Incompressible Smoothed Particle Hydrodynamics for Violent Free-Surface Flows
Steven Lind1, Peter Stansby2, Ben Rogers2

1Mathematics Division, Manchester Metropolitan University
2School of Mechanical, Aerospace & Civil Engineering, University of Manchester

The projection-based incompressible smoothed particle hydrodynamics (ISPH) method has been shown to be highly accurate and stable for internal flows. Importantly, for many problems the pressure field is virtually noise-free in contrast to the weakly compressible SPH approach (Lee et al. 2008). However, for almost inviscid free surface flows, instabilities at the free surface can develop due to errors associated with the truncated kernels. A new algorithm is presented which gives stable and accurate solutions for a wide range of incompressible free surface and internal flows at high Reynolds number. Developing the previous method of Xu et al. (2009), particles are shifted according to Ficks law, which provides a uniform distribution of particles whose properties can be interpolated from the original positions. This technique of improving particle distributions prevents, in a general way, the highly anisotropic particle arrangements that can result in numerical instability. The algorithm is validated against a number of challenging internal and free-surfaces flows for which analytical or highly accurate numerical solutions are available. The development of a two-phase air-water (compressible-incompressible) SPH method will also be discussed, where applications of interest include violent wave-structure interaction.

References
Lee, E.-S., Moulinec, C., Xu, R., Violeau, D., Laurence, D., Stansby, P., 2008. Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method. J. Comput. Phys. 227, 84178436.
Xu, R., Stansby, P. K., Laurence., D., 2009. Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach. J. Comput. Phys. 228, 67036725.