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README.md

vic2d

A command-line two-dimensional fluid simulator using a novel semi-Lagrangian advection technique

Building vic2d

We are now using CMake to build the code, though you can still use the unmaintained unix Makefile.

git clone https://github.com/markstock/vic2d.git
cd vic2d
mkdir build
cd build
cmake -DCMAKE_BUILD_TYPE=Release ..
make

Or, Windows users can run the cross-compiled binary included in this distribution (vic2d.exe).

Running vic2d

To get a list of options, run

vic2d -h

Note that all diffusivities are coefficients, so for Reynolds number 10000, you should set momentum diffusivity with -vd 0.0001

Also note that the actual resolution of the output images will be one higher than that given on the command-line. So -x 1024 -y 1024 will generate square PNG images with 1025 pixels on a side. And any input images for such a run should have 1025 pixels on a side. I know, this is not intuitive. I created it this way because for the multigrid solver to function efficiently, you should try to run at resolutions that are small multiples of large factors of 2, so 2560 (5 * 128) is much better than 2544 (159 * 16), and those numbers are easier to remember.

For some sample command lines and output, including links to YouTube videos, check out the old vic2d page.

Theory

This code uses a vortex method solver, which means that pressure doesn't enter in the equations: the formulation is in velocity-vorticity coordinates. The velocity-vorticity inversion is accomplished with MUDPACK, a multigrid solution method. Interpolation to and from the grid is done with a 4th order kernel (M4'). Advection uses a semi-Lagrangian method, in which the vorticity at each grid point is drawn from a 4th order (Runge-Kutta) backward-looking projection. All of these methods contribute to the code's remarkable lack of numerical diffusion - you can run problems with Reynolds numbers in the hundreds of millions - though the drawback is that the simulation is not unconditionally stable.

The idea for a semi-Lagrangian vortex methods comes from a 1969 paper on atmospheric physics that I, unfortunately, cannot find any more.

Thanks

This code uses libpng and mudpack, a multigrid solver. All the rest of this ugly, ugly code is mine.

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Two-dimensional semi-Lagrangian vortex method for very low viscosity fluid simulation

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