Current engineering applications require models to reduce costs and increase time efficiency, it is always easier to model and test a turbine with a CAD (Computer-aided Design) program a than to build a new turbine every time you want to make a slight change to the design. Current CAD programs provide insight into future products as we are able to calculate stresses and loads directly within the program. But, when it comes to modeling fluids they have always come up short. Even equipment that works with fluids, such as pumps have to use generalized approximations. Other unbounded phenomenon such waves, tides and floods are incredibly difficult to approximate.

Computational Fluid Dynamics (CFD) has traditionally been used to model systems that involve these fluids. With the help of CFD programs, it is possible to calculate and observe most of the challenging fluid properties, such as density change, turbulence, cavitation and shock waves. CFD technology is purely mathematical, and based on a set of differential equations called the Navier-Stokes Equations. These equations have their limitations though. The biggest of which is that they are impossible to solve in three dimensions.

To use these equations, a series of approximations need to be used where the fluids change their behavior. It is such an important problem, that the Clay Mathematics Institute has defined a $1 million prize to anyone who can solve the Navier-Stokes Equations.

To make 3D fluid models work today, CFD programs make approximations and assumptions. Fluids are defined as a set of very small solid bodies in a mesh that interact with each other. The program can then calculate how each node of the mesh changes over time. These flow problems work great in small, enclosed systems without any turbulence, but any attempt to calculate something more complex than a few meters square requires the use of supercomputers. When it comes to unbounded fluids such as ocean or atmospheric models, the effective use of mesh systems breaks down almost completely.

Nearly 40 years ago, two astrophysics researchers, Gingold and Monaghan, encountered this problem while trying to model the movement of unbounded fluids in space. To deal with it, they developed Smoothed-Particle Hydrodynamics (SPH) for simulating fluid flows. SPH is a mesh-free method unlike the traditional CFD methods, which can easily handle large deformations and adapt to topological changes in structure.

To perform calculations on SPH, a fluid is defined as a set of irregularly spaced nodal points where their physical properties are known. This method then defines particles that can interact with their neighbors, rather than creating an entire mesh geometry as in traditional CFD applications, drastically reducing the calculations that need to be made.

Since SPH was developed for astrophysical studies, the number of applications that it has been applied to on Earth is still quite low, although there is huge potential for it.

As this technology makes it way into Earth-based models, it will help researchers solve free-surface models with large deformations easily. The current models are based on open-source code and are not included in CFD programs – representing a niche for organizations that want to create more detailed models of, for example, flood corridors in Florida or Japanese Tsunami. SPH can also be used to model volcanic lava flows, more accurate die casting, resin transfer moulding and the mixing of particulates in liquids.

The use of SPH in calculations are expected to explode in the near future. The more we can understand and predict the world around us, the more people we can help. Not only will SPH allow us to easily solve many challenging problems that face researchers today, but we will be able to solve many new problems that we do not even know exist yet.