SPH Method Applied to Naval-Hydrodynamic Problems

Andrea Colagrossi, Giuseppina Colicchio
2006 unpublished
Introduction. Common problems in naval hydrodynamic and coastal engineering are the studies of general internal and external flows. Classic methods of solution have to face break down when dealing with large deformations and fragmentations of the air-water interface. Possible algorithms of solutions can be based on fixed-grid solvers of the fluid dynamic equations coupled with techniques to capture the interface evolution, like Level Set (LS) or Volume Of Fluid (VOF). These methods proved to be
more » ... suitable in many circumstances but still much work is required to improve them in terms of solution validity. An alternative meshless technique is the Smoothed Particle Hydrodynamics (SPH) method. For it, no computational grid is introduced in the domain (meshless character) and the flow evolution is described following the motion of a set of fluid particles (Lagrangian character). It has been applied to the study of some internal (sloshing and dam-break problem) and external flows (breaking and post-breaking evolution of bores propagation toward beaches and bow breaking waves generated by fast slender vessels). Governing equations. The SPH formulation assumes the fluid inviscid and the flow free to have rotational motion; so that the problem is governed by the Euler equation. Moreover, the SPH method considers the flow as weakly-compressible, meaning that the speed of sound c = dp/dρ is at least one order of magnitude greater than the maximum flow velocity. Since the flow is assumed isentropic, two additional equations are then required to complete the problem: a continuity equation for the density field ρ, and an equation of state directly linking the latter quantity to the pressure field. The resulting system of PDE is: