficient numerical techniques
to address this kind of problems, current models need to be further improved to
address realistic applications. In this context, we propose a numerical
approach to the simulation of multiphase, viscous flows where a compressible
and an incompressible phase interact in the low-Mach number regime. In this
frame, acoustics is neglected but large density variations of the compressible
phase can be accounted for as well as heat transfer, convection and diffusion
processes. The problem is addressed in a fully Eulerian framework exploiting a
low-Mach number asymptotic expansion of the Navier-Stokes equations. A Volume
of Fluid approach (VOF) is used to capture the liquid-gas interface, built on
top of a massive parallel solver, second order accurate both in time and space.
The second-order-pressure term is treated implicitly and the resulting pressure
equation is solved with the eigenexpansion method employing a robust and novel
formulation. We provide a detailed and complete description of the theoretical
approach together with information about the numerical technique and
implementation details. Results of benchmarking tests are provided for five
different test cases