PinchOff: Plateau-Rayleigh Pinch-Off in Basilisk

Overview

PinchOff contains axisymmetric two-phase VOF simulations of the Rayleigh-Plateau instability and pinch-off scaling of a liquid cylinder. The cases reproduce the similarity laws \(r_{min} \sim (t_0 - t)^{2/3}\) and \(u_{max} \sim (t_0 - t)^{-1/3}\) using adaptive mesh refinement and interface tracking. Two variants are provided: an inviscid setup (plateau-basilisk-website.c) and a viscous setup (plateau-viscous.c).

Background references: Popinet (2009) and Popinet & Antkowiak (2011).

Physics

Problem Description

A liquid cylinder of radius \(R = 0.2\) is perturbed by a sinusoidal mode with wavenumber \(k = \pi\) and amplitude \(A = 0.1\) in an axisymmetric domain. Surface tension drives the Rayleigh-Plateau instability, leading to necking, pinch-off, and satellite drop formation. The interface is tracked with a VOF field, and the mesh is refined to keep at least five cells across the local radius up to maxlevel = 18.

Governing Equations

The solver integrates the axisymmetric incompressible Navier-Stokes equations for two phases with surface tension:

\[\nabla \cdot \mathbf{u} = 0\]

\[\rho\left(\frac{\partial \mathbf{u}}{\partial t} + \mathbf{u} \cdot \nabla \mathbf{u}\right) = -\nabla p + \nabla \cdot (2\mu \mathbf{D}) + \sigma \kappa \delta_s \mathbf{n}\]

The VOF field \(f\) satisfies:

\[\frac{\partial f}{\partial t} + \mathbf{u} \cdot \nabla f = 0\]

Dimensionless Parameters and Defaults

The simulations are nondimensionalized with \(\sigma = 1\) and \(\rho_1 = 1\). Key defaults are:

Parameter	Meaning	plateau-viscous	plateau-basilisk-website
\(\rho_1/\rho_2\)	Density ratio	100	100
\(\mu_1/\mu_2\)	Viscosity ratio	100	inviscid (default \(\mu = 0\))
\(\sigma\)	Surface tension	1	1
\(R\)	Initial cylinder radius	0.2	0.2
\(k\)	Perturbation wavenumber	\(\pi\)	\(\pi\)
\(A\)	Perturbation amplitude	0.1	0.1
`maxlevel`	Max AMR level	18	18

Basilisk (Required)

First-time install (or reinstall):

curl -sL https://raw.githubusercontent.com/comphy-lab/basilisk-C/main/reset_install_basilisk-ref-locked.sh | bash -s -- --ref=v2026-01-29 --hard

Subsequent runs (reuses existing basilisk/ if same ref):

curl -sL https://raw.githubusercontent.com/comphy-lab/basilisk-C/main/reset_install_basilisk-ref-locked.sh | bash -s -- --ref=v2026-01-29

Note: Replace v2026-01-29 with the latest release tag from https://github.com/comphy-lab/basilisk-C/releases.

Set BASILISK to the Basilisk src path and keep the Basilisk checkout outside this repository:

# .project_config (gitignored)
export BASILISK=/path/to/basilisk/src

You can also export BASILISK directly in your shell.

Repository Structure

├── simulationCases/
│   ├── plateau-basilisk-website.c
│   ├── plateau-viscous.c
│   ├── runCode.sh
│   └── Makefile
└── .github/                  Website assets and workflows

src-local/ and postProcess/ are not present currently.

Running the Code

Using Scripts (Recommended)

cd simulationCases

# MPI run (4 ranks) using the default script
./runCode.sh plateau-viscous

# Visualization build/run (single rank, OpenGL)
./runCode.sh --view plateau-viscous

# Inviscid variant
./runCode.sh plateau-basilisk-website

runCode.sh expects a .project_config file in the repo root (used to set BASILISK) and a working qcc. The script defaults to plateau; this repository does not include plateau.c, so pass the case name explicitly.

Manual Compilation

Basilisk Makefile (serial):

make -C simulationCases plateau-viscous
./simulationCases/plateau-viscous

Note: runCode.sh creates simulationCases/<case>/ output directories. In a clean clone, make -C simulationCases <case> builds an executable with the same name. If a directory with that name already exists, prefer runCode.sh or build into a different target name.

Serial qcc:

qcc -O2 -Wall -disable-dimensions simulationCases/plateau-viscous.c -o plateau-viscous -lm
./plateau-viscous

OpenMP (shared memory):

qcc -O2 -Wall -disable-dimensions -fopenmp simulationCases/plateau-viscous.c -o plateau-viscous -lm
export OMP_NUM_THREADS=8
./plateau-viscous

MPI (distributed memory):

CC99='mpicc -std=c99' qcc -Wall -O2 -D_MPI=1 -disable-dimensions simulationCases/plateau-viscous.c -o plateau-viscous -lm
mpirun -np 4 ./plateau-viscous

Visualization build (OpenGL):

qcc -O2 -Wall -disable-dimensions simulationCases/plateau-viscous.c -o plateau-viscous -L$BASILISK/gl -lglutils -lfb_tiny -lm
./plateau-viscous

Parameters (Compile-Time)

These cases use compile-time constants. Edit them in the .c files and recompile:

Parameter	Location	Description	Default
`maxlevel`	plateau-*.c	Maximum AMR level	18
`R`	plateau-*.c	Base radius	0.2
`k`	plateau-*.c	Perturbation wavenumber	pi
`A`	plateau-*.c	Perturbation amplitude	0.1
`rho1`, `rho2`	plateau-*.c	Densities	1, 1e-2
`mu1`, `mu2`	plateau-viscous.c	Viscosities	1e-2, 1e-4
`sigma`	plateau-*.c	Surface tension	1

HPC Cluster Execution

Use your scheduler to launch the MPI binary, for example:

srun -n 4 ./plateau-viscous

Post-Processing

Outputs are written in the run directory:

prof-<t>: interface profiles from output_facets
movie.mp4: interface and mesh visualization (when using view.h)
log: time series of (t, r_min, u_max) when you redirect stderr

Example:

./plateau-viscous 2> log

Use the gnuplot snippets in the case headers to fit the scaling laws from log.

Citation

If you use this code, please cite Basilisk and the relevant pinch-off literature. Add paper and software DOIs here when available.

Paper

@article{TBD,
  title = {TBD},
  author = {TBD},
  journal = {TBD},
  year = {TBD},
  doi = {TBD}
}

Software

@software{PinchOffTBD,
  title = {PinchOff: Plateau-Rayleigh pinch-off in Basilisk},
  author = {TBD},
  year = {2026},
  url = {https://github.com/<org>/<repo>},
  note = {Add Zenodo DOI when available}
}