Finite Differences Navier-Stokes Solver

This project implements a solver based on finite differences for the Navier-Stokes equations. The solver is designed to handle multiple physics problems, with the final goal of solving Brinkman flow for a generic geometry. It allows computations on a default cubic domain as well as on an input mesh using the Brinkman penalization method.

Our multiphysics solver is capable of solving a variety of problems, including Navier-Stokes and parabolic problems. This flexibility enables a broad range of simulations in fluid dynamics.

Requirements

To compile and run the project, make sure you have the following tools and libraries installed and configured:

• Compiler: GCC with C++20 support
• Libraries:
  • PETSc
  • VTK
  • Eigen

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Installation

1. Load the required modules:
   Before compiling or running the program, load the necessary modules. Ensure that your environment is correctly set up by running:

   source /u/sw/etc/bash.bashrc
   module load gcc-glibc
   module load eigen
   module load vtk
   module load petsc

2. Compile the project: After loading the modules, compile the project according to the chosen by running:

   make clean
   make FILES="navier_stokes.cpp" #for Navier-Stokes and Brinkman problem
   make FILES="stokes.cpp" #for Navier-Stokes and Brinkman problem
   make FILES="inviscid_euler.cpp" #for Navier-Stokes and Brinkman problem
   make FILES="advection_diffusion.cpp" #for Navier-Stokes and Brinkman problem
   make FILES="parabolic.cpp" #for parabolic problems
   

3. Usage To run the solver, execute the following command:

   ./bin/main

   For the Brinkman solver, the name of the .stl file must be specified. An example mesh is provided. To run the solver on the example mesh, execute the following command:

   ./bin/main caroitd.stl

   The program will compute the solution and store the results in the results directory.

Simulation Results

Velocity Magnitude for Navier-Stokes incompressible flow at Re=1	Velocity Magnitude for Navier-Stokes incompressible flow at Re=2000
Parabolic Flow with μ=10	Brinkman Flow Simulation Re=200

These examples showcase the solver's ability to handle various flow regimes and conditions.

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Developed by Davide Galbiati and Alessandra Gotti