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

Interaction 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 mequations 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

MLPG_R Method for Numerical Simulation of 2D Breaking Waves

Following our previous work, the Meshless Local Petrov-Galerin method based on Rankine source solution (MLPG_R) will be extended in this paper to deal with breaking waves. For this purpose, the governing equation for pressure is improved and a new technique called Mixed Particle Number Density and Auxiliary Function Method (MPAM) is suggested for identifying the free surface particles. Due to complexity of the problem, two dimensional (2D) breaking waves are only concerned here. Various cases are investigated and some numerical results are compared with experimental data available in literature to show the newly developed method is robust

Applications of MLPG_R & Sale/QALE-Fem for Wave - Structure Interactions

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

MLPG_R method for modelling 2D flows of two immiscible fluids

This is a first attempt to develop the Meshless Local Petrov-Galerkin method with Rankine source solution (MLPG_R method) to simulate multiphase flows. In this paper, we do not only further develop the MLPG_R method to model two-phase flows but also propose two new techniques to tackle the associated challenges. The first technique is to form an equation for pressure on the explicitly identified interface between different phases by considering the continuity of the pressure and the discontinuity of the pressure gradient (i.e. the ratio of pressure gradient to fluid density), the latter reflecting the fact that the normal velocity is continuous across the interface. The second technique is about solving the algebraic equation for pressure, which gives reasonable solution not only for the cases with low density ratio but also for the cases with very high density ratio, such as more than 1000. The numerical tests show that the results of the newly developed two-phase MLPG_R method agree well with analytical solutions and experimental data in the cases studied. The numerical results also demonstrate that the newly developed method has a second-order convergent rate in the cases for sloshing motion with small amplitudes

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

This is the first paper to present a hybrid method coupling a 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

Variable Spaced Particle in Meshfree Method to handle wave‐floating body interactions

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

A hybrid stabilization technique for simulating water wave - Structure interaction by incompressible Smoothed Particle Hydrodynamics (ISPH) method

The Smoothed Particle Hydrodynamics (SPH) method is emerging as a potential tool for studying water wave related problems, especially for violent free surface flow and large deformation problems. The incompressible SPH (ISPH) computations have been found not to be able to maintain the stability in certain situations and there exist some spurious oscillations in the pressure time history, which is similar to the weakly compressible SPH (WCSPH). One main cause of this problem is related to the non-uniform and clustered distribution of the moving particles. In order to improve the model performance, the paper proposed an efficient hybrid numerical technique aiming to correct the ill particle distributions. The correction approach is realized through the combination of particle shifting and pressure gradient improvement. The advantages of the proposed hybrid technique in improving ISPH calculations are demonstrated through several applications that include solitary wave impact on a slope or overtopping a seawall, and regular wave slamming on the subface of open-piled structure

Numerical investigation of breaking waves and their interactions with structures using MLPG_R method

Meshless Local Petrov-Galerkin method based on Rankine source solution (MLPG_R) has been developed by Dr. Qingwei Ma (Ma, 2005b) and has been used to simulate the nonlinear water wave problems in 2D cases without the occurrence of the breaking waves. In this thesis, MLPG_R method has been further developed to numerically simulate breaking waves and the interactions between breaking waves and structures in 2D and 3D cases. The main difference between this meshless method and conventional mesh-based methods is that the governing equations are solved in terms of particle interaction models, without the need of computational meshes. Therefore, this method avoids the time-consuming mesh generating and updating procedures which may be necessary and may need to be frequently performed in the mesh-based methods. Furthermore, in order to simulate the breaking waves well, several novel numerical techniques are developed and adopted. The numerical technique for implementing the solid boundary condition for meshless methods is proposed, which is more robust than others in terms of accuracy and efficiency. A technique for meshless interpolation (SFDI scheme) is adopted, which is as accurate as the more costly moving least square (MLS) method generally but requires much less computational time than the latter. A newly developed technique for identifying the free surface particles is presented, which is much more robust than those existing in literature. A semi-analytical method for numerical evaluation of integrals in a local domain and on its surface is presented to form the matrix for the algebraic equations, which makes it possible to modelling the 3D problems on personal computers. The newly extended MLPG_R method is applied to simulate the waves generated by a wave maker and their propagations, overturning and breaking over flat and sloped seabed. And it is also applied to 2D and 3D dam breaking cases and violent sloshing cases. The convergence properties of this method in different cases are investigated. Some of the results have been validated by experimental data and numerical results obtained by other methods. Satisfactory agreements are achieved. Based on these numerical investigations, a number of conclusions have been made, including that the breaking waves can cause large pressure with several peaks when they impact on structures; the behaviour of pressure strongly depends on the relative locations of structures to the breaking point of breaking waves. Breaking waves in a sloshing container can also cause more than one peaks, which is correlated with the direction change of water motion within the container. These investigations can give us better understanding of the impact pressure, breaking wave and interactions between breaking wave and structures

A hybrid approach coupling mlpg-r with QALE-FEM for modelling fully nonlinear water waves

The paper reports a progress on the development of a hybrid approach coupling the Meshless Local Petrov-Galerkin Method based on Rankine Solution (MLPG-R) and the Quasi Arbitrary Langangian-Eulerian Finite Element Method (QALE-FEM) for modelling nonlinear water waves. The former is to solve the one-phase incompressible Naiver-Stokes model using a fractional step method (projection method), whereas the latter is to solve the Fully Nonlinear Potential Theory (FNPT) using a time-marching procedure. They are fully coupled using a zonal approach. The hybrid approach takes the advantage of the QALE-FEM on modelling fully nonlinear water waves with relatively higher computational efficiency and that of the MLPG-R on its capacity on dealing with viscous effects and breaking waves. The model is validated by comparing the numerical prediction with the experimental data for a unidirectional focusing wave. A good agreement has been achieved