FLATiron

1. About

FLATiron is a hierarchical, modular, finite element library for flow physics and transport phenomena. FLATiron - interpreted as FLAT-FE ( FLow and Transport using Finite Elements) - is named after the famous rock formations in Boulder, Colorado (the site of development of this package). The toolkit is based on the open-source finite element library named FEniCS, and leverages the underlying dolfinx and Unified Form Language (ufl) modules heavily in its design. The library has been developed based on research and development activities at FLOWLab at the University of Colorado Boulder. The complete documentation for the FLATiron toolkit is available here. Additionally, a collection of community learning and training resources for users and developers of FLATiron toolkit can be found on the Open Science Framework portal at this link.

2. Features

FLATiron is a library of modular implementations of stabilized finite element methods for fluid flow and transport processes. The library was designed by leveraging the ease of going from mathematical weak formulations of flow and transport problems to high-performance computing modules that is enabled by the finite element library FEniCSx; the underlying dolfinx, ffcx, and basix libraries; and the associated ufl syntaxes. A few key features include:

• Petrov-Galerkin stabilization for Navier-Stokes and advection-diffusion equations.
• Brinkman formulation for immersed porous media.
• Jump stabilized formulations for advection-diffusion transport.
• Integration of chemical reaction models in transport problems (suited for biochemical cascades).
• Fluid-thermal coupling and bioheat transport modeling capabilities.

3. Installation instructions

FLATiron is installed in two steps.

• The library relies on the dolfinx v0.9.0 library. It's recommended that dolfinx is installed using a package manager like Anaconda. This is the first requisite step.
• Thereafter, the gmsh for meshing needs to be installed. An additional library for accessing advanced file I/O capabilities, named adios4dolfinx is needed.
• Finally, the FLATiron module can be installed using pip.

Detailed installation instructions, and additional details for dolfinx base libraries are provided on the install page of FLATiron documentation available here: Install

4. Demos

For those looking to get started with using FLATiron, as well as looking to get started with stabilized finite element simulations for flow and transport problems, we have provided a collection of well documented demos along with FLATiron. These are curated with complete documentation, which you can access at the following links:

• Library Demos:
  • Link: https://flatiron-docs.readthedocs.io/en/latest/lib_demo.html
  • These are primarily meant to help users define their own physics problems using the modules provided.

5. Modules

Module documentation is available at the FLATiron documentation page at the following link: Modules. Comments and feedback on module documentation can be shared by opening an Issue on the GitHub page, or by emailing the contributors directly below.

6. How to cite our code

The best, and recommended, way to cite the FLATiron toolkit is by referencing the official FLATiron toolkit article published in the journal SoftwareX as linked below:

• Rovito, N., Holmes, J., Teeraratkul, C., and Mukherjee, D. "The FLATiron Toolkit: A Versatile Multiphysics Platform For Flow And Transport Phenomena Using The Finite Element Method." SoftwareX. 35.102968. 2026.

Additionally, below, we have provided a list of research papers that have described the underlying techniques and modules which have informed the design and implementation of the FLATiron toolkit:

• Laroche, A., Rovito, N., Liu, A., Allaeys, I., Adeoye, O., Heitsch, L., Pizella, S., Bark, D., Di Paola, J., Lee, J.M., Campbell, R., Mukherjee, D., Boilard, E., Denorme, F. "Mechanisms Of Von Willebrand Factor Activation Driving No-Reflow In Ischemic Stroke." Proceedings of the National Academy of Sciences. U.S.A. 123(30) e2610397123. 2026.

• Teeraratkul, C., Tomaiuolo, M., Stalker,T.J., and Mukherjee, D., "A Stabilized Finite Element Technique For Transport Phenomena Within And Around Immersed Porous Bodies In Flow." Physics of Fluids. 37(10):101916. 2025.

• Venkatesh, S., Teeraratkul, C., Rovito, N., Mukherjee, D., and Lynch, M. E., “High-Fidelity Computational Fluid Dynamics Modeling to Simulate Perfusion through a Bone-Mimicking Scaffold,” Computers in Biology and Medicine. 186, p. 109637. 2025. ‌

• Teeraratkul, C., Tomaiuolo, M., Stalker, T.J., and Mukherjee, D. “Investigating Clot-flow Interactions By Integrating Intravital ImagingWith In Silico Modeling For Analysis Of Flow, Transport, And Hemodynamic Forces.” Scientific Reports. 14(1):696. 2024.

• Rovito, N., and Mukherjee, D. In Silico Analysis Of Flow-mediated Drug Transport For Thrombolytic Therapy In Acute Ischemic Stroke. In: ASME International Mechanical Engineering Congress and Exposition, Vol. 88667, pp. V008T10A026. 2025.

Did you use FLATiron toolkit in one of your research publications too? Send us an email so we can include your publications in the list above? This is a big way for us to understand how our toolkit is enabling impactful research ‌

7. Questions and issues

For questions and issues, please either directly reach out to the contributors below, or report an Issue on our GitHub page.

8. License

FLATiron is released under the GNU-LGPL License.

9. Contributors

FLATiron project is created, developed, and maintained by the FLOWLab at the University of Colorado Boulder led by Prof. Debanjan Mukherjee (email: debanjan@colorado.edu).

• Dr. Chayut Teeraratkul (email: chayut.teeraratkul@colorado.edu): Lead developer, researcher, and contributor.
• Nick Rovito (email: nick.rovito@colorado.edu): Lead developer, researcher, and contributor.
• Jessica Holmes (email: jessica.holmes-1@colorado.edu): Researcher, and contributer.