---
title: 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](http://www.lmm.jussieu.fr/~antkowiak/)
and [Régis WUNENBURGER](https://regiswunenburger.wixsite.com/sitesu) at
[Sorbonne Université](https://www.sorbonne-universite.fr/en), in the lab
[Institut Jean Le Rond $\partial$'Alembert](http://www.dalembert.upmc.fr/ijlrda/).
The defense of the PhD is broadcast on
[*YouTube*](https://www.youtube.com/watch?v=wwa9gNFYL7o),
and the manuscript can be read online on the
[HAL portal](https://theses.hal.science/tel-04965377), whereas a
summarized presentation of the main goals of the thesis for the
[BGUM 2023](http://basilisk.fr/BGUM2023/cailler.pdf) can be found on this
very website.
2025-03-11
# Existing Directories
* [`collapsing_cavities`](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`](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`](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`](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`](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`](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`](test-cases/vel_tan/);
+ An implementation of *Legendre* polynomials of fractional degree, in
[`legendre_polynomials`](test-cases/legendre_polynomials/).
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