The direct numerical simulations (DNS) for this paper were conducted using Basilisk (http://basilisk.fr/). As Basilisk is a free software program written in C, it can be readily installed on any Linux machine, and it should be straightforward to then run the driver code to re-produce the DNS from this paper. Given this, the numerical solutions presented in this paper are a result of many high-fidelity simulations, which each took approximately 24 CPU hours running between 4 to 8 cores. Hence the difficulty in reproducing the results should mainly be in the amount of computational resources it would take, so HPC resources will be required. The DNS in this paper were used to validate the presented analytical solutions, as well as extend the results to a longer timescale. Reproducing these numerical results will build confidence in these results, ensuring that they are independent of the system architecture they were produced on.
It uses the drake R package that should make reproducibility of R projects much easier (just run make.R and you're done). However, it does depend on very specific package versions, which are provided by the accompanying docker image.