Introduction

This is a Fortran implementation of the vortex method, a numerical technique for simulating fluid flow. The code solves the two-dimensional incompressible Euler and Navier-Stokes equations using a Lagrangian particle-based approach, where the fluid is represented by a collection of discrete vortices.

Dependencies

To run this program, you need a Fortran 77 compiler (tested with GNU Fortran, Intel, PGI, and HPE/Cray) and make.

Build

By default, the program uses GNU Fortran. To build the program, run:

$ (cd lib && make)
$ (cd example/gauss && make)
$ (cd example/omegaI && make)

Edit the conf.mk file to use a different Fortran compiler,

Unit tests

Navigate to the example/unit directory and run the following command (you will need to have gnuplot installed)

$ make
$ ./make_box.gp data/points

This will create a box for paritcles in data/points

Run

To run the program, navigate to one of the example directories and run the main executable. Here are two examples:

Elliptic Lamb–Oseen vortex:

$ cd example/gauss
$ ./main
 initial number of Particles        60025
           Particles :    60025      Time :  0.3405
...	   

Melander, McWilliams, and Zabusky vortex:

$ cd example/omegaI
$ ./main
 initial number of Particles       672400
           Particles :   672400      Time : 12.1381
...

Postprocessing

You can use the tool/heat.awk script to generate a heatmap from the simulation data. Here's an example:

$ awk -f tool/heat.awk example/gauss/w.00000001.dat > heat.ppm
$ convert heat.ppm heat.png

Results

References

Cottet, G. H., & Koumoutsakos, P. D. (2000). Vortex methods: theory and practice (Vol. 8). Cambridge: Cambridge university press.