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Welcome to the 🌀FlowControl Wiki! [UNDER CONSTRUCTION]
- Content under construction
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The FlowControl toolbox is an open-source toolbox addressing the simulation and control of 2D incompressible flows. It aims at providing a user-friendly way to simulate flows with actuators and sensors, a possibility to readily define new use-cases and support for operators & frequency responses computations.
This page contains introductory information about the toolbox. For more in-depth content, feel free to consult the Wiki.
The toolbox is shipped with two benchmarks for flow control and allows for easy implementation of new cases.
The core of the toolbox is in Python and relies on FEniCS 2019.1.0 as a backend.
The conda environment required to run the code can be extracted from the file environment.yml. Additional path tweaking may be required for all FEniCS (dolfin module) and custom modules to be found.
[coming soon]
- By default, the toolbox integrates in time the
Incompressible Navier-Stokes equations. For a 2D flow defined by its velocity
${v}({x}, t) = [v_1({x}, t), v_2({x}, t)]$ and pressure$p({x}, t)$ inside a domain${x} = [x_1, x_2] \in\Omega$ , the equations read as follows:
- The only numerical parameter of the non-dimensional equations, the Reynolds number defined as
$Re = \frac{UL}{\nu}$ , balances convective and viscous terms.
The toolbox allows the user to define actuators for forcing and sensors to probe the flow. It also provides utility for controller design and implementation.
Two classic oscillator flows used for flow control are shipped with the current code.
| Use-case | Description |
|---|---|
| Cylinder | Flow past a cylinder at Re=100 |
| Cavity | Flow over an open cavity at Re=7500 |
The following articles were based on previous versions of the code:
- Jussiau, W., Leclercq, C., Demourant, F., & Apkarian, P. (2022). Learning linear feedback controllers for suppressing the vortex-shedding flow past a cylinder. IEEE Control Systems Letters, 6, 3212-3217.
- Jussiau, W., Leclercq, C., Demourant, F., & Apkarian, P. (2024). Data-driven stabilization of an oscillating flow with linear time-invariant controllers. Journal of Fluid Mechanics, 999, A86.
- Jussiau, W., Demourant, F., Leclercq, C., & Apkarian, P. (2025). Control of a Class of High-Dimensional Nonlinear Oscillators: Application to Flow Stabilization. IEEE Transactions on Control Systems Technology.
The philosophy of the toolbox for enabling the implementation of new use-cases easily, is the following:
- Define a new use-case: inherit the
FlowSolverabstract class - Attach
Sensors andActuators to an instance of aFlowSolversubclass - Run a simulation using an input signal
uthat can be open-loop or generated by aControllerfor closed-loop
See the toolbox Wiki for more information on how to perform these steps.
The toolbox provides additional utility related to flow control:
- Compute dynamic operators A, B, C, D and mass matrix E,
- Restart a simulation from a saved file,
- Define an arbitrary number of actuators and sensors (e.g. feedback and performance sensors),
- Export time series (measurements from sensors, perturbation kinetic energy...) and fields for visualization,
- Modify the equations, the numerical schemes and the solvers used for the time simulation,
- Parallel execution native to FEniCS,
- Can be used as backend in an optimization tool (as in Jussiau, W., Demourant, F., Leclercq, C., & Apkarian, P. (2025). Control of a Class of High-Dimensional Nonlinear Oscillators: Application to Flow Stabilization. IEEE Transactions on Control Systems Technology.).
The current roadmap is as follows:
- Complete the documentation 📖,
- Refactor and release additional control-related tools,
- Update the project to FEniCSx,
- Sort and check all utility functions,
- General form for operator computation,
- Docker/venv/pip.