Numerical simulation of a solitary wave interaction with submerged multi-bodies

The problems of a solitary wave passing over rectangular cylinders have been analysed. The numerical simulation is based on the full nonlinear two-dimensional Navier-Stokes equations which are solved by the finite difference method. The free surface is dealt with by the Volume of Fluid method (VOF). Results for a solitary wave passing over a single cylinder are compared with the experimental data of Seabra-Santos, Penouard and Temperville^[2] and better agreement is obtained than those obtained from the long wave equation based on the potential flow theory. Results are also given for two cylinders with different gaps. The project supported by the National Natural Science Foundation of China and the Development Foundation of Science and Technology of Shanghai Education Committee and the Royal Society.     

Simulation of sharp gas–liquid interface using VOF method and adaptive grid local refinement around the interface

The volume of fluid (VOF) method is used to perform two‐phase simulations (gas–liquid). The governing Navier–Stokes conservation equations of the flow field are numerically solved on two‐dimensional axisymmetric or three‐dimensional unstructured grids, using Cartesian velocity components, following the finite volume approximation and a pressure correction method. A new method of adaptive grid local refinement is developed in order to enhance the accuracy of the predictions, to capture the sharp gas–liquid interface and to speed up the calculations. Results are compared with experimental measurements in order to assess the efficiency of the method. Copyright © 2004 John Wiley & Sons, Ltd.     

Patched grid and adaptive mesh refinement strategies for the calculation of the transport of vortices

This paper presents two techniques allowing local grid refinement to calculate the transport of vortices. one is the patched grid (PG) method which allows non‐coincident interfaces between blocks. Treatment of the non‐coincident interfaces is given in detail. The second one is the adaptive mesh refinement (AMR) method which has been developed in order to create embedded sub‐grids. The efficiency of these two methods is demonstrated by some validating tests. Then the PG and AMR strategies are applied in the computation of the transport of vortices. We start with a simple vortex flow in a cubic box. Then, the flowfield around a complex aircraft configuration is calculated using the two refinement techniques. Results are compared with a fine, referenced grid calculation. Copyright © 2002 John Wiley & Sons, Ltd.     

Study of water waves with submerged obstacles using a vortex method with Helmholtz decomposition

The present study develops a 2‐D numerical scheme that combines the vortex method and the boundary integral method by a Helmholtz decomposition to investigate the interaction of water waves with submerged obstacles. Viscous effects and generation of vorticity on the free surface are neglected. The second kind of Fredholm integral equations that govern the strengths of vortex sheets along boundaries are solved iteratively. Vorticity is convected and diffused in the fluid via a Lagrangian vortex (blob) method with varying cores, using the particle strength exchange method for diffusion, with particle redistribution. A grid‐convergence study of the numerical method is reported. The inviscid part of the method and the simulation of the free‐surface motion are tested using two calculations: solitary wave propagation in a uniform channel and a moving line vortex in the fluid. Finally, the full model is verified by simulating periodic waves travelling over a submerged rectangular obstacle using nonuniform vortex blobs with a mapping of the redistribution lattice. Overall, the numerical model predicts the vortices' evolution and the free‐surface motion reasonably well. Copyright © 2008 John Wiley & Sons, Ltd.     

The diffraction of a solitary wave by a circular cylinder

This paper contributes to the diffraction of a solitary wave by a cylinder, governed by the Boussinesq eq. The Spectrum Method is used to transform 2·D eqs.into a set of 1·D eqs., which is solved by F. D. M. The example given in the paper shows that this method is both accurate and cost effective.     

Study on flow past two spheres in tandem arrangement using a local mesh refinement virtual boundary method

A local mesh refinement virtual boundary method based on a uniform grid is designed to study the transition between the flow patterns of two spheres in tandem arrangement for Re=250. For a small gap (L/D=1.5), the flow field is axisymmetric. As the spacing ratio increases to 2.0, the pressure gradient induces the circumferential fluid motion and a plane‐symmetric flow is constructed through a regular bifurcation. For L/D?2.5, the vortices are periodically shed from the right sphere, but the planar symmetry remains. The case for L/D=3.0 is picked up to give a detail investigation for the unsteady flow. The shedding frequency of vortical structure from the upper side of the right sphere is found to be double of the frequency of the lower side. With the flow spectra of various gaps given, the underlying competitive mechanism between the two shedding frequencies is studied and a critical spacing gap is revealed. Copyright © 2005 John Wiley & Sons, Ltd.     

孤立波作用下细长港响应的数值研究

采用Boussinesq数值波浪模型,模拟了不同波高的孤立波分别对常水深和变水深细长港作用时港内的响应.对数值模型的结果进行小波分析和频谱分析并与现有的理论值比较.结果表明,孤立波传入一侧为开敞水域的细长港时,港内激发振荡的能量主要集中在细长港前三个自振模态上,港口的响应频率与理论固有频率非常接近,这为估算细长港池的固有频率提供了一种可行性方法.     

Diffraction of a solitary wave by a thin wedge part 2. Effects of viscous boundary layers

Based on the study on the Mach reflection of a solitary wave in [3], we continue to investigate effects of the boundary layers on the bottom and the vertical side wall. By using matched asymptotic methods, the two-dimensional KdV equation is modified to account for effects of viscosity. Numerical can be neglected. The results including the side wall's effects agree satisfactorily with those of Melville's experiments. Finally, we establish the simplified concept of the side wall effect and conclude that it represents the physical reason for the discrepancy between the experiments and the previous calculations based on the inviscid fluid flow theory.     

A solitary group of two-dimensional deep-water waves due to a concentrated force-couple

In 1986, Yih found a solitary group of deep-water waves caused by a travelling and oscillatory concentrated force. In this paper, such a single group caused by a travelling and oscillatory force-couple is presented. The expression of wave elevation is also derived and an intuitive explanation of the results is provided.     

Vortex shedding and evolution induced by a solitary wave propagating over a submerged cylindrical structure

The shedding and evolution of the vortical structures generated by a solitary wave propagating over a submerged cylindrical structure are investigated experimentally and numerically. The cylindrical structure consists of two concentric cylinders and represents a simplified model for an offshore submerged intake structure typically used in coastal power plants. Flow visualization by dye injection is used to identify the dominant vortical structures near the structure. The flow visualization results show an unexpected flow reversal that causes shedding of secondary vortical structures. The experimental results are used to check a three-dimensional volume of fluid-large eddy simulation (VOF-LES) numerical model. The VOF-LES model is then used to further study the flow structure. A total of six dominant vortical structures generated by the wave motion are identified, followed by two more generated by the flow reversal. In summary, this paper provides the vorticity evolution for a complex fluid–structure interaction problem and a three-dimensional numerical simulation tool has also been validated, which can be extended to study more complex geometries and wave conditions.     

Diffraction of a solitary wave by a thin wedge

The diffraction of a solitary wave by a thin wedge with vertical walls is studied when the incident solitary wave is directed along the wedge axis. The method of multiple scales is extended to this problem and reduces the task to that of solving the two-dimensional KdV equation with proper boundary and initial conditions. The finite-difference numerical procedure is carried out with the fractional step algorithm in which difference schemes are all implicit. Except the maximum run-up at the wall, the results in this paper are found to corroborate the Melville's experiments not only qualitatively but also quantitatively. The maximum run-up of our results agrees well with Funakoshi's numerical one but it is considerably larger than that in Melville's experiment. An important reason for this discrepancy is believed to be the effect of viscous boundary layer on the vertical side wall.     

A coupled boundary element–finite difference model of surface wave motion over a wall turbulent flow

An effective numerical technique is presented to model turbulent motion of a standing surface wave in a tank. The equations of motion for turbulent boundary layers at the solid surfaces are coupled with the potential flow in the bulk of the fluid, and a mixed BEM–finite difference technique is used to model the wave motion and the corresponding boundary layer flow. A mixing‐length theory is used for turbulence modelling. The model results are in good agreement with previous physical and numerical experiments. Although the technique is presented for a standing surface wave, it can be easily applied to other free surface problems. Copyright © 2005 John Wiley & Sons, Ltd.     

Decay of a potential vortex and propagation of a heat wave in a second grade fluid

The propagation of a heat wave in an incompressible second grade fluid within the context of a potential vortex is studied. The solutions for the Newtonian fluid can be obtained from those for fluids of second grade as a limiting case.     

Interaction of a solitary wave and a front step simulated by level set method

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A numerical study of the motion of a wave running up a beach

The main difficulty for the numerical calculation of the wave running up a beach is the treatment of its moving water boundary. In this paper a scheme of turning the free boundary problem into a fixed boundary problem is designed. The calculated run-up height is consistent with the experiments. Some interesting wave phenomena are also found.     

Application of Chimera grid to modelling cell motion and aggregation in a narrow tube

A computational scheme using the Chimera grid method is presented for simulation of three‐dimensional motion and aggregation of two red blood cells (RBCs) in a narrow tube. The cells are modelled as rigid ellipsoidal particles; the computational scheme is applicable to deformable fluid‐filled particles. Attractive energy between two RBCs is modelled by a depletion interaction theory and used for simulating aggregation of two cells. Through the simulation, we show that the Chimera grid method is applicable to the simulation of three‐dimensional motion and aggregation of multiple RBCs in a microvessel and microvascular network. Copyright © 2006 John Wiley & Sons, Ltd.     

A numerical study of the vortex motion in oscillating flow around a circular cylinder at low and middlieKc numbers

A new hybrid model, which is based on domain decomposition and proposed by the authors, is used for calculating the flow around a circular cylinder at low and middle Keulegan-Carpenter numbers (Kc=2−18) respectively. The vortex motion patterns in asymmetric regime, single pair (or transverse) regime and double pair (or diagonal) regime are successfully simulated. The calculated drag and inertial force coefficients are in better agreement with experimental data than other recent computational results. The project supported by the National Natural Science Foundations of China and the LNM, Institute of Mechanics, Academia Sinica     

An adaptive local grid refinement and peak/valley capture algorithm to solve nonlinear transport problems with moving sharp-fronts

Highly nonlinear advection–dispersion-reaction equations govern numerous transport phenomena. Robust, accurate, and efficient algorithms to solve these equations hold the key to the success of applying numerical models to field problems. This paper presents the development and verification of a computational algorithm to approximate the highly nonlinear transport equations of reactive chemical transport and multiphase flow. The algorithm was developed based on the Lagrangian-Eulerian decoupling method with an adaptive ZOOMing and Peak/valley Capture (LEZOOMPC) scheme. It consists of both backward and forward node tracking, rough element determination, peak/valley capturing, and adaptive local grid refinement. A second-order tracking was implemented to accurately and efficiently track all fictitious particles. Shanks’ method was introduced to deal with slowly converging case. The accuracy and efficiency of the algorithm were verified with the Burger equation for a variety of cases. The robustness of the algorithm to achieve convergent solutions was demonstrated by highly nonlinear reactive contaminant transport and multiphase flow problems.