VelociFlow | CFD Solver

[WORK IN PROGRESS]

This project serves as part of my BSc thesis in Computer Science. It is a CFD (Computational Fluid Dynamics) solver for the 2D incompressible Navier-Stokes equations. The solver is based on the SIMPLE algorithm for pressure-velocity coupling, solved in an orthogonal cartesian colocated grid. The simulation library is written in C++, while the visualizations are written in Python.

How to run

1. Clone the repository
2. Select an example to run
   • Open VelociFlow-main/CMakeLists.txt
   • Change the name of the .cpp file in the add_executable line to the .cpp file you want to run
3. Compile
   • cd VelociFlow-main
   • mkdir build
   • cd build
   • cmake ..
   • make
4. Run
   • ./Simulation
   • Wait for the simulation to finish (or press q to stop it earlier)
5. Visualize
   • cd VelociFlow-main/Visualization
   • python -m venv venv
   • venv/bin/pip install -r requirements.txt
   • Create a settings.json file (look at settings-steady.json and settings-steady.json examples)
   • Open visualize.py
   • Change the name of the .json file in the settings_file variable to the name of your settings.json file
   • venv/bin/python3 visualize.py

Equations

Equations being discretized and solved using the Finite Volume Method (FVM) in 2D:

• Incompressible Navier Stokes

$$ \begin{aligned} \begin{cases} \large \nabla \cdot \vec{v} = 0 \ \\ \large \rho \bigg[ \dfrac{\partial \vec{v}}{\partial t} + (\vec{v} \cdot \nabla)\vec{v} \bigg] = -\nabla p + \mu \nabla^2\vec{v} \end{cases} \end{aligned} $$

• Convection - Diffusion

$$ \begin{aligned} \large \dfrac{\partial \vec{v}}{\partial t} + (\vec{v} \cdot \nabla)\vec{v} = \mu \nabla^2\vec{v} \end{aligned} $$

• Single Convection - Diffusion

$$ \begin{aligned} \large \dfrac{\partial \phi}{\partial t} + (\vec{v} \cdot \nabla)\phi = \Gamma \nabla^2\phi \end{aligned} $$

• Diffusion

$$ \begin{aligned} \large \dfrac{\partial \phi}{\partial t} = \Gamma \nabla^2 \phi \end{aligned} $$

Gallery

Lid-driven cavity	Kelvin-Helmholtz
Pipe	Backward-facing step
Pipe with obstacles	Von Karman

Features

Creating simulations

• 2D Simulations (both steady and unsteady)
  • Incompressible Navier Stokes (using the SIMPLE algorithm)
  • Convection - Diffusion
  • Single Convection - Diffusion
  • Diffusion
• Boundary conditions
  • Velocity inlet
  • Fixed pressure
  • No-slip wall
  • Slip wall
  • Moving wall
  • Periodic
  • Free
• Grid types
  • Orthogonal cartesian colocated
• Diffusion schemes
  • Central differencing
• Convection schemes
  • Upwind
  • Central differencing
  • QUICK Hayase
• Time schemes
  • Implicit Euler
• Dye injection (for tracing the flow)
• Ability for early stopping and restarting of the Incompressible Navier-Stokes simulations (by pressing q)
• Residual types
  • Unscaled
  • Scaled
  • Normalized
• Residual norm types
  • $\large L^1$
  • $\large L^2$
  • $\large L^\infty$
• Stopping rules (based on tolerance)
  • Absolute
  • Relative

Visualizing the results

• Create single images for steady simulations
• Create video animations for unsteady simulations
• Selecting a field to plot
  • Velocity Magnitude
  • Velocity X
  • Velocity Y
  • Pressure
  • Dye
  • Phi
  • Vorticity
  • Streamlines
  • Quivers
• Setting min and max values
• Selecting a color map
• Select a specific frame of an unsteady simulation
• Ability to blur and smooth out the result
• Produce real time animations based on $\Delta t$
• Set the frames per second (FPS) of an animation
• Include streamlines (only on velocity magnitude)
• Include quivers (only on velocity magnitude)
• Set density of streamlines and quivers
• Set color of streamlines and quivers
• Option to only show the graphics without the grid

Things to implement in the future

• Code documentation
• Features usage documentation
• Parallelizing code execution (CPU or GPU)
• Simulate real dye color mixing
• Time dependent boundary conditions
• SIMPLE algorithm variations (SIMPLER, SIMPLEC, etc.)
• Multiphase flow
• Convergence monitors