# 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)

*SIAM J. Appl. Math*, vol. 43, n°2, 1983, pp. 268-277].

We reformulate the problem in self-similar coordinates

*X = (ρ/σt*and

^{2})^{1/3 }x*Y = (ρ/σt*, where

^{2})^{1/3 }y*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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