Sriram Venkatachalam

The paper presents coupling between a mesh-based finite-element model for Boussinesq equations (FEBOUSS Agarwal et al., 2022) with a meshless local Petrov–Galerkin model for the Navier–Stokes equations (MLPG_R Agarwal et al., 2021) in 3D. Boussinesq equation models are widely used for simulating wave-propagation over large domains with uneven topography using a 2D surface mesh. Mesh-less models inherently capture large free-surface deformations and have shown promise in simulating wave-structure interaction, run-up and breaking phenomenon. The hybrid approach in this paper assumes a 3D MLPG_R sub-domain surrounded by the 2D mesh of FEBOUSS. The coupling interface in MLPG_R consists of relaxation zones that can be placed along multiple boundaries of the sub-domain for exchanging particle velocity from FEBOUSS. This hybrid model is therefore capable of simulating directional waves, that has not been reported previously. The paper first presents the procedure for calculating the depth-resolved velocities in 3D from the Boussinesq model. The resultant velocities are compared against theory, experiments and other models. The following sections present the coupling algorithm along a single and multiple coupling interfaces in MLPG_R. Validation results for this hybrid model are provided using surface elevation and velocity measurements for regular waves, including directional cases. In general, the results from the hybrid model are reported to have marginal over-prediction of peaks compared to purely MLPG_R simulation. Finally, the interaction of a vertical cylinder with direction regular wave is simulated using the 3D hybrid model.

The estimation of forces and responses due to the nonlinearities in ocean waves is vital in the design of offshore structures, as these forces and responses would result in the extreme loads. Simulation of such events in a laboratory is quite laborious. Even for the preparation of the driving signals for the wave boards, one needs to resort to numerical models. In order to achieve this task, the two-dimensional time domain nonlinear problem has received considerable attention in recent years, in which a mixed Eulerian and Lagrangian method (MEL) is being used. Most of the conventional methods need the free surface to be smoothed or regridded at a particular/every time step of the simulation due to Lagrangian characteristics of motion even for a short time. This would cause numerical diffusion of energy in the system after a long time. In order to minimize this effect, the present study aims at fitting the free surface using a cubic spline approximation with a finite element approach for discretizing the domain. By doing so, the requirement of smoothing/regridding becomes a minimum. The efficiency of the present simulation procedure is shown for the standing wave problem. The application of this method to the problem of sloshing and wave interaction with a submerged obstacle has been carried out. © 2006 Elsevier Ltd. All rights reserved.

A finite element model for depth integrated form of Boussinesq equations is presented. The equations are solved on an unstructured triangular mesh using standard Galerkin method with mixed interpolation scheme. The elemental integrals are calculated analytically and time-stepping is done using Runge–Kutta 4th order method. It is extended to simulate ship-generated waves using moving pressure fields. The unstructured formulation provides the flexibility of mesh refinement as needed, for capturing wave transformation or moving pressure field. The model is verified against experimental and numerical results for wave transformation over the Whalin shoal. The results for moving pressure field are compared against numerical results from FUNWAVE. Further, a simulation of ship navigating a curved path is presented. Finally, a real-life application and validation against field measurements is provided for waves generated by a fast ferry moving along a GPS tracked path in Tallinn Bay, Estonia.

The motion of sloshing waves under random excitation in the sway and heave modes have been simulated in a numerical wave tank. The fully nonlinear wave is numerically simulated using the finite element method with the cubic spline and finite difference approximations, in which the need for smoothing and regridding is minimal. The present model predictions are compared with that of Frandsen [Frandsen JB. Sloshing motions in the excited tanks. J Comput Phys 2004;196:53-87] for the regular wave excitation in the vertical and horizontal modes. The sloshing due to the simulated random excitation with different peak frequencies relative to the natural sloshing frequency has been subjected to frequency domain analysis. The results showed that irrespective of peak excitation frequency, the peaks appear at the natural frequencies of the system and the peak magnitude appears close to the natural frequency for the sway excitation. The higher magnitude is seen when the excitation frequency is equal to the first mode of natural frequency, due to the resonance condition. In the case of heave excitation, even though the peaks appear at the natural frequencies, the magnitude of the spectral peak remains the same for different excitation frequencies. © 2006 Elsevier Ltd. All rights reserved.