soft-hydraulic-ale-fsi

Arbitrary Lagrangian–Eulerian fluid–structure interaction (FSI) solvers for soft hydraulics problems — pressure-driven flow sin compliant microchannels where the fluid and elastic solid are two-way coupled.

Built on FEniCSx / DOLFINx and customized specifically for 2D problems, using quasi-direct coupling for unsteady problems and a monolithic approach for steady problems.

Purpose

Simulate and analyze the deformation of a soft elastic wall driven by viscous (and inertial) flow, targeting elastoinertial regimes relevant to microfluidics and soft robotics. The code supports both steady and transient problems, Newtonian and shear-thinning (Carreau) fluids, and benchmarking against analytical solutions.

Repository contents

File / folder	Description
ALE-FSIx_2D.ipynb	Main transient solver — time-dependent ALE-FSI simulation in DOLFINx
ALE-FSIx_2D_steady.ipynb	Steady solver — monolithic steady ALE-FSI formulation
build_gmsh_x.py	Mesh generation helper: two-subdomain (fluid + solid) rectangle mesh via gmsh, returns tagged DOLFINx mesh
strip_widgets.py	Utility to strip notebook widget metadata before committing
dolfin-2019/	Legacy solvers based on the original FEniCS (DOLFIN 2019)
theory_steady/	Analytical theory notebooks for steady FSI (including shear-thinning models)
theory_oscillatory/	Analytical theory notebooks for oscillatory/streaming FSI (elastoinertial rectification) in channels and tubes

Key features

• ALE-FSI discretization (fluid momentum + continuity + solid momentum + mesh motion coupled together)
• Monolithic steady solver and quasi-directly coupled unsteady solver (monolithic solid+fluid, separate mesh motion)
• Uses gmsh-based meshing with tagged subdomains and boundary facets
• Allows both velocity-inlet and pressure-inlet, both with pressure-outlet boundary conditions
• Implements Carreau viscosity model for shear-thinning fluids
• Implements 2D-restricted neo-Hookean solid with isochoric–volumetric splitting to handle strong compression for confined elastic layers
• Implements velocity-based damping in the unsteady solid momentum equation for robust convergence to steady state (if desired)
• Offers analytical steady-state benchmarks
• In-built post-processing and Matplotlib visualization

Dependencies

• FEniCSx / DOLFINx (next-generation FEniCS), see this useful guide for setting it up and customizing your environment
• Gmsh Python API
• PETSc / petsc4py, MPI / mpi4py
• NumPy, SciPy, Matplotlib

Cautionary note for DOLFIN version

To run the legacy codes from the dolfin-2019 folder, it is recommended to use a fresh Conda environment, let's call it fenics2019, with this precise command:

    conda create -n fenics2019 -c conda-forge fenics mshr

Any other installation order may result in mshr failing. Then, install any further Python tools and libraries through pip install rather than with conda to ensure that no dependencies get updated and break legacy dolfin and mshr. Complicated, I know. 😵‍💫

Credits

Largely developed (ca. Fall 2025–Spring 2026) and maintained by Ivan C. Christov, Purdue University, with assistance from GitHub Copilot and Claude.

Initial unsteady code forked from an earlier version based on David Kamensky's fitted-fsi-example.