Nicolas CAILLER's sandbox

General Description

This is Nicolas Cailler’s sandbox, in which you will find Basilisk C codes upon self-similar solutions for the collapse of fluid interfaces and other scale invariant problems.

The work done with Basilisk has been undertaken during a PhD thesis (2021–2024) supervised by Arnaud ANTKOWIAK and Régis WUNENBURGER at Sorbonne Université, in the lab Institut Jean Le Rond \partial’Alembert.

The defense of the PhD is broadcast on YouTube, and the manuscript can be read online on the HAL portal, whereas a summarized presentation of the main goals of the thesis for the BGUM 2023 can be found on this very website.

2025-03-11

Existing Directories

• collapsing_cavities: We show how the horizon of a finite-time singularity is crossed for (self-similar) collapsing cavities, such as a bursting bubble.

• keller_miksis: The surface-tension-driven recoil of a liquid wedge is investigated, a problem addressed by Keller & Miksis in 1983. The scale invariant nature of the phenomenon is exhibited, and we provide with Basilisk an update of the authors’ results.

• lamb_oseen: A numerical study of the Lamb–Oseen vortex, highlighting the self-similar behaviour of the developing flow, firstly when working from the physical space, and secondly by performing direct numerical simulations in the associated self-similar space.

• self_sim_DNS: For the first time is implemented and documented an incompressible Navier–Stokes solver directly written in self-similar coordinates, therefore enabling to spontaneously and spectacularly converge towards steady solutions for scale invariant phenomena. Performing a DNS in the “right” space allows us to compute simulations that would not be possible otherwise, in terms of running time.

• sierou_lister: The self-similar surface-tension-driven recoil of a 3D–AXI liquid cone is investigated, a problem addressed by Sierou & Lister in 2004. We recover and extend the results of the authors, especially by applying stronger far-field dipolar flows upon the overall capillary one. In particular, self-similar capillary-inertial jet structures are discovered for the strongest intensities.

• test_cases: Tests and useful explanations on customized libraries widely used in the other projects of this sandbox are found there. In particular:

  • The management of ghost cell volume fraction values for boundaries crossed by a no-closed, mobile interface, in vel_tan;
  • An implementation of Legendre polynomials of fractional degree, in legendre_polynomials.