scholarly journals Numerical Analysis of Second-Order Mean Wave Forces by a Stabilized Higher-Order Boundary Element Method

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Yan-Lin Shao
Keyword(s):  
Free Surface ◽  
Boundary Element Method ◽  
Coordinate System ◽  
Matrix Equation ◽  
Wave Structure ◽  
Second Order ◽  
Surface Conditions ◽  
Structure Interaction ◽  
Wave Structure Interaction ◽  
Body Fixed Coordinate System

A stabilized higher-order boundary element method (HOBEM) based on cubic shape functions is presented to solve the linear wave-structure interaction with the presence of steady or slowly varying velocities. The m-terms which involve second derivatives of local steady flow are difficult to calculate accurately on structure surfaces with large curvatures. They are also not integrable at the sharp corners. A formulation of the boundary value problem in a body-fixed coordinate system is thus adopted, which avoids the calculation of the m-terms. The use of body-fixed coordinate system also avoids the inconsistency in the traditional perturbation method when the second-order slowly varying motions are larger than the first-order motions. A stabilized numerical method based on streamline integration and biased differencing scheme along the streamlines will be presented. An implicit scheme is used for the convective terms in the free surface conditions for the time integration of the free surface conditions. In an implicit scheme, solution of an additional matrix equation is normally required because the convective terms are discretized by using the variables at current time-step rather than that from the previous time steps. A novel method that avoids solving such matrix equation is presented, which reduces the computational efforts significantly in the implicit method. The methodology is applicable on both structured and unstructured meshes. It can also be used in general second-order wave-structure interaction analysis with the presence of steady or slowly varying velocities.

scholarly journals Numerical Analysis of Second-Order Mean Wave Forces by a Stabilized Higher Order Boundary Element Method

2018 ◽  
Author(s):  
Yan-Lin Shao
Keyword(s):  
Free Surface ◽  
Boundary Element Method ◽  
Coordinate System ◽  
Boundary Element ◽  
Matrix Equation ◽  
Wave Structure ◽  
Surface Conditions ◽  
Structure Interaction ◽  
Wave Structure Interaction ◽  
Body Fixed Coordinate System

A stabilized Higher-Order Boundary Element Method (HOBEM) based on cubic shape functions is presented to solve the linear wave-structure interaction with the presence of steady or slowly varying velocities. The m-terms which involves second derivatives of local steady flow are difficult to calculate accurately on structure surfaces with high curvatures. They are also not integrable at the sharp corners. A formulation of the Boundary Value Problem (BVP) in a body-fixed coordinate system is thus adopted, which avoids the calculation of the m-terms. The use of body-fixed coordinate system also avoid the inconsistency in the traditional perturbation method when 2nd order slowly-vary motions are larger than the linear motions. The stabilized numerical method presented in this paper is based on streamline integration and biased differencing scheme along the streamlines. The presence of convective terms in the kinematic and dynamic free surface conditions will lead to instable solution if the explicit method is used. Thus a fully implicit scheme is used in this paper for the time integration of kinematic and dynamic free surface conditions. In an implicit scheme, solution of an additional matrix equation is normally required due to the fact that the presence of convective terms are approximated using the variables at current time step rather than the previous time steps only. A method that avoids solving such matrix equation is presented in this paper, which will reduce the computational efforts in the implicit method. The methodology is applicable on unstructured meshes. It can also be used in general second order wave-structure interaction analysis with presence of steady or slowly-varying velocities.

scholarly journals Wave-Structure Interaction for a Stationary Surface-Piercing Body Based on a Novel Meshless Scheme with the Generalized Finite Difference Method

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1147
Author(s):  
Ji Huang ◽  
Hongguan Lyu ◽  
Chia-Ming Fan ◽  
Jiahn-Hong Chen ◽  
Chi-Nan Chu ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Wave Structure ◽  
Second Order ◽  
Computational Domain ◽  
Ocean Engineering ◽  
Time Step ◽  
Structure Interaction ◽  
Wave Structure Interaction

The wave-structure interaction for surface-piercing bodies is a challenging problem in both coastal and ocean engineering. In the present study, a two-dimensional numerical wave flume that is based on a newly-developed meshless scheme with the generalized finite difference method (GFDM) is constructed in order to investigate the characteristics of the hydrodynamic loads acting on a surface-piercing body caused by the second-order Stokes waves. Within the framework of the potential flow theory, the second-order Runge-Kutta method (RKM2) in conjunction with the semi-Lagrangian approach is carried out to discretize the temporal variable of governing equations. At each time step, the GFDM is employed to solve the spatial variable of the Laplace’s equation for the deformable computational domain. The results show that the developed numerical method has good performance in the simulation of wave-structure interaction, which suggests that the proposed “RKM2-GFDM” meshless scheme can be a feasible tool for such and more complicated hydrodynamic problems in practical engineering.

Wave-Structure Interaction of Focussed Waves With REEF3D

2016 ◽  
Author(s):  
Hans Bihs ◽  
Mayilvahanan Alagan Chella ◽  
Arun Kamath ◽  
Øivind A. Arnsten
Keyword(s):  
Free Surface ◽  
Level Set ◽  
Wave Structure ◽  
High Order ◽  
Navier Stokes ◽  
Numerical Wave Tank ◽  
Wave Tank ◽  
Structure Interaction ◽  
Numerical Wave ◽  
Wave Structure Interaction

For the stability of offshore structures, such as offshore wind foundations, extreme wave conditions need to be taken into account. Waves from extreme events can become critical from design perspective. In a numerical wave tank, extreme waves can be generated through focussed waves. Here, linear waves are generated from a wave spectrum. The wave crests of the generated waves coincide at a pre-selected location and time. In order to test the generated waves, the time series of the free surface elevation are compared with experimental benchmark cases. The numerically simulated free surface shows good agreement with the measurements from experiments. In further computations, the wave impact of the focussed waves on a vertical circular cylinder is investigated. The focussed wave generation is implemented in the numerical wave tank module of REEF3D, which has been extensively and successfully tested for various wave hydrodynamics and wave-structure interaction problems in particular and for free surface flows in general. The open-source CFD code REEF3D solves the three-dimensional Navier-Stokes equations on a staggered Cartesian grid. Solid boundaries are taken into account with the ghost cell immersed boundary method. For the discretization of the convection terms of the momentum equations, the conservative finite difference version of the fifth-order WENO (weighted essentially non-oscillatory) scheme is used. For temporal treatment, the third-order TVD (total variation diminishing) Runge-Kutta scheme is employed. For the pressure, the projection method is used. The free surface flow is solved as two-phase fluid system. For the interface capturing, the level set method is selected. The level set function can be discretized with high-order differencing schemes. This makes it the appropriate solution for wave propagation problems based on Navier-Stokes solvers, which requires high-order numerical methods to avoid artificial wave damping. The numerical model is fully parallelized based on the domain decomposition, using MPI (message passing interface) for internode communication.

scholarly journals Investigation of a Stochastic Inverse Method to Estimate an External Force: Applications to a Wave-Structure Interaction

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
S. L. Han ◽  
Takeshi Kinoshita
Keyword(s):  
External Force ◽  
Inverse Method ◽  
Inverse Function ◽  
Wave Structure ◽  
Dynamic Responses ◽  
Structure Interaction ◽  
External Forces ◽  
Interaction Problem ◽  
Wave Structure Interaction

The determination of an external force is a very important task for the purpose of control, monitoring, and analysis of damages on structural system. This paper studies a stochastic inverse method that can be used for determining external forces acting on a nonlinear vibrating system. For the purpose of estimation, a stochastic inverse function is formulated to link an unknown external force to an observable quantity. The external force is then estimated from measurements of dynamic responses through the formulated stochastic inverse model. The applicability of the proposed method was verified with numerical examples and laboratory tests concerning the wave-structure interaction problem. The results showed that the proposed method is reliable to estimate the external force acting on a nonlinear system.

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