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

Zhou, J. (2010). Numerical investigation of breaking waves and their interactions with structures using MLPG_R method. (Unpublished Doctoral thesis, City University London)


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.

Publication Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
T Technology > TC Hydraulic engineering. Ocean engineering
Departments: Doctoral Theses
School of Science & Technology > School of Science & Technology Doctoral Theses
School of Science & Technology > Engineering
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