2D Fluid Dynamics Simulation

A 2D fluid dynamics simulation library implemented in C++. Poisson's equation is solved over a two-dimensional grid using the Jacobi iteration method. Contains a serial implementation, and a hybrid implementation using MPI and OpenMP.

Dependencies

• MPI 3.1 (other versions might work)
• OpenMP 4.5 (other versions might work)

Usage

The headers in inc/poisson2d/fluid_dynamics contain the following classes:

• Grid: A 2D grid class that stores the data
• Bound: A class that stores boundary conditions as std::function objects
• Solver: A class that that solves Poisson's equation using the Jacobi iteration method
• SolverMpi : Extends Solver to solve the problem in parallel using MPI and OpenMP
• MpiGrid2D : Abstraction layer for MPI communication on a Cartesian grid

To use the library, include the appropriate header file:

• poisson2d.h : Serial implementation contains Grid, Bound and Solver classes
• poisson2d_mpi.h : MPI implementation additionally contains SolverMpi and MpiGrid2D classes

Building

To build the example programs and tests, run the following commands:

mkdir build
cmake -S . -B build
make -C build --no-print-directory

which will create the following executables:

• FDSimSerial: Serial example
• FDSimMPI: MPI example
• FDSimUnitTests: Unit tests

Running

Serial example

The serial executable FDSimSerial can be run with the following command:

build/FDSimSerial -L 102 -epsilon 1e-2 -max_iter 3000

where the arguments are:

• -L : The size of the grid
• -epsilon : The convergence criterion
• -max_iter : The maximum number of iterations

MPI example

The parallelized executable FDSimMPI can be run with the following command:

export OMP_NUM_THREADS=4
mpirun -np 9 --oversubscribe build/FDSimMPI -L 102 -epsilon 1e-6 -max_iter 10000

where the arguments are the same as the serial example, with the additional -np flag to specify the number of MPI processes.

Visualizing the results

The output of the example simulation is stored in a file named velocity.bin. To visualize the results, run the python script plot.py in the plot directory:

python3 plot/plot.py

which will generate a plot of the velocity field in the plot/plots directory. For the example above, the plots will be saved as

• plot/plots/velocity_stream.png

• plot/plots/velocity_magnitude.png

Tests

The unit tests can be run with the following command:

build/test/FDSimUnitTests