Sriram Venkatachalam

This is the first paper to present a hybrid method coupling an Improved Meshless Local Petrov Galerkin method with Rankine source solution (IMLPG_R) based on the Navier-Stokes (NS) equations, with a finite element method (FEM) based on the fully nonlinear potential flow theory (FNPT) in order to efficiently simulate the violent waves and their interaction with marine structures. The two models are strongly coupled in space and time domains using a moving overlapping zone, wherein the information from both the solvers is exchanged. In the time domain, the Runge-Kutta 2nd order method is nested with a predictor-corrector scheme. In the space domain, numerical techniques including 'Feeding Particles' and two-layer particle interpolation with relaxation coefficients are introduced to achieve the robust coupling of the two models. The properties and behaviours of the new hybrid model are tested by modelling a regular wave, solitary wave and Cnoidal wave including breaking and overtopping. It is validated by comparing the results of the method with analytical solutions, results from other methods and experimental data. The paper demonstrates that the method can produce satisfactory results but uses much less computational time compared with a method based on the full NS model. © 2014 Elsevier Inc.

Hydroelasticity is an important problem in the field of ocean engineering. It can be noted from most of the works published as well as theories proposed earlier that this particular problem was addressed based on the time independent/ frequency domain approach. In this paper, we propose a novel numerical method to address the fluid-structure interaction problem in time domain simulations. The hybrid numerical model proposed earlier for hydro-elasticity (Sriram and Ma, 2012) as well as for breaking waves (Sriram et al 2014) has been extended to study the problem of breaking wave-elastic structure interaction. The method involves strong coupling of Fully Nonlinear Potential Flow Theory (FNPT) and Navier Stokes (NS) equation using a moving overlapping zone in space and Runge kutta 2nd order with a predictor corrector scheme in time. The fluid structure interaction is achieved by a near strongly coupled partitioned procedure. The simulation was performed using Finite Element method (FEM) in the FNPT domain, Particle based method (Improved Meshless Local Petrov Galerkin based on Rankine source, IMPLG-R) in the NS domain and FEM for the structural dynamics part. The advantage of using this approach is due to high computational efficiency. The method has been applied to study the interaction between breaking waves and elastic wall.

This paper discusses the possibility to study propagation, shoaling and run-up of these waves over a slope in a 300-meter long large wave flume (GWK), Hannover. For this purpose long bell-shaped solitary waves (elongated solitons) of different amplitude and the same period of 30 s are generated. Experimental data of long wave propagation in the flume are compared with numerical simulations performed within the fully nonlinear potential flow theory and KdV equations. Shoaling and run-up of waves on different mild slopes is studied hypothetically using nonlinear shallow water theory. Conclusions about the feasibility of using large scale experimental facility (GWK) to study tsunami wave propagation and run-up are made.

This paper presents the application of the Improved Meshless Local Petrov Galerkin method with Rankine source (Sriram and Ma, 2012) Sriram and Ma (2012) for wave interaction with porous structure model. The mathematical model is based on a unified governing equation that incorporates both pure fluid and porous region. The porous flow model is based on the empirical resistance coefficients. The interface between the pure fluid and porous region is numerically treated using background nodes having the porosity information and interpolated over the particle using simplified finite difference interpolation method. The model is validated using the available experimental results for wave damping over the permeable bed. The developed model is used to analyse the different shape of the seawall such as flaring shaped seawall, recurve wall and vertical wall. Then the validated model is used for analysing the overtopping amount due to the effect of porous layer in-front of the different sea wall profile. Numerical expression for overtopping amount has been provided for the different configurations from the numerical model.

The nonlinear viscous flow generated from forced heaving oscillation of 2D floating body in calm water is carried out numerically using Improved Meshless Local Petrov-Galerkin (IMLPGR) method based on Rankine Source function. In the present particle-based method, the gradient calculation has been improved using ghost particle method. However, for estimating pressure, only single layer of the boundary particles are used. This is the first paper to extend the application of the IMLPGR for heave oscillations of the floating body. Simulations are carried out for vertical oscillation of rectangular shaped mono hull and twin hull. Hydrodynamics of these hulls for various amplitude and frequency of oscillations are performed and the numerical results agree well with existing literature results.

In this work, the motion of a two-dimensional rectangular freely floating body under waves is simulated using Improved Meshless Local Petrov-Galerkin method with Rankine Source function (IMLPG_R) with variable spacing resolutions. The IMLPG_R method is a particle method that solves Navier–Stokes equations using the fractional step method to capture the wave properties. However, many existing particle methods are computationally intensive to model the wave-floating body due to the requirement of fine particles, needing uniform distribution throughout the domain. To improve the computational efficiency and capture the body response properly, variable spaced particle distribution with fine resolution near the floating body and coarse resolution far from the body is implemented. Numerical schemes to handle variable resolutions are reported. An iterative scheme to handle the wave-floating body is implemented in the particle method. Two test cases, one with small wave and another with steep waves, are simulated for uniform particle distribution and the result shows good agreement with literature. Based on this, the performance of the variable spaced particle distribution is tested in coupling with floating body solver. The application of the method for wave impact load from the green water loading of the floating structure is also simulated.

In this paper, the particle method for handling oscillation of floating body using variable particle spacing is reported. Heave oscillation of floating mono hull and twin hull on the free surface in a viscous fluid is performed using Improved Meshless Local Petrov-Galerkin method based on Rankine Source function (IMLPG_R). The IMLPG_R method is a particle-based method that will solve the interaction between fluid and floating body using Navier-Stokes equation. The pressure at each time step is estimated from Pressure Poisson equation, in order to incorporate the heaving of the floating bodies, some improvements like free surface identification, gradient calculations has been introduced in the present paper to handle the variable resolutions in modelling. Simulations are performed for different frequency and amplitude of oscillations for mono and twin hull forced motions to show the robustness of the developed model to handle both small and steep oscillations.

Jackets are structures used in the offshore industry as a bottom supported platform for oil and gas production. The jackets have to be built in order to withstand the harsh sea environment. Such designs demand in depth analysis to predict the loads acting on the structure and its response. Depending on the sea states in which the structure needs to be installed, breaking load can be important. Estimation of breaking load for single cylinder exists in literature, since the breaking load on the jacket structure needs a lot more clarity. The aim of this paper is to estimate the impact force on a model jacket using Duhamel integral, which was not explored before. The impact load so far analyzed was compared with theoretical explanations given by Goda, et al. (1966), Wienke and Oumeraci (2005). The scope of the study is limited to plunging type of breakers. Five loading cases include wave breaking at far-front of a structure, in front of structure, on the front leg, on the rear leg and a non-breaking case was considered.

The simulation of nonlinear waves can be carried out by using the conventional methods like Finite Element Method (FEM), Boundary Element Method (BEM) based on Mixed Eulerian and Lagrangian (MEL) formulation. The simulation based on FEM has the advantages of extending the code easily to viscous flow and to three-dimensional (3D) tank with complex geometry. While adopting FEM, the derivatives are usually found from differentiating the shape function, which is the direct differentiation of the velocity potential. The approximation of velocity field thus obtained is inferior than the approximation of the velocity potential. In time-dependent problems, this play an important role. Thus, researchers have been focusing on obtaining the derivatives through different methods such as Global Projection, Local Finite Difference (FD), mapped FD, least square method or by using cubic spline approximation. The present chapter shows a detailed review of these methods for calculating the derivatives including the advantages and disadvantages in the context of simulation of nonlinear free surface waves using structured/unstructured FEM.

A proper design of offshore and coastal structures requires further knowledge about extreme wave events. Such waves are highly nonlinear and may occur unexpectedly due to diverse reasons. One of these reasons is wave-wave interaction and the wave focusing technique represents one option to generate extreme wave events in the laboratory. The underlying mechanism is the superimposition and phasing of wave components at a predefined location. To date, most of the existing methods to propagate target wave profile backwards to the position of the wave generator apply linear wave theory. The problem is that the generated waves with different frequencies generate new components which do not satisfy the linear dispersion relation. As a result, small changes in the wave board control signal generally induce large and random shifts in the resulting focused wave. This means that iterations are necessary to get the required wave profile at the correct position in the flume. In this study, a Self Correcting Method (SCM) is applied to optimize the control signal of the wave maker in a Numerical Wave Tank (NWT). The nonlinearities are included in the control signal and accurate wave focusing is obtained irrespective of the prevailing seabed topography (horizontal or sloping) and type of structure (reflective or absorbing). The performance of the proposed SCM is numerically investigated for a wide variety of scenarios and validated by scale model tests in the Large Wave Flume (Großer Wellen Kanal, GWK), Hannover, Germany. Moreover, the application of the proposed SCM in the Numerical Wave Tank to generate a tsunami at a predefined position and the comparison of the results with the time series recorded in the Pago Pago harbour (Samoa) is very encouraging. The strengths and limitations of the proposed SCM are discussed, including the potential for further developments. © 2014 Elsevier B.V.