PinchOff: Plateau-Rayleigh Pinch-Off in Basilisk

Overview

PinchOff provides axisymmetric two-phase VOF simulations of the Rayleigh-Plateau instability and pinch-off dynamics of a liquid cylinder. The code reproduces the universal similarity scalings $r_{\min} \sim (t_0 - t)^{2/3}$ and $u_{\max} \sim (t_0 - t)^{-1/3}$ using adaptive mesh refinement and interface tracking with the Basilisk C framework.

Two simulation variants are included:

• plateau-basilisk-website.c — inviscid reference case (matches Basilisk tutorial)
• plateau-viscous.c — viscous extension with finite viscosity ratio

Background references: Popinet (2009), Popinet & Antkowiak (2011)

Physical Problem

Governing Equations

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

$$ \nabla \cdot \mathbf{u} = 0 $$

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

The volume fraction field $f$ satisfies:

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

where $\rho$ and $\mu$ are piecewise-constant densities and viscosities, $\sigma$ is the surface tension coefficient, $\kappa$ is the interface curvature, and $\delta_s$ is the interfacial delta function.

Problem Setup

A liquid cylinder of radius $R = 0.2$ is perturbed by a sinusoidal mode:

$$ r(x, t=0) = R \left(1 + A \sin(kx)\right) $$

with wavenumber $k = \pi$ and amplitude $A = 0.1$. 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 adapted to maintain at least five grid cells across the local cylinder radius, up to maxlevel = 18.

Dimensionless Parameters

Simulations are nondimensionalized with $\sigma = 1$ and $\rho_1 = 1$. Key parameters:

Parameter	Meaning	plateau-viscous	plateau-basilisk-website
$\rho_1/\rho_2$	Density ratio	100	100
$\mu_1/\mu_2$	Viscosity ratio	100	0 (inviscid)
$\sigma$	Surface tension	1	1
$R$	Cylinder radius	0.2	0.2
$k$	Wavenumber	$\pi$	$\pi$
$A$	Perturbation amplitude	0.1	0.1
maxlevel	Max AMR level	18	18

Prerequisites

Basilisk Installation

PinchOff requires the Basilisk C solver. Install or update to a locked reference:

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 comphy-lab/basilisk-C/releases.

Environment Configuration

Set the BASILISK environment variable to the Basilisk src directory. Keep the Basilisk checkout outside this repository.

Option 1: Local config file (gitignored, repo-specific)

# .project_config
export BASILISK=/path/to/basilisk/src

Option 2: Shell environment (global)

export BASILISK=/path/to/basilisk/src  # Add to ~/.bashrc or ~/.zshrc

Repository Structure

PinchOff/
├── simulationCases/          Simulation entry points
│   ├── plateau-basilisk-website.c
│   ├── plateau-viscous.c
│   ├── runCode.sh           Wrapper script (MPI/OpenGL builds)
│   └── Makefile             Basilisk Makefile
├── .github/                 Website generation and workflows
│   ├── docs/               Generated site output
│   ├── assets/             CSS, JS, fonts for docs
│   └── workflows/          CI/CD for documentation
├── AGENTS.md               Agent/build instructions
└── README.md               This file

Note: src-local/ and postProcess/ directories are not currently present.

Building and Running

Quick Start (Recommended)

Use the provided shell script for MPI or visualization builds:

cd simulationCases

# MPI run (4 processes)
./runCode.sh plateau-viscous

# Visualization build with OpenGL
./runCode.sh --view plateau-viscous

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

Requirements:

• .project_config file in repo root (or BASILISK environment variable)
• qcc compiler in $PATH

Note: The script defaults to a case named plateau (not included). Always specify the case name explicitly.

Manual Compilation

Basilisk Makefile (Serial)

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

Caution: If a directory simulationCases/plateau-viscous/ already exists (from a previous run), the Makefile may fail. Use runCode.sh or build with 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

Compile-Time Parameters

Parameters are defined as constants in the source files. Edit and recompile to change:

Parameter	Location	Description	Default
maxlevel	plateau-*.c	Maximum AMR level	18
R	plateau-*.c	Cylinder radius	0.2
k	plateau-*.c	Perturbation wavenumber	$\pi$
A	plateau-*.c	Perturbation amplitude	0.1
rho1, rho2	plateau-*.c	Phase densities	1, 0.01
mu1, mu2	plateau-viscous.c	Phase viscosities	0.01, 0.0001
sigma	plateau-*.c	Surface tension	1
tpinch	plateau-*.c	Approximate pinch-off time	0.75626

HPC Execution

Launch MPI binaries with your cluster scheduler:

# SLURM example
srun -n 16 ./plateau-viscous

# PBS/Torque example
mpirun -np 16 ./plateau-viscous

Output and Post-Processing

Output Files

Simulations write the following files in the run directory:

• log — time series of $(t, r_{\min}, u_{\max})$ written to stderr
• prof-<t> — interface profiles at specific times (from output_facets)
• movie.mp4 — interface and mesh animation (when using view.h)

Example: Capture time series to a log file:

./plateau-viscous 2> log

Scaling Analysis

Use the gnuplot fitting scripts embedded in the C file headers to extract similarity exponents from log:

# Define breakup time as the time when axial velocity is maximum
t0="`awk '{ if (NF == 3 && $3 > max) { max = $3; t0 = $1; } } END{ print t0 }' < log`"

# Fit minimum radius scaling
set logscale
fit [1e-7:1e-3] a*x**(2./3.) 'log' u (t0 - $1):2 via a
plot [1e-8:][1./2**18:]'log' u (t0 - $1):2 ps 0.5, a*x**(2./3.)

# Fit maximum velocity scaling
fit [1e-7:1e-3] a*x**(-1./3.) 'log' u (t0 - $1):3 via a
plot [1e-8:]'log' u (t0 - $1):3 ps 0.5, a*x**(-1./3.)

The fits should yield exponents $2/3$ and $-1/3$ over several orders of magnitude.

Citation

If you use this code, please cite the Basilisk solver and the relevant literature on pinch-off similarity solutions.

Paper

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

Software

@software{PinchOff,
  title   = {PinchOff: Plateau-Rayleigh Pinch-Off in Basilisk},
  author  = {TBD},
  year    = {2026},
  url     = {https://github.com/<org>/<repo>},
  note    = {Zenodo DOI: TBD}
}

References

• Popinet, S. (2009). "An accurate adaptive solver for surface-tension-driven interfacial flows." J. Comput. Phys., 228(16), 5838–5866. doi:10.1016/j.jcp.2009.04.042
• Popinet, S., & Antkowiak, A. (2011). "Numerical simulation of a viscous liquid pinch-off." Journal TBD. [Reference details TBD]

Authors

TBD — Add author names and affiliations.

License

TBD — No LICENSE file is currently included. Add a LICENSE file to clarify terms of use and redistribution.