HPC to resolve turbulence

Turbulence is the only problem classical mechanics which remains unsolved. It is mathematically described by the Navier-Stokes equations, which are derived from applying the mass, momentum and energy conservation to a fluid particle (a group of fluid molecules that can be considered to move together). The Navier-Stokes equations entail a set of partial differential equations which still does not have an analytical solution. In fact, the mathematical resolution of these equations is one of the problems of the millennium and who solves it will be given a million of US Dollars.

Despite being an extremely complex phenomenon, turbulence is present in our daily life and it has a great effect on it. The air drag force is the main energy consumer in our means of transport such as trains, aircrafts, cars or even bikes. Also, turbulence is the main sound generator in those vehicles and it can drive us mad on windy days.

The complexity of the mathematics behind airflows imposed the need of using wind tunnels since the early days of aeronautics and aerodynamics. Those huge infrastructures are really useful because they enable to recreate the flow conditions and analyse the behaviour of the bodies under these circumstances. Be that as it may, they require a huge investment to build and each test is an expensive process inside the development loop, limiting the amount of configurations that can be compared. A part from the need of the building and the energy to recreate the airflow, the main drawback from wind tunnel testing is having to build a full-of-sensors mock-up of the prototype for every change that is tested.

It is easy to see then, that having the ability of computing the airflow around the body instead of having to recreate it would reduce the costs of the development of vehicles, it would allow to test more configurations and consequently achieve better results. Here it is where High Performance Computing makes its appearance in solving this historical problem. This urgent need has encouraged several mathematicians and physicians to develop numerical methods to resolve the Navier Stokes equations, creating the science of Computational Fluid Dynamics.

Generally speaking, CFD is based on discretizing the domain in several volumes and compute the fluid magnitudes in them. The number of volumes needed will depend on the pressure and velocity gradients in each region, as the greater the gradients, a smaller size of the volumes is needed. It goes without saying that the more volumes we use, the more computational resources are needed and in the end the power and capacity of our computers are the limiting factors of the preciseness of the results.

Thanks to HPC is possible to split he volumes in the domain between the number of processors available, which allows to run much finer meshes and with the increasing performance of modern machines every time it is more feasible to solve all the flow structures in big CFD cases. However, nowadays it is still computationally unfeasible to resolve most industrial cases with enough accuracy to fully rely on CFD simulations, so turbulence and wall models have to be used.

Despite this situation, every year of HPC development, CFD gains more importance, power and accuracy which leads to the conclusion that thanks to this super technology we will be able to compute ever flow in the future.