Hydrodynamic Assessment of A New Nature-Based Armour Unit on Rubble Mound Breakwater for Coastal Protection

This research proposes a novel nature-based design of a new concrete armour unit for the cover layer of a rubblemoundbreakwater. Armour units are versatile with respect to shape, orientation, surface condition details, and porosity.Therefore, a detailed analysis is required to investigate the exact state of their hydraulic interactions and structuralresponses. In this regard, the performance results of several traditional armour units, including the Antifer cube,Tetrapod, X-block and natural stone, are considered for the first step of this study. Then, the related observed resultsare compared with those obtained for a newly designed (artificial coral) armour unit. The research methodology utilizesthe common wave flume test procedure. Furthermore, several verified numerical models in OpenFOAM code areused to gain the extra required data. The proposed armour is configured to provide an effective shore protection as anenvironmental-friendly coastal structure. Thus it is designed with a main trunk including deep grooves to imitate thetypical geometry of a coral type configuration, so as to attain desirable performance. The observed results and ananalytic hierarchy process (AHP) concept are used to compare the hydraulic performance of the studied traditionaland newly proposed (artificial coral) armour units. The results indicate that the artificial coral armour unit demonstratesacceptable performance. The widely used traditional armour units might be replaced by newer designs for betterwave energy dissipation, and more importantly, for fewer adverse effects on the marine environment.

On Dissipation and Dispersion Errors Optimization,A-Stability and SSP Properties

In a recent paper(Du and Ekaterinaris,2016)optimization of dissipation and dispersion errors was investigated.A Diagonally Implicit Runge-Kutta(DIRK)scheme was developed by using the relative stability concept,i.e.the ratio of absolute numerical stability function to analytical one.They indicated that their new scheme has many similarities to one of the optimized Strong Stability Preserving(SSP)schemes.They concluded that,for steady state simulations,time integration schemes should have high dissipation and low dispersion.In this note,dissipation and dispersion errors for DIRK schemes are studied further.It is shown that relative stability is not an appropriate criterion for numerical stability analyses.Moreover,within absolute stability analysis,it is shown that there are two important concerns,accuracy and stability limits.It is proved that both A-stability and SSP properties aim at minimizing the dissipation and dispersion errors.While A-stability property attempts to increase the stability limit for large time step sizes and by bounding the error propagations via minimizing the numerical dispersion relation,SSP optimized method aims at increasing the accuracy limits by minimizing the difference between analytical and numerical dispersion relations.Hence,it can be concluded that A-stability property is necessary for calculations under large time-step sizes and,more specifically,for calculation of high diffusion terms.Furthermore,it is shown that the oscillatory behavior,reported by Du and Ekaterinaris(2016),is due to Newton method and the tolerances they set and it is not related to the employed temporal schemes.