For a long time, SPH used an empirical term to describe viscosity and shear effects.  However, as demonstrated by numerous researchers (e.g. Morris et al. 1997), this is inadequate for describing viscous flow effects properly. 

At present, we are researching how to capture coherent turbulent structures within complex free-surface flow fields by enhancing the description of viscous effects.  To this end, we have implemented the particle equivalent of a Sub-Grid Scale (SGS) description in a type of Large-Eddy Simulation (LES) simulation.  Similar work has been for Incompressible SPH (I-SPH) for free-surface flows by  Lo & Shao (2002), etc., but to date, not for (slightly) compressible SPH.

The animations on this page represent our first attempts to implement a combined SPH and sub-particle scale (SPS) scheme.  As our model is still slightly compressible, we have used Favre-averaging with a standard Smagorinsky viscosity model.  For the solid walls, we have used Monaghan's repulsive force boundary condition  (Monaghan & Kos 1999).

For my ICCE2004 presentation complete with animations, click here (62MB) - please be patient!

2-D Weakly Plunging Breaking Wave on a Beach
This 2-D breaking wave (surf similarity number 0.4) demonstrates the one of the key advantages of using SPH to model free-surface hydrodynamics.  The overturning wavefront is nicely captured, and this is then followed by the highly turbulent flow field predicted by the SPS-LES scheme as the turbulent bore propagates up the beach generating turbulent flow structures that persist beyond the passage of the original wave (avi: 5.5MB).



3-D Weakly Plunging Breaking Wave on a Beach
This 3-D breaking wave is essentially the same case as for the 2-D case above, only in 3-D.  The simulation is too coarse, but is a taster of things to come.  As part of the effort towards capturing coherent turbulent structures (focussing on their formation mechanisms, role and importance), the same SPH-SPS scheme has been implemented and looks to be capturing some eddies even at this coarse resolution (avi: 14MB).
The following animation is the same case, but looking at the vertical vorticity in a horizontal plane at an intermediate water depth (avi: 17MB):


Solitary Wave with periodic Open Boundaries
Clearly, this is not a turbulent flow field!  However, this case demonstrates that SPH-SPS does not produce any spurious flow phenomena (i.e. is not doing anything it shouldn't), and also shows that a solitary wave can be propagated without loss of form which is difficult to do with empirical viscosity.