This code was developed as part of the Transonic Aerodynamics course at Polytechnique Montréal by Corentin Latimier, Tristan Defer and Paramvir Lobana.

Objective

The purpose of this solver is to compute fluid flow around airfoils by solving the Euler equations using the Finite Volume Method (FVM). The key objectives are:

• Accuracy: Efficiently capture flow characteristics in subsonic, transonic, and supersonic regimes.
• Speed: The solver is entirely vectorized, enabling faster computations and efficient handling of large grids.

The figures below show the typical pressure field for different flow regimes (from left to right: supersonic, transonic, subsonic), with results obtained for an angle of attack of 1.25°.

Input and Output

Input

The solver requires the following input:

• Mesh Grid: The computational mesh must be provided in Plot3D format. This format defines the grid points and the structure of the mesh.
• Farfield Mach Number: The freestream Mach number used to define the flow conditions at infinity.
• Angle of Attack (AOA): The angle of attack of the airfoil, typically specified in degrees.

Output

The solver generates the following outputs:

• Cp Curve: The pressure coefficient (Cp) curve along the surface of the airfoil, visualizing pressure distribution.
• Aerodynamic Coefficients:
  • Cl: Lift coefficient.
  • Cd: Drag coefficient.
  • Cm: Moment coefficient (calculated at the quarter chord).
• Computational Time: The total time taken for the simulation to run.
• Residuals Plot: A plot showing the convergence of the residuals during the simulation.
• .dat File: Data file containing the simulation results, which can be imported into Tecplot 360 for further post-processing and visualization.

Boundary Conditions

• Inflow and Outflow: Implemented using Riemann invariants for both subsonic and supersonic flow conditions.
• Wall Boundary: A no-slip condition is implemented to simulate the effects of a solid wall on the flow field.

Numerical Schemes

The solver includes the following numerical methods:

• Convective Fluxes: Central scheme with artificial dissipation.
• Time Integration:
  • Explicit Euler time integration scheme.
  • Runge-Kutta 2nd order (RK2) integration scheme.
• Time Stepping:
  • Global time step for all grid cells.
  • Local time step for increased efficiency (acceleration technique).

Code Structure

• NACA0012grids/: Contains all the grids used.
• modules/: Source files of the solver (Python).
• examples/: Verification results for NACA0012 airfoil, including:
  • Flow regimes: Subsonic (M = 0.5), Transonic (M = 0.8), and Supersonic (M = 1.5).
  • Angles of Attack: 0° and 1.25°.
• main.py: Main script to modify and adapt the simulation to your specific case.

Dependencies

The solver relies on the following Python libraries and built-in modules:

• os: Used for file and directory manipulation, including creating directories with makedirs.
• time: Utilized for performance tracking and timing the computation process.
• matplotlib: A plotting library for visualizing results
• numpy: A fundamental library for numerical computing, used for array manipulation and mathematical operations.