--- 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/). ![*Collapsing conical cavity*](collapsing_cavities/collapsing_data/visc-zenon_gas_refined_s50_N8-10_m50_tinv1_amr_unif_R15_p_u.mp4)(height="200")