Simulating Flows with SPH: Recent Developments and Applications

The chapter discusses recent theoretical developments and practical applications of the Smoothed Particle Hydrodynamics (SPH) method with specific concern to liquids. SPH is a meshless Lagrangian technique for the approximate integration of spatial derivatives, using particle interpolation over a compact support, without the usage of a structured grid. Its main related advantage is the capability of simulating the computational domain with large deformations and high discontinuities, bearing no numerical diffusion because advection terms are directly evaluated. SPH has recently become very popular for the simulation of fluid motion using computers, covering different fields, e.g. free surface flows, multiphase flows, turbulence modelling. In the following, recent theoretical achievements of SPH are firstly presented, concerning (1) numerical schemes for approximating governing equations, such as the Navier Stokes ones, most widely adopted in fluid dynamics, (2) smoothing or kernel function properties needed to perform the function approximation to the Nth order, (3) restoring consistency of kernel and particle approximation, yielding the SPH approximation accuracy. Secondly computation aspects related to the neighbourhood definition are discussed. Field variables, such as particle velocity or density, are evaluated by smoothing interpolation of the corresponding values over the nearest neighbour particles located inside a cut-off radius “rc”. The generation of a neighbour list at each time step takes a considerable portion of CPU time. Straightforward determination of which particles are inside the interaction range requires the computation of all pair-wise distances, a procedure whose computational time would be of the order O(N2), and therefore unpractical for large domains. Finally, some practical applications are presented, primariliy concerning free surface flows. The capability to easily handle large deformation is shown

Numerical wave interaction with tetrapods breakwater

ABSTRACT: The paper provides some results of a new procedure to analyze the hydrodynamic aspects of the interactions between maritime emerged breakwaters and waves by integrating CAD and CFD. The structure is modeled in the numerical domain by overlapping individual three-dimensional elements (Tetrapods), very much like the real world or physical laboratory testing. Flow of the fluid within the interstices among concrete blocks is evaluated by integrating the RANS equations. The aim is to investigate the reliability of this approach as a design tool. Therefore, for the results' validation, the numerical run-up and reflection effects on virtual breakwater were compared with some empirical formulae and some similar laboratory tests. Here are presented the results of a first simple validation procedure. The validation shows that, at present, this innovative approach can be used in the breakwater design phase for comparison between several design solutions with a significant minor cost. KEY WORDS: Volume of Fluid (VOF), Wave, Run up, Reflection, Rubble mound, Numerical simulations, Tetrapod Flow 3D®, RANS equation

A CFD approach to rubble mound breakwater design

The paper provides some developments of a numerical approach ("Numerical Calculation of Flow Within Armour Units", FWAU) to the design of rubble mound breakwaters. The hydrodynamics of wave induced flow within the interstices of concrete blocks is simulated by making use of advanced, but well tested, CFD techniques to integrate RANS equations.While computationally very heavy, FWAU is gaining ground, due to its obvious advantages over the "porous media", i.e. the possibility of accounting for the highly non stationary effects, the reduced need of ad hoc calibration of filtration parameters and also – in perspective – the evaluation of hydrodynamic forces on single blocks. FWAU however is a complex technique, and in order to turn it into a practical design tool, a number of difficulties have to be overcome.The paper presents recent results about this validation, as well as insight into fluid dynamical aspects. Keywords: Numerical simulation, Breakwaters, Run up, Reflection, Rubble moun

Wave run-up prediction and observation in a micro-tidal beach

Abstract. Extreme weather events bear a significant impact on coastal human activities and on the related economy. Forecasting and hindcasting the action of sea storms on piers, coastal structures and beaches is an important tool to mitigate their effects. To this end, with particular regard to low coasts and beaches, we have developed a computational model chain based partly on open-access models and partly on an ad-hoc-developed numerical calculator to evaluate beach wave run-up levels and flooding. The offshore wave simulations are carried out with a version of the WaveWatch III model, implemented by CCMMMA (Campania Centre for Marine and Atmospheric Monitoring and Modelling – University of Naples Parthenope), validated with remote-sensing data. The waves thus computed are in turn used as initial conditions for the run-up calculations, carried out with various empirical formulations; the results were finally validated by a set of specially conceived video-camera-based experiments on a micro-tidal beach located on the Ligurian Sea. Statistical parameters are provided on the agreement between the computed and observed values. It appears that, while the system is a useful tool to properly simulate beach flooding during a storm, empirical run-up formulas, when used in a coastal vulnerability context, have to be carefully chosen, applied and managed, particularly on gravel beaches

Simulating fluid-structure interaction with SPH

Fluid-structure interaction (FSI) is the condition according to which a fluid comes in contact and interacts with a structure. A simple application of the impulse-momentum theorem yields as a result the developing of pressure waves, propagating inside both media. The present work presents a critical assessment of the Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method to simulate the first stages of a 2D fluid impacting onto a rigid vertical wall. The effects on the results in terms of the sound speed c0, appearing inside the state equation, as well as of the velocity va of the approaching fluid are here investigated

Using SPH to compute slamming loads on vertical structures

The evaluation of slamming loads on structures is a challenging problem in both civil and industrial engineering. For instance, waves on coastal works and ship structures may occasionally induce high pressure peaks, causing significant stresses, despite their short duration. Similar problems arise in debris flow impact on structures. The work here presented is aimed at clarifying some aspects of a corrected version of the Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) technique which need to be re-examined in order to improve the performance of the method in highly critical fluid-solid impact problems. The paper is particularly focused on the first stages – here specified as short term – of the phenomenon, where compressibility plays a key role. A test case is considered whereby a rectangular mass of fluid particles, 3.95 m long and 0.5 m high impacts against a vertical obstacle, with velocities ranging from 2 m/s to 10 m/s. The employed WCSPH code is applied with various computational options for the state equations and for the boundary conditions. Results show that the pressure distribution on the wall quickly increases as the impact process takes place, from the bottom to the free surface, with value which may reach up to tens of atmospheres according to fluid compressibility. The effects on the results of Tait equation parameters are investigated, as well as the effects of additional repulsive central forces – the so called "Lennard Jones" – on the boundary. Results should provide useful suggestions concerning the SPH practise for slamming loads