dnsbox is a fortran code for the direct numerical simulation (DNS) of the sinusoidally forced Navier-Stokes equations (Kolmogorov flow) in a triply periodic domain.

To compile in a Linux environment, you need the development libraries of:

• openmpi
• fftw3
• BLAS
• LAPACK

and GFortran (version 9 or higher). On Ubuntu, the packages "build-essential gfortran libfftw3-dev libopenmpi-dev libblas-dev liblapack-dev" should be sufficient.

To compile the simulator, do

make

Simulations are started from a pair of files: state.000000 containing the state data and parameters.in containing the physical, output and debugging parameters.

Such a sample initial condition that leads to turbulence with a lifetime longer than 10 000 is in test/. To run it, you can create a folder, say, rundir,

mkdir rundir

copy the simulator binary (dns.x), the initial condition (state.000000) and the parameter input file (parameters.in) there,

cp dns.x rundir/
cp test/* rundir/

go to rundir,

cd rundir

and run the simulator on N cores, detaching from the terminal, and redirecting stdout (1) and stderr (2) to the file log,

nohup mpirun -np N dns.x > log 2>&1 &

Take note of the output process ID, say 123456, you can use it to kill the simulation,

kill 123456

unless it stops by itself due to laminarization, runtime limits (see parameters.in) or errors.

One can also start simulations from random initial conditions by setting IC to -1.

As the run goes on, it will write state files (state.123456) and a file containing observables and time-stepper data (stat.gp). To visualize stat.gp, you can do

dnsstats ./ 0 -1

If you use dnsbox in your research, please cite

• [YHB2021] G. Yalnız, B. Hof, N. B. Budanur, Coarse Graining the State Space of a Turbulent Flow Using Periodic Orbits. Physical Review Letters 126, 244502 (2021), arXiv:2007.02584.

• N. B. Budanur, H. Kantz,
  Scale-dependent Error Growth in Navier--Stokes Simulations. Physical Review E 106, 045102 (2022), arXiv:2209.01064.

• G. Yalnız, B. Hof, N. B. Budanur, Coarse Graining the State Space of a Turbulent Flow Using Periodic Orbits. Physical Review Letters 126, 244502 (2021), arXiv:2007.02584.