National Institute of Standards and Technology における超伝導研究及び生活

The numerical simulation of flows with interfaces and free-surface flows is a vast topic, with applications to domains as varied as environment, geophysics, engineering, and fundamental physics. In engineering, as well as in other disciplines, the study of liquid-gas interfaces is important in combustion problems with liquid and gas reagents. The formation of droplet clouds or sprays that subsequently burn in combustion chambers originates in interfacial instabilities, such as the Kelvin-Helmholtz instability. What can numerical simulations do to improve our understanding of these phenomena? The limitations of numerical techniques make it impossible to consider more than a few droplets or bubbles. They also force us to stay at low Reynolds or Weber numbers, which prevent us from finding a direct solution to the breakup problem. However, these methods are potentially important. First, the continuous improvement of computational power (or, what amounts to the same, the drop in megaflop price) continuously extends the range of affordable problems. Second, and more importantly, the phenomena we consider often happen on scales of space and time where experimental visualization is difficult or impossible. In such cases, numerical simulation may be a useful prod to the intuition of the physicist, the engineer, or the mathematician. A typical example of interfacial flow is the collision between two liquid droplets. Finding the flow involves the study not only of hydrodynamic fields in the air and water phases but also of the air-water interface. This latter part

Direct numerical simulation of free-surface and interfacial flow

https://hal.archives-ouvertes.fr/hal-01445436/document

Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries

https://hal.archives-ouvertes.fr/hal-01445445/document

An accurate adaptive solver for surface-tension-driven interfacial flows

A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations

Volume-of-Fluid Interface Tracking with Smoothed Surface Stress Methods for Three-Dimensional Flows

Methods for the solution of boundary integral equations have changed significantly during the last two decades. This is due, in part, to improvements in computer hardware, but more importantly, to the development of fast algorithms which scale linearly or nearly linearly with the number of degrees of freedom required. These methods are typically iterative, based on coupling fast matrix-vector multiplication routines with conjugate-gradient-type schemes. Here, we discuss methods that are currently under development for the fast, direct solution of boundary integral equations in three dimensions. After reviewing the mathematical foundations of such schemes, we illustrate their performance with some numerical examples, and discuss the potential impact of the overall approach in a variety of settings.

/pdf/fast-direct-solvers-for-integral-equations-in-complex-three-3wwdj2pbew.pdf

Fast direct solvers for integral equations in complex three-dimensional domains

A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D

In this Brief Communication we consider the shape of the rim of a very viscous film retracting with velocity U0 under surface tension. We demonstrate that the film has a growing rim if and only if the Stokes length ν/U0 is smaller than the radial extent of the film. If the Stokes length is larger than the radial extent of the film the retracting edge has no rim and the film is perfectly flat. These results are discussed in light of recent experiments on the bursting of viscoelastic films.

Denis Gueyffier

Papers

Volume-of-Fluid Interface Tracking with Smoothed Surface Stress Methods for Three-Dimensional Flows

Fast direct solvers for integral equations in complex three-dimensional domains

A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D

On the bursting of viscous films

A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows