Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session T35: Multiphase Flows: Modeling and Theory II
4:25 PM–6:09 PM,
Monday, November 20, 2023
Room: 202A
Chair: Gretar Tryggvason, Johns Hopkins University
Abstract: T35.00003 : Surface-tension driven flows: self-similar DNS
4:51 PM–5:04 PM
Presenter:
Nicolas CAILLER
(Sorbonne University)
Authors:
Nicolas CAILLER
(Sorbonne University)
Régis Wunenburger
(Sorbonne University)
Arnaud Antkowiak
(Sorbonne University)
We reformulate the problem in self-similar coordinates X = (ρ/σt2)1/3 x and Y = (ρ/σt2)1/3 y, where σ is surface tension, ρ mass density, x and y the physical space variables, t time and using τ = ln t as time variable. This transformation simply adds two new terms to the usual Navier-Stokes equations: a second advection term, and a source term.
The direct numerical simulation of this reformulated problem actually converges towards KM solution, which is stationary in (X, Y) coordinates, and demonstrates the stability of the scale-invariant solution. The numerical advantage of the use of (X, Y, τ) variables over (x, y, t) variables is that the characteristic length and time scales displayed by the solution are O(1) over the whole computation time span. This allows us to study the perturbation of the route towards self-similar behavior, caused by viscosity.
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