Quasi ALE finite element method for nonlinear water waves

This paper presents further development of the quasi arbitrary Lagrangian–Eulerian finite element method (QALE‐FEM) based on a fully non‐linear potential theory to numerically simulate non‐linear responses of 3D moored floating bodies to steep waves. In the QALE‐FEM (recently developed by the authors and applied to 2D floating bodies), the complex unstructured mesh is generated only once at the beginning of calculation and is moved to conform to the motion of boundaries at other time steps by using a robust spring analogy method specially suggested for these kind of problems, avoiding the necessity of high‐cost remeshing. In order to tackle challenges associated with 3D floating bodies, several new numerical techniques are developed in this paper. These include the technique for moving the mesh near body surfaces, the scheme for calculating velocity on 3D body surfaces and the modified semi‐implicit time integration method for floating bodies procedure (ISITIMFB‐M) that is more efficient for dealing with the full coupling between waves and bodies. Using the newly developed techniques and methods, various cases for 3D floating bodies with motions of up to six degrees of freedom (DoFs) are simulated. These include a SPAR platform, a barge‐type floating body and one or two Wigley Hulls in head seas or in oblique waves. For some selected cases, the numerical results are compared with experimental data available in the public domain and satisfactory agreements are achieved. Many results presented in this paper have not been found elsewhere to the best knowledge of the authors. Copyright © 2008 John Wiley & Sons, Ltd.

A comparative study of the opening and closing process of two types of mechanical heart valves using ALE finite element method

Interactions between fully nonlinear water waves and cylinder arrays in a wave tank

Arbitrary Lagrangian-Eulerian finite element method for liquid sloshing with contact angle hysteresis in microgravity

Using a local radial basis function collocation method to approximate radiation boundary conditions

A novel arbitrary Lagrangian–Eulerian finite element method for a parabolic/mixed parabolic moving interface problem

An energy diminishing arbitrary Lagrangian–Eulerian finite element method for two-phase Navier–Stokes flow

An arbitrary Lagrangian–Eulerian finite element method for interactions of airflow and a moving AGV in a cleanroom

Chatter is one of the most encountered vibration problems in high-speed rolling of thin steel sheets in tandem mills. Due to its negative cause on product quality and maintenance costs, chatter is a technical and economical problem in rolling mills. To study chatter in rolling, it is necessary to set up models for the rolling process as well as the mill stand. Existing models of rolling process are analytic and are based on many simplifying assumptions. In current work the finite element method is utilized for the first time to model the chatter vibrations in rolling, which relaxes many of these assumptions. The model has the benefit of mass translation to the computational region by using Arbitrary Lagrangian Eulerian (ALE) technique, which tremendously reduces huge computational requirements of common Lagrangian models. Four chatter mechanisms in rolling are reviewed in this paper, but the presented model is updated for simulating the negative damping effect by means of some online velocity sensors and signal filtering method in applying the ALE boundary conditions. Using this new model, single stand negative damping mechanism of chatter and its effect on the sheet surface is understood more accurately. Simulation results are in comprehensive agreement with the experimental and industrial observations.

The diffraction of waves by three bottom fixed vertical circular cylinders is investigated by using the boundary element method. This method has been successfully applied to the isolated vertical circular cylinder and now is used to study the interaction between waves and multiple vertical cylinders. In this paper, a numerical analysis by the boundary element method is developed by the linear potential theory. The numerical analysis by the boundary element method is based on Green's second theorem and introduced to an integral equation for the fluid velocity potential around the vertical circular cylinders. To verify this method, the results obtained in present study are compared with the results computed by the multiple scattering method. The results of the comparisons show strong agreement. Also in this paper, several numerical examples are given to illustrate the effects of various parameters on the wave exciting force such are the separation distance, the wave number and the incident wave angle. This numerical computation method might be used broadly for the design of various offshore structures to be constructed in the future.

Finite-amplitude solitary waves in water of arbitrary uniform depth are considered. A numerical scheme based on series truncation is presented to calculate the highest solitary wave. It is found that the ratio of the amplitude of the wave versus the depth is 0.83322. This value is compared with the values obtained by previous investigators. In addition, another numerical scheme based on an integral-equation formulation is derived to compute solitary waves of arbitrary amplitude. These calculations confirm and extend the calculations of Byatt-Smith & Longuet-Higgins (1976) for very steep waves.

This paper presents the first classical Convolutional Neural Network (CNN) that can be applied directly to data from unstructured finite element meshes or control volume grids. CNNs have been hugely influential in the areas of image classification and image compression, both of which typically deal with data on structured grids. Unstructured meshes are frequently used to solve partial differential equations and are particularly suitable for problems that require the mesh to conform to complex geometries or for problems that require variable mesh resolution. Central to our approach are space-filling curves, which traverse the nodes or cells of a mesh tracing out a path that is as short as possible (in terms of numbers of edges) and that visits each node or cell exactly once. The space-filling curves (SFCs) are used to find an ordering of the nodes or cells that can transform multi-dimensional solutions on unstructured meshes into a one-dimensional (1D) representation, to which 1D convolutional layers can then be applied. Although developed in two dimensions, the approach is applicable to higher dimensional problems. To demonstrate the approach, the network we choose is a convolutional autoencoder (CAE), although other types of CNN could be used. The approach is tested by applying CAEs to data sets that have been reordered with a space-filling curve. Sparse layers are used at the input and output of the autoencoder, and the use of multiple SFCs is explored. We compare the accuracy of the SFC-based CAE with that of a classical CAE applied to two idealised problems on structured meshes, and then apply the approach to solutions of flow past a cylinder obtained using the finite-element method and an unstructured mesh.

To improve the force endurance capacity of plate breakwaters, a step‐type plate breakwater was proposed. The performance of the step‐type breakwater was investigated by numerical simulation method. First, a two‐dimensional numerical regular wave tank was constructed using FLUENT software, and the effectiveness of the tank application was verified by comparing with theoretical value and test data. Then, the numerical tank was used to simulate various working conditions, and the variation rules of the breakwater transmission coefficient with wave height, period, perforation rate, relative plate width, wave steepness, and number of layers were obtained. Finally, the difference in the wave dissipation mechanism between the step‐type breakwater and the “”‐type breakwater was discussed. The results indicated that the transmission coefficient of the step‐type breakwater was small, which also proved to be good at dissipating long‐period waves. In general, the wave dissipation performance of the step‐type breakwater was better than that of the “”‐type breakwater. The research can provide some clues for the research and design of corresponding breakwaters.

This paper summarizes numerical results of hydrogen absorption simulated in an axisymmetric tank geometry containing magnesium hydride heated to 300 °C and at moderate storage pressure 1 MPa. The governing equations are solved with a fully implicit finite volume numerical scheme used by a commercial software FLUENT. The effect of the different kinetic reaction equations modeling hydrogen absorption was studied by the introduction of a specific subroutine at each time step in order to consider which one will provide results close to available experimental results. Spatial and temporal profiles of temperature and concentration in hydride bed are plotted. Results show that suitable method for our two-dimensional study is a CV-2D technique because it generates the smallest error especially during the beginning of the reaction. Also, its computational time is the shortest one compared to the other methods.

Hydroelastic analysis of floating structures with liquid tanks and comparison with experimental tests