Wave Overtopping on Coastal Structures Essay Example | Topics and Well Written Essays - 3500 words

Wave Overtopping on Coastal Structures - Essay mannequinTraditionally, laboratory experiments and field observations have been used to occupy this turbulent oceanographic phenomenon and empirical formulae have been derived from these but ascetical limitations existed since parameters to which these derivations fitted were local (Shao, 2006). Thus, in recent time, universal derivations that can fit across a wide station of parametric requirements of structure geometry, water conditions and wave dynamics are considered essential and desirable. To this end, fluid dynamics proves a close to reliable model generator but traditional Eulerian approaches that discretise governing equivalences over a computational field divided into a grid system based on local parameters develop problems of quantitative diffusion that transcends localised grid patterns and tend to encompass the entire grid so that the discretised development of the equation into an unified whole is seriously affected (Shao, 2006). More recently, to solve this diffusion belief for traditional dynamics, a segment method has been developed wherewith the discretised equation utlises individual fractions in the merge as centres of development. The diffusion effect is effectively smooth by a expireal kernel that identifies and utilises the combined functions of the angular and linear momentums of each particle (Shao, 2006). The smoothing out of the diffusion effect generated at each particle location within the flow thus allows the fluid, in this case seawater in wave form, to be accounted for as an incompressible unrivalled (Shao, 2006). One such method that utilises this unique strategy is the moving particle semi-implicit method (MPS) applied somewhat successfully by Japanese scientists to wave flow patterns (Shao, 2006). The model that this paper will demonstrate is the smoothed particle hydrodynamic (SPH) method as developed and tested by Shao, 2006.The paper shall now study a little of ho w this manner of computational strategy developed.Smoothed Particle Hydrodynamics (SPH) The smoothed particle hydrodynamic method was one of the earliest meshfree methods applying Langrangian description of motion. It was primarily proposed by Lucy (1977) and Gingold and Monaghan (1977) (source Zhang and Batra, 2004) for problems in astrophysics in three-d space (Zhang and Batra, 2004). In the constituted smoothed particle hydrodynamic (SPH) method, for a function f at a point x within a domain , the approximate value of is given as below = (Eqn. 2.1, p. 137, Zhang and Batra, 2004)In this equation, is the kernel or smoothing function. The approximate value of of f depends upon two parameters - the kernel W and the dilation h, the last providing support for W. It is essential that the kernel W should have the following properties -I) = 0, for ,II) ,III) , here is the Dirac delta function,IV) , andV) =. (Zhang and Batra, 2004)This conventional SPH method is not even zero-order consi stent at the boundaries (Zhang and Batra, 2004). This forced Liu et al, 1995a,b, to introduce a corrective function that is a polynomial of the spatial coordinates, making the method order consistent (Zhang and Batra, 2004). Chen et al, (1999a,b) and Zhang and Batra, 2004, also seek to improve the conventional SPH method consistency in some manner. It is notable that the smoothed particle hydrodynamics method is a macroscopic model but it can be considered both as a continuum and particle method (Meakin et al, 2007). This is in particular context to the fact that the computational efficiency of purely particle methods is low in comparison to purely continuum ones (Meakin