For that purpose I wrote a C++ code that runs on CPU-cluster by parallelizing it with MPI. The whole code can be found at my github page.
As a test problem, I chose the Kelvin-Helmholtz instability, which consists of 2 separate fluids flowing in opposite directions. If a small perturbation is introduced, the shear flow will become unstable and produce turbulence like structures and eddies. Below, a simulation with a resolution of 1152x1152 grid points is shown. That simulation was conducted on 1152 CPUs on the JUWELS HPC system.