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1.
This paper aims at investigation of the dynamic properties of gravity cage exposed to waves by use of a numerical model. The numerical model is developed, based on lumped mass method to set up the equations of motion of the whole cage; meanwhile the solutions of equations are solved by the Runge-Kutta-Verner fifth-order and sixth-order method. Physical model tests have been carried out to examine the validity of the numerical model. The results by the numerical simulation agree well with the experimental data. 相似文献
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In this paper, a numerical model is established. A modified N-S equation is used as a control equation for the wave field and porous flow area. The control equations are discreted and solved by the finite difference method. The free surface is tracked by the VOF method. The pressure field and velocity field of the whole flow area are solved by the reiterative iteration method. Finally, compared with the physical model test results of wave flume, the numerical model established in the present study is validated. 相似文献
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1994年发生在台湾海峡的一次地震海啸的数值模拟 总被引：19，自引：0，他引：19
建立了一个地震海啸数值模式,模式包含越洋海啸传播部分和近岸海啸变形部分,在越洋海啸传播部分中采用线性浅水方程,使用蛙跃格式求解,并且选择合适的空间步长与时间步长,使差分格式中产生的数值频散与包辛尼斯克方程中的物理频散一致,这样在不影响海啸数值计算精度的前提下,节省了计算机的机时与内存.在近岸海啸变形部分的计算中,考虑了非线性对流项与海底摩擦项.同时该模式采用了多重网格嵌套技术,提高了所关心地区的计算精度.利用这个地震海啸模式模拟了1994年发生在台湾海峡的一次地震海啸,结果与观测记录较吻合.这个模型已用于我国沿海核电站可能最大地震海啸的数值计算. 相似文献
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In this study, the Navier-Stokes equations and the pressure Poisson equation for two-dimensional time-dependent viscous flows are solved with a finite difference method in a curvilinear coordinate system. With this numerical procedure, the vortex shedding flow past a circular cylinder near a wall is investigated. The flow is calculated for a broad range of gap ratios for different Reynolds numbers ranging from 80 to 1000. Based on the numerical solutions, the vortex shedding is observed using various methods, and the mechanism for the vortex shedding suppression at small gap ratios is analyzed. The critical gap ratio at which the vortex shedding is suppressed is identified at different Reynolds numbers. 相似文献
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A new set of equations of motion for wave propagation in water with varying depth is derived in this study. The equations expressed by the velocity potentials and the wave surface elevations include first-order non-linearity of waves and have the same dispersion characteristic to the extended Boussinesq equations. Compared to the extended Boussinesq equations, the equations have only two unknown scalars and do not contain spatial derivatives with an order higher than 2. The wave equations are solved by a finite element method. Fourth-order predictor–corrector method is applied in the time integration and a damping layer is applied at the open boundary for absorbing the outgoing waves. The model is applied to several examples of wave propagation in variable water depth. The computational results are compared with experimental data and other numerical results available in literature. The comparison demonstrates that the new form of the equations is capable of calculating wave transformation from relative deep water to shallow water. 相似文献
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Presented here is a compact explicit difference scheme of high accuracy for solving the extended Boussinesq equations.For time discretization,a three-stage explicit Runge-Kutta method with TVD property is used at predicting stage,a cubic spline function is adopted at correcting stage,which made the time discretization accuracy up to fourth order;For spatial discretization,a three-point explicit compact difference scheme with arbitrary order accuracy is employed.The extended Boussinesq equations derived by Beji and Nadaoka are solved by the proposed scheme.The numerical results agree well with the experimental data.At the same time,the comparisons of the two numerical results between the present scheme and low accuracy difference method are made,which further show the necessity of using high accuracy scheme to solve the extended Boussinesq equations.As a valid sample,the wave propagation on the rectangular step is formulated by the present scheme,the modelled results are in better agreement with the experimental data than those of Kittitanasuan. 相似文献
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This paper presents the numerical solution of a new nonlinear mild-slope equation governing waves with different frequency components propagating in a region of varying water depth. There are two new nonlinear equations. The linear part of the equations is the mild-slope equation, and one of the models has the same non-linearity as the Boussinesq equations. The new equations are directly applicable to the problems of nonlinear wave-wave interactions over variable depth. The equations are first simplified with the parabolic approximation, and then solved numerically with a finite difference method. The Crank-Nicolson method is used to discretize the models. The numerical models are applied to a set of published experimental cases, which are nonlinear combined refraction-diffraction with generation of higher harmonic waves. Comparison of the results shows that the present models generally predict the measurements better than other nonlinear numerical models which have been applied to the data set. 相似文献
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The incompressible viscous uniform and shear flow past a circular cylinder is studied. The two-dimensional Navier-Stokes equations are solved by a finite element method. The governing equations are discretized by a weighted residual method in space. The stable three-step scheme is applied to the momentum equations in the time integration. The numerical model is firstly applied to the computation of the lid-driven cavity flow for its validation. The computed results agree well with the measured data and other numerical results. Then, it is used to simulate the viscous uniform and shear flow over a circular cylinder for Reynolds numbers from lO0 to lO00. The transient time interval before the vortex shedding occurs is shortened considerably by introduction of artificial perturbation. The computed Strouhal number, drag and lift coefficients agree well with the experimental data. The computation shows that the finite element model can be successfully applied to the viscous flow problem. 相似文献
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研究并行算法解决应用并行计算机完成规模尽可能大的偏微分方程的数值求解问题。利用Hopf-Cole变换,将一维非线性Burgers方程转化为线性扩散方程,基于第二类Saul’yev型非对称格式和Crank-Nicolson格式对扩散方程进行差分离散,建立解Burgers方程的交替分段并行差分格式,并讨论该方法的稳定性,给出了数值算例。此算法把剖分节点分成若干组,在每组上构造能够独立求解的差分方程,因此具有并行本性,适合在高性能多处理器的并行计算机上使用。数值试验的结果表明此方法是有效的,且有较高的精度。 相似文献
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In the present study, three-dimensional sloshing phenomena occurring in liquid cargo tanks are numerically simulated. The Navier-Stokes equations and continuity equation are used for the governing equations, and solved with a finite difference method in a rectangular fixed staggered mesh system. The positions of free surface are defined by the Marker density method satisfying the free-surface boundary conditions, and the flows of the gas and liquid regions are simulated simultaneously. The irregular leg length and star method is employed on the cells near the free surface for the computations of pressure. The computation results are compared with other experimental results to verify the consistency of the present numerical method, and the agreements are reasonably good. Furthermore, the flow characteristics inside a partially filled liquid tank of a real sized ship oscillating regularly and irregularly are computed to verify the possibility of practical application of the present method. 相似文献
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Martin J. Petersen 《Ocean Engineering》1982,9(4):295-329
This paper described a procedure for simulation of the outer dynamics in ship collisions.The simulation procedure is derived using the transient equations for the horizontal motion of a ship. The hydrodynamic forces acting on the ships' hull during the collision are calculated by a strip method, where the forces acting on each section are described by means of unit response functions. These functions are determined by cosine transformation of the sectional dampings. The sectional added masses and dampings, and thereby also the sectional unit response functions, are calculated by an approximate method. The deformations of the slip structures during the collisions are modelled as non-linear springs.The resulting system of non-linear equations is solved using a numerical time-integration procedure.A number of different collision situations are simulated by means of the procedure. 相似文献
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This is a numerical study on the time development of surface waves generated by a submerged body moving steadily in a two-layer fluid system, in which a layer of water is underlain by a layer of viscous mud. The fully nonlinear Navier-Stokes equations are solved on FLUENT with the Volume-of-Fluid (VOF) multiphase scheme in order to simulate the free surface waves as well as the water-mud interface waves as functions of time. The numerical model is validated by mimicking a reported experiment in a one-layer ... 相似文献
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A novel computational approach is introduced for the efficient computation of equilibrium solutions of seasonally forced ocean biogeochemical models. The essential idea is to formulate the problem as a large system of nonlinear algebraic equations to be solved with a class of methods known as matrix-free Newton–Krylov (MFNK). MFNK is a combination of Newton-type methods for superlinearly convergent solution of nonlinear equations, and Krylov subspace methods for solving the Newton correction equations. The basic link between the two methods is the Jacobian-vector product, which may be probed approximately without forming and storing the elements of the true Jacobian. To render this approach practical for global models with O(106) degrees of freedom, a flexible preconditioning strategy is developed. The result is an essentially “black-box” numerical scheme than can be applied to most existing biogeochemical models. The method is illustrated by applying it to find the equilibrium solutions of two realistic biogeochemical problems. Compared with the conventional approach of direct time integration, the preconditioned-MFNK scheme is shown to be roughly two orders of magnitude more efficient. Several potential refinements of the basic algorithm that may yield further performance gains are discussed. The numerical scheme described here addresses a fundamental challenge to using ocean biogeochemical models more effectively. 相似文献
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A numerical approach for predicting motion and tension of extensible marine cables during laying operations in a rough sea is presented here. The solution methodology consists of dividing the cable into straight elements, which must satisfy an equilibrium equation and compatibility relations. The system of nonlinear differential equations is solved by the Runge–Kutta method, taking the effect of regular and/or irregular waves into account explicitly.
Illustrative applications of the method are given for a typical cable laying ship. The results are presented as rms values of the cable dynamic tension and corresponding dynamic factor for two different types of cable and several values of cable stiffness. The effect of axial deformation on the maximum tension at the shipboard pulley location is highlighted. 相似文献
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A two-dimensional scour model based on coupled system of shallow water equations (SWEs) and sediment transport on unstructured mesh is developed. The coupled system of hydrodynamic and morphodynamic equations is solved by finite volume method using Godunov scheme. Roe's approximate Riemann solver is used to calculate the inviscid fluxes. The use of unstructured mesh makes the model applicable to complex domains. However, it is difficult to evaluate the eigenvalues and eigenvectors of the Jacobian matrix in the global coordinate. The method proposed herein to deal with this difficulty is to transform the system into the local coordinate with one of the axes in the same direction as the interface outward normal vector. In the local coordinate system, the Jacobian matrix is simplified and the eigenvalues are analyzed using asymptotic method. Regular expansion breaks down when the flow is near critical. Uniformity of the expansion is achieved by changing the scales. Rotational invariance theorem is used to relate the interfacial fluxes in the global and local coordinate systems. Special treatment of the source term on unstructured grid makes the scheme stable and physically balanced (both mass and momentum). The method proposed in this paper for the eigen-system is very efficient comparing to iterative numerical methods. Results from the test cases show good agreement with the experiments. 相似文献
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A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations
A numerical scheme for solving the class of extended Boussinesq equations is presented. Unlike previous schemes, where the governing equations are integrated through time using a fourth-order method, a second-order Godunov-type scheme is used thus saving storage and computational resources. The spatial derivatives are discretised using a combination of finite-volume and finite-difference methods. A fourth-order MUSCL reconstruction technique is used to compute the values at the cell interfaces for use in the local Riemann problems, whilst the bed source and dispersion terms are discretised using centred finite-differences of up to fourth-order accuracy. Numerical results show that the class of extended Boussinesq equations can be accurately solved without the need for a fourth-order time discretisation, thus improving the computational speed of Boussinesq-type numerical models. The numerical scheme has been applied to model a number of standard test cases for the extended Boussinesq equations and comparisons made to physical wave flume experiments. 相似文献
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In this paper, a numerical model is established for estimating the wave forces on a submerged horizontal circular cylinder. For predicting the wave motion, a set of two-dimensional Navier-Stokes equations is solved numerically with a finite element method. In order to track the moving non-linear wave surface boundary, the Navier-Stokes equations are discretized in a moving mesh system. After each computational time step, the mesh is modified according to the changed wave surface boundary. In order to stabilize the numerical procedure, a three-step finite element method is applied in the time integration. The water sloshing in a tank and wave propagation over a submerged bar are simulated for the first time to validate the present model. The computational results agree well with the analytical solution and the experimental data.Finally, the model is applied to the simulation of interaction between waves and a submerged horizontal circular cylinder.The effects of the KC number and the cylinder depth on the wave forces are studied. 相似文献
19.
1 .Introduction The dynamics of soft mud under surface water waves is of great importance to the sedimentationprocesses in approach channels and harbors ,and has long been drawing attention. Advancements innumerous engineering applications inthe shallowco… 相似文献
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A finite-difference scheme and a modified marker-and-cell (MAC) algorithm have been developed to investigate the interactions of fully nonlinear waves with two- or three-dimensional structures of arbitrary shape. The Navier–Stokes (NS) and continuity equations are solved in the computational domain and the boundary values are updated at each time step by the finite-difference time-marching scheme in the framework of a rectangular coordinate system. The fully nonlinear kinematic free-surface condition is implemented by the marker-density function (MDF) technique developed for two fluid layers.To demonstrate the capability and accuracy of the present method, the numerical simulation of backstep flows with free-surface, and the numerical tests of the MDF technique with limit functions are conducted. The 3D program was then applied to nonlinear wave interactions with conical gravity platforms of circular and octagonal cross-sections. The numerical prediction of maximum wave run-up on arctic structures is compared with the prediction of the Shore Protection Manual (SPM) method and those of linear and second-order diffraction analyses based on potential theory and boundary element method (BEM). Through this comparison, the effects of non-linearity and viscosity on wave loading and run-up are discussed. 相似文献