Impulsive control of stochastic system under the sense of stochastic asymptotical stability

This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution's stochastic asymptotical stability. From the comparison theory, it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterministic comparison system. As a general application of this theory, it controls the chaos of stochastic Lü system using impulsive control method, and numerical simulations are employed to verify the feasibility of this method.     

基于微控制器数字硬件实现的网格涡卷超混沌系统

基于微控制器(MCU)设计了一个通用的四维混沌系统数字硬件实验电路,由此实现了9×7网格涡卷的混沌和超混沌吸引子的生成.本文基于由Colpitts振荡器模型延伸出的四维多涡卷超混沌系统,通过引入单位锯齿波函数替换原系统中的三角波函数,构建了一个便于MCU数字硬件实现的新的网格涡卷超混沌系统,并对新系统网格涡卷吸引子的形成机理进行了分析和数值仿真.通过采用Euler算法对新系统进行离散化,在实验电路的有效动态范围内可以生成比原系统更多网格涡卷数量的吸引子.实验结果有效验证了本文基于MCU实现的网格涡卷超混沌     

Numerical investigations of wave overtopping at coastal structures

Under the numerical modelling work package of the EU funded CLASH project, the time accurate, free surface capturing, incompressible Navier–Stokes solver AMAZON-SC has been applied to study impulsive wave overtopping at Samphire Hoe, near Dover in the United Kingdom. The simulations show that the overtopping process on this vertical, sheet pile, seawall is dominated by impulsive, aerated, near vertical overtopping jets. In order to perform the simulations AMAZON-SC has been extended to incorporate an isotropic porosity model and for validation purposes the solver has been applied to study overtopping of a low crested sea dike and a 10:1 battered wall. The results obtained for the battered wall and Samphire Hoe tests are in good agreement both with predicted overtopping discharges calculated using the UK overtopping manual and with available experimental results.     

A new adaptive Cartesian-grid CIP method for computation of violent free-surface flows

A new adaptive Cartesian-grid for the CIP (constrained interpolation profile) method is proposed and applied to two-dimensional numerical simulations of violent free-surface flows. The CCUP (CIP combined and unified procedure) method is employed and combined with this adaptive Cartesian-grid for robust and efficient computation. This adaptive grid is capable of tracking regions where flows vary violently, and a much finer grid is then concentrated automatically on these regions to adapt to the violent changing of the flow. Unlike the abacus-like Soroban grid which is an adaptive meshless grid with complicated algorithms and inefficiency of evaluation of frequently computed spatial derivatives, the present approach not only simplifies computational algorithm but also enhances efficiency of frequently-computed spatial derivatives. It is also different from most of the remeshing schemes that no additional CPU-time for the value-mapping from the old grid to the new grid is taken in this adaptive grid system provided that the advection velocity is interpolated, since the value-mapping process is accomplished simultaneously within the advection process. To validate the accuracy and efficiency of this newly-proposed CFD model, several two-dimensional benchmark problems are performed, and the results are compared with experimental measurements and other published numerical results. Numerical simulations show that the proposed numerical model is robust, accurate, and efficient for strongly nonlinear free-surface flows.     

Design of Mooring System for Oil Storage Vessels

The floating oil storage system has been proposed as a new facility for Strategic Petroleum Reserve (SPR) in China. Mooring is one of the key technologies to ensure the safety, reliability, and performance of the oil storage system. This paper describes the concept, analysis, design and reliability of the mooring system. For mooring system design of these oil vessels, analysis is essential of the behavior of the vessel in connection with mooring facilities of nonlinear resilience. A nonlinear mathematical model for analyzing a moored vessel is established and solved. Some results of numerical simulations are presented. Assessment of the safety regarding the mooring system in terms of failure probability is carried out. Another simulation model for calculating the failure probability of the mooring system is proposed. The design parameters that have an influence on the characteristics of the failure probability have been identified. The simulation results show that the mooring system has an annual reliab     

Storm surge simulation along the Meghna estuarine area: an alternative approach

In this study, numerical prediction of surges associated with a storm was made through the method of lines (MOL) in coordination with the newly proposed RKARMS (4, 4) method for the meghna estuarine region, along the coast of Bangladesh. For this purpose, the vertically integrated shallow water equations (SWEs) in Cartesian coordinates were firstly transformed into ordinary differential equations (ODEs) of initial valued, which were then soloved using the new RKARMS (4, 4) method. Nested grid technique was employed for resolving the complexities of the region of interest with minimum cost. Fresh water discharge through the lower Meghna River was taken into account along the north east corner of the innermost child scheme. Numerical experiments were performed with the severe cyclone on April 1991 that crossed the coast over the study area. Simulated results by the study were found to be in good agreement with some reported data and were found to compare well with the results obtained by the MOL in addition with the classical 4th order Runge-Kutta (RK (4, 4)) method and the standard finite difference method (FDM).     

On the determination of the mesh size for numerical simulations of shock wave propagation in near field underwater explosion

It is well known that the accuracy of mesh-based numerical simulations of underwater explosion strongly relies on the mesh size adopted in the analyses. Although a numerical analysis of underwater explosion can be performed with enough accuracy by using considerably fine meshes, such fine meshes may lead to substantially increase in the CPU time and the usage of computer memory. Thus, how to determine a suitable mesh size in numerical simulations is always a problem confronted when attempting to study the shock wave propagation resulting from underwater explosion and the subsequent response of structures. Considering that there is currently no universally accepted method for resolving this problem, this paper aims to propose a simple method to determine the mesh size for numerical simulations of near field underwater explosion. To this end, the mesh size effects on the shock wave propagation of underwater explosion are carefully investigated for different charge weights, through which the correlation between mesh sizes and charge weights is identified. Based on the numerical study, a dimensionless variable (λ), defined as the ratio of the radius of charge to the side length of element, is introduced to be the criterion for determining the mesh size in simulations. It is interesting to note that the presented method is suitable for various charge weights. By using the proposed meshing rule, adequate balance between solution accuracy and computational efficiency can be achieved for different blast scenarios in numerical simulations of underwater explosion.     

Numerical study on added resistance of ships by using a time-domain Rankine panel method

This paper considers the numerical computation of added resistance on ships. As a method of solution, a higher-order Rankine panel method is applied in time domain. Furthermore, two different formulations, Neumann-Kelvin and double-body linearizations, are applied to investigate the difference between computational results. The quantities of added resistance are obtained by integrating the second-order pressure on the body surface. Computational results are validated by comparing with experimental data and other computational results on several models, and fair agreements are found for all the models. The components of added resistance are observed with regard to integral terms, radiation and diffraction components. This study continues to the computation of added resistance in irregular waves. This kind of computational approach can provide some important information to understand the uncertainty level of towing-tank measurement of added resistance. In this study, a series of long numerical simulations are carried out, and their statistical variations are observed for different time windows. Based on this observation, an appropriate criterion and averaging method are proposed for the prediction of added resistance in irregular waves.     

基于Boussinesq水波模型的聚焦波模拟

基于最高导数为3阶的单层Boussinesq方程,建立了聚焦波的时域波浪计算模型。数值模型求解采用了预报?校正的有限差分法。对于时间差分格式,预报和校正分别采用3阶Adams-Bashforth格式和4阶Adams-Moulton格式。首先,针对不同水深条件下水槽中传播的强非线性波进行模拟,并将数值结果与流函数的数值解析解进行了比较,结果表明无论是波面位移、波面处的水平速度和垂向速度均与解析解符合较好,最大波峰面的速度分布伴随水深的增加与解析解吻合程度变差,非线性速度分布的适用范围与线性解析解适应范围kh<3.5基本一致。其次,对深水聚焦波演化进行了模拟研究,研究中聚焦波的生成采用在边界点累加不同频率线性规则波的方法。应用聚焦波物理模型实验结果验证模型,计算聚焦位置处的波面位移和沿水深的速度分布与实验结果的对比表明,波面位移吻合程度较好,垂向的水平速度分布基本吻合。最后,保持中心频率(周期)不变,数值模拟了周期范围变化下最大聚焦波峰面以及波峰面水平速度的变化趋势,结果表明波峰面值和波峰面水平速度随着周期范围缩小而增大。     

Stochastic simulations of ocean waves: An uncertainty quantification study

The primary objective of this study is to introduce a stochastic framework based on generalized polynomial chaos (gPC) for uncertainty quantification in numerical ocean wave simulations. The techniques we present can be easily extended to other numerical ocean simulation applications. We perform stochastic simulations using a relatively new numerical method to simulate the HISWA (Hindcasting Shallow Water Waves) laboratory experiment for directional near-shore wave propagation and induced currents in a shallow-water wave basin. We solve the phased-averaged equation with hybrid discretization based on discontinuous Galerkin projections, spectral elements, and Fourier expansions. We first validate the deterministic solver by comparing our simulation results against the HISWA experimental data as well as against the numerical model SWAN (Simulating Waves Nearshore). We then perform sensitivity analysis to assess the effects of the parametrized source terms, current field, and boundary conditions. We employ an efficient sparse-grid stochastic collocation method that can treat many uncertain parameters simultaneously. We find that the depth-induced wave-breaking coefficient is the most important parameter compared to other tunable parameters in the source terms. The current field is modeled as random process with large variation but it does not seem to have a significant effect. Uncertainty in the source terms does not influence significantly the region before the submerged breaker whereas uncertainty in the incoming boundary conditions does. Considering simultaneously the uncertainties from the source terms and boundary conditions, we obtain numerical error bars that contain almost all experimental data, hence identifying the proper range of parameters in the action balance equation.     

New Numerical Scheme for Simulation of Hyperbolic Mild-Slope Equation

The original hyperbolic mild-slope equation can effectively take into account the combined effects of wave shoaling, refraction, diffraction and reflection, but does not consider the nonlinear effect of waves, and the existing numerical schemes for it show some deficiencies. Based on the original hyperbolic mild-slope equation, a nonlinear dispersion relation is introduced in present paper to effectively take the nonlinear effect of waves into account and a new numerical scheme is proposed. The weakly nonlinear dispersion relation and the improved numerical scheme are applied to the simulation of wave transformation over an elliptic shoal. Numerical tests show that the improvement of the numerical scheme makes efficient the solution to the hyperbolic mild-slope equation. A comparison of numerical results with experimental data indicates that the results obtained by use of the new scheme are satisfactory.     

On the motions of the underwater remotely operated vehicle with the umbilical cable effect

In this paper, a hydrodynamic model is developed to simulate the six degrees of freedom motions of the underwater remotely operated vehicle (ROV) including the umbilical cable effect. The corresponding hydrodynamic forces on the underwater vehicle are obtained by the planar motion mechanism test technique. With the relevant hydrodynamic coefficients, the 4th-order Runge–Kutta numerical method is then adopted to solve the equations of motions of the ROV and the configuration of the umbilical cable. The multi-step shooting method is also suggested to solve the two-end boundary-value problem on the umbilical cable with respect to a set of first-order ordinary differential equation system. All operation simulations for the ROV including forward moving, ascending, descending, sideward moving and turning motions can be analyzed, either with or without umbilical cable effect. The current effect is also taken into consideration. The present results reveal that the umbilical cable indeed significantly affects the motion of the ROV and should not be neglected in the simulation.     

Transient response of harbours to long waves under resonance conditions

This paper presents the results of a study aimed at quantifying the time–response of harbour basins to long waves under resonance conditions. On the basis of numerical simulations reproducing long waves in the yacht harbour of Rome (Ostia, Italy), it shows that the results valid for periodic forcing waves, acting for an infinitely long time, as those provided by models based on elliptic equations like the Helmoltz and the mild-slope equations, can be misleading with respect to the more realistic ones that can be obtained using time-varying wave equations. Taking advantage of the similarity between the processes studied here and a simple one-dimensional resonator, a method is also proposed to roughly estimate a time–response parameter of each mode of the harbour, using results from steady-state numerical model results, commonly applied for studying harbour resonance in engineering practice. On the basis of further numerical simulations, aimed at reproducing schematic harbour layouts, the effect on resonance of the position of the entrance and of an outer harbour is studied. The results indicate that the effects of design solutions to reduce resonance, by placing the entrance at the middle of the harbour, or using the outer harbour as a resonator, can be correctly evaluated only when considering the time needed for the oscillations to fully develop.     

Improvement on open boundaries on a time dependent numerical model of wave propagation in the nearshore region

An improvement on the simulation of outgoing waves on a time dependent numerical model for water wave propagation in the nearshore region is presented. The governing equations consist of a system of first order partial differential equations (PDEs), the equation of continuity and the equation of motion. A comparative study of first order radiation boundary conditions (BCs) and first order radiation BCs combined with sponge layers is presented for cases where outgoing waves leave the numerical domain of calculation through the open boundary. A reduction of spurious reflections from the numerical open boundaries can be obtained with an irrelevant increase in terms of computational cost.     

低速十字路口交通流模型相图

研究由两个单车道构成低速十字路口交通流模型.模型中两车道上的车辆更新遵循无交通灯管制下的并行规则.依据构建相图的原则并采用局部占有概率方法,建立相图,给出相图中的各部分区域的流量表达式.两车道均采用周期边界条件和确定性FI模型进行数值模拟,模拟结果与理论分析精确一致.模型中两条车道的行车规则更接近实际道路交通,该结果为交通管理提供一定的指导作用.     

渤海油田浅水软刚臂系泊FPSO触底分析

在线性三维势流理论的基础上,采用时域计算方法对BZ25—1油田16万吨级FPSO不同吃水条件下的碰底情况作了分析研究。数值计算结果与模型试验进行了比较,两者吻合较好,说明应用时域计算方法可以从理论上预报FPSO在浅水中的触底情况。这对我国渤海等浅水海域油田应用FPSO系统进行开发具有一定的意义。     

Internal wave excitation from a collapsing mixed region

The collapse of a uniform density fluid (a “mixed region”) into a surrounding ambient fluid with complex stratification is examined by way of laboratory experiments and fully nonlinear numerical simulations. The analysis focuses upon the consequent generation of internal gravity waves and their influence upon the evolution of the collapsing mixed region. In experiments and simulations for which the ambient fluid has uniform density over the vertical extent of the mixed region and is stratified below, we find the mixed region collapses to form an intrusive gravity current and internal waves are excited in the underlying stratified fluid. The amplitude of the waves is weak in the sense that the intrusion is not significantly affected by the waves. However, scaling the results to the surface mixed layer of the ocean we find that the momentum flux associated with the waves can be as large as 1 N/m². In simulations for which the ambient fluid is stratified everywhere, including over the vertical extent of the mixed region, we find that internal waves are excited with such large amplitude that the collapsing mixed region is distorted through strong interactions with the waves.     

Numerical computations of resonant sloshing using the modified isoAdvector method and the buoyancy-modified turbulence closure model

Sloshing is an interfacial-flow phenomenon which brings two challenges on how to locate the position of the interface and avoid the unphysical motion of the interface. In order to locate the the position of the interface, a new geometric Volume-of-Fluid (VOF) method called isoAdvector is adopted to pursue a sharp interface. Aiming to make the isoAdvector method compatible with the dynamic mesh adopted to handle the tank motion, the motion-flux correction is introduced, and a moving-velocity correction for face-interface intersection line (FIIL) is proposed. An approximation formula is adopted to effectively reconstruct the moving-velocity field of the meshes at each cell center based on the motion fluxes on each cell face. In order to avoid the unphysical motion of the interface due to the excessive turbulence level in the transition region at the interface, the buoyancy-modified k − ω SST model is adopted. The numerical results of wave elevations and forces are compared with the experiments. The comparisons suggest that (i) the moving-velocity correction for FIIL is important to update the volume fraction; (ii) the modified isoAdvector method can capture the the position of the interface more accurately than the algebraic VOF method; (iii) the unphysical motion of the interface can be avoided by using the buoyancy-modified k − ω SST model in long-time simulations. In addition, a new post-processing approach is proposed to evaluate the interface thickness. The decrease of interface thickness improves the accuracies of wave elevations by using the modified isoAdvector method. The adoption of both the modified isoAdvector method and the buoyancy-modified k − ω SST model improves the computational accuracies of wave elevations and hydrodynamic loads in long-time simulations.     

Characteristics of the boundary layer at the bottom of a solitary wave

The results of direct numerical simulations of the boundary layer generated at the bottom of a solitary wave are described. The numerical results, which agree with the laboratory measurements of Sumer et al. (2010) show that the flow regime in the boundary layer can be laminar, laminar with coherent vortices and turbulent. The average velocity and bottom shear stress are computed and the results obtained show that the logarithmic law can approximate the velocity profile only in a restricted range of the parameters and at particular phases of the wave cycle. Moreover, the maximum value of the bottom shear stress is found to depend on the dimensionless wave height only, while the minimum (negative) value depends also on the dimensionless boundary layer thickness. Diagrams and simple formulae are proposed to evaluate the minimum and maximum bottom shear stresses and their phase shift with respect to the wave crest.