An implementation of the Viscous Vortex Domains (VVD) method.

The VVD method is a mesh-free method of computational fluid dynamics for directly numerically solving 2D Navier-Stokes equations in Lagrange coordinates. It doesn't implement any turbulence model and free of arbitrary parameters.

• Installation
• Flow simulation
• Results postprocessing
  • vvxtract
  • vvplot, vvencode
  • gpquick
  • vvawk
• Building from source

curl -s https://packagecloud.io/install/repositories/vvflow/stable/script.deb.sh -o vvflow.deb.sh
sudo bash ./vvflow.deb.sh
sudo apt install vvflow

Binary packages are hosted at packagecloud.io. For today, those are available for ubuntu 22.04 (jammy) and 24.04 (noble).

You can also try installing it on other dists, more modern dists are usually compatible. To do so specify the version manually:

sudo os=ubuntu dist=noble bash ./vvflow.deb.sh
sudo apt install vvflow

⚠️ For performance reasons it's recommended to build vvflow from source.

Don't hesitate to open an issue if you encounter any problems.

Both defining the CFD problem and running the simulation is performed by the command vvflow. It's a Lua interpreter, so it supports everything that Lua supports (and even more).

For a start, one can copy the example simulation from doc:

cp -R /usr/share/doc/vvflow/example/ ./vvflow-demo
cd ./vvflow-demo
chmod +x ./cyl_re600.lua
./cyl_re600.lua
export OMP_NUM_THREADS=1 # disable multi-threading for now
vvflow --progress ./cyl_re600.h5

This will compose the CFD problem as described in cyl_re600.lua and run the simulation (for a minute or two).

The vvflow can be run on a PBS cluster:

#!/bin/bash
qsub -d. -l nodes=1:ppn=6 -N testrun <<'EOF'
    export OMP_NUM_THREADS=$PBS_NUM_PPN;
    exec vvflow cyl_re600.h5;
EOF

The results are saved to the current working directory during the simulation:

• stepdata_cyl_re600.h5 - time series of integral parameters (forces, bodies dispositions, etc.)
• results_cyl_re600/*.h5 - snapshots of the simulation space over time

Those are raw data, which can be processed using the following tools:

• vvxtract
• vvplot, vvencode
• gpquick
• vvawk

The vvxtract tool is primarily used to process stepdata files:

$ vvxtract stepdata_cyl_re600.h5 --list
body00/delta_position
body00/force_friction
body00/force_holder
body00/force_hydro
body00/holder_position
body00/speed_slae
time

$ vvxtract stepdata_cyl_re600.h5 time body00/force_hydro | head -n5
#time   body00/force_hydro[1]   body00/force_hydro[2]   body00/force_hydro[3]
+0.000000e+00   +3.140723e+01   -2.354987e-14   -1.770759e-15
+5.000000e-02   +4.766549e-01   +2.608255e-06   +7.130145e-15
+1.000000e-01   +8.190494e-01   -1.868534e-03   -5.548347e-05
+1.500000e-01   +7.309763e-01   -1.069637e-04   +5.027510e-05

The vvxtract tool can also process results files. In this case it acts as the opposite of the vvflow and outputs the simulation space info in a Lua-like format.

To visuzalize the simulation space use the vvplot tool. It requires gnuplot program, so ensure it is installed first:

sudo apt install gnuplot
vvplot results_cyl_re600/000150.h5 ./ -BV -x -1,4 --size 480x360

Draw an animation:

mkdir -p images_cyl_re600
for f in $(ls results_cyl_re600/*.h5); do
    vvplot $f images_cyl_re600 -BV -x -2,20
    echo $f
done

A single movie can be encoded with the vvencode tool. Install FFmpeg first if you don't have it yet.

sudo apt install ffmpeg
vvencode 'images_cyl_re600/*.png' cyl_re600.mp4

The gpquick tool is useful for previewing stepdata files:

vvxtract stepdata_cyl_re600.h5 time body00/force_holder \
| gpquick --points -u 1:3 -y -0.5 0.5 --size 480 360 -o fy_raw.png;
open fy_raw.png

This is a bunch of helpful awk scripts, like command-line MS-Excel. It is supposed to be used in combination with vvxtract.

• vvawk.avg: the arithmetic mean in a column.
• vvawk.sd: the standard deviation in a column.
• vvawk.zeros: find zeroes.
• vvawk.mavg: the moving average in a column.
• vvawk.drv: the derivative.
• vvawk.ampl: the amplitude in a column - avg(max) - avg(min).

Example of moving average:

vvxtract stepdata_cyl_re600.h5 time body00/force_holder \
| vvawk.mavg -v col=3 - \
| gpquick --lines -u 1:3 -y -0.5 0.5 --size 480 360 -o fy_mavg.png;
open fy_mavg.png

Install build and runtime dependencies:

sudo apt-get update
sudo apt-get install build-essential cmake make git liblapack-dev gnuplot

Build the project:

git clone https://github.com/vvflow/vvflow.git
cd vvflow
cmake -Bbuild -S. \
    -DCMAKE_BUILD_TYPE=RelWithDebInfo \
    -DCMAKE_INSTALL_PREFIX=$HOME/.local/vvflow \
    -DCMAKE_INSTALL_RPATH=$HOME/.local/vvflow/lib
make -C build
make -C build install

Update the PATH shell environment accordingly:

echo 'export PATH="$HOME/.local/vvflow:$PATH"' >> ~/.bashrc
source ~/.bashrc