Improved MLPG_R method for simulating 2D interaction between violent waves and elastic structures

Abstract

This is the submitted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractInteraction between violent water waves and structures is of a major concern and one of the important issues that has not been well understood in marine engineering. This paper will present first attempt to extend the Meshless Local Petrov Galerkin method with Rankine source solution (MLPG_R) for studying such interaction, which solves the Navier-stokes equations for water waves and the elastic vibration equations for structures under wave impact. The MLPG_R method has been applied successfully to modeling various violent water waves and their interaction with rigid structures in our previous publications. To make the method robust for modeling wave elastic-structure interaction (hydroelasticity) problems concerned here, a near-strongly coupled and partitioned procedure is proposed to deal with coupling between violent waves and dynamics of structures. In addition, a novel approach is adopted to estimate pressure gradient when updating velocities and positions of fluid particles, leading to a relatively smoother pressure time history that is crucial for success in simulating problems about wavestructure interaction. The developed method is used to model several cases, covering a range from small wave to violent waves. Numerical results for them are compared with those obtained from other methods and from experiments in literature. Reasonable good agreement between them is achieved.

A hybrid method for modelling two dimensional non-breaking and breaking waves

“…where ^ in the above equations corresponds to the estimation based on the modified pressure gradient (Koshizuka and Oka [25] and Sriram and Ma [27]). …”

“…On the other hand, the meshfree (or particle) methods have been recognised as promising approaches in recent years, particularly for modelling violent waves and their interaction with structures owing to their advantages that meshes are not required and numerical diffusion associated with convection terms is eliminated compared to traditional mesh based methods. The notable papers based on particle methods for the topics related to wave-structure interactions include but are not limited to references [22][23][24] for using smoothed particle hydrodynamics (SPH), [25] for using moving particle semi-implicit method (MPS), [26][27] for using Meshless Local Petrov Galerkin with Rankine Source (MLPG_R). Some simplified test cases reported in the literature using these models showed a good agreement with the experimental measurements, see for example, [1][2][3][4][5][6][7][8][9][10]28] for the FNPT models and [22][23][24][25][29][30][31] for the NS models.…”

“…This makes the FEM more advantageous over the BEM if coupled with the methods based on the NS model that always needs the information in whole flow field, not only on boundaries. (4) The IMLPG_R method [27,31] is based on a weak form of the Poisson's equation. In the weak form, there are only unknown functions without any derivatives.…”

“…Due to this feature, the IMLPG_R method is potentially more accurate than other meshless methods, like the incompressible SPH [22] and MPS [25], based on the Poisson's equation, which numerically approximate the second order derivatives directly. Our previous work [27,31,[44][45][46] has demonstrated the advantages of the IMLPG_R method.…”

MLPG_R method for modelling 2D flows of two immiscible fluids

“…where , and and (32) The pressure in the two liquid domains is derived by means of the linearized Bernoulli equation and is expressed as (33) In numerical tests, an initial velocity potential is given at the time when across the tank. Then the fluids start to move.…”