Parametric study of the wave-induced residual liquefaction around an embedded pipeline

Wave-induced liquefaction in a porous seabed around submarine pipeline may cause catastrophic consequences such as large horizontal displacements of pipelines on the seabed, sinking or floatation of buried pipelines. Most previous studies in relation to the wave and seabed interactions with embedded pipeline dealt with the wave-induced instaneous seabed response and possible resulting momentary liquefaction (where the soil is liquefied instantaneously during the passage of a wave trough), using theory of poro-elasticity. Studies for the interactions between a buried pipeline and a soil undergoing build-up of pore pressure and residual liquefaction have been comparatively rare. In this paper, this complicated process was investigated by using a new developed integrated numerical model with RANS (Reynolds averaged Navier–Stokes) equations used for governing the incompressible flow in the wave field and Biot consolidation equations used for linking the solid–pore fluid interactions in a porous seabed with embedded pipeline. Regarding the wave-induced residual soil response, a two-dimensional poro-elastoplastic solution with the new definition of the source term was developed, where the pre-consolidation analysis of seabed foundation under gravitational forces including the body forces of a pipeline was incorporated. The proposed numerical model was verified with laboratory experiment to demonstrate its accuracy and effectiveness. The numerical results indicate that residual liquefaction is more likely to occur in the vicinity of the pipeline compared to that in the far-field. The inclusion of body forces of a pipeline in the pre-consolidation analysis of seabed foundation significantly affects the potential for residual liquefaction in the vicinity of the pipeline, especially for a shallow-embedded case. Parametric studies reveal that the gradients of maximum liquefaction depth with various wave and soil characteristics become steeper as pipeline burial depth decreases.     

Refined seaward boundary conditions for modelling shallow water waves in semi-enclosed water bodies

Based on the theory of characteristics, this research elaborates on the numerical treatment of two types of seaward boundary conditions for modelling long-wave dynamics in truncated estuarine and coastal domains. These seaward boundary conditions are devised for the solution of the fully non-linear shallow water equations in the time domain. The first type is the clamped boundary, at which the water level variation is given and the velocity is computed along the characteristic line going out of the domain. The second type is the non-reflecting boundary, where the incident wave information is introduced and the reflected waves from inside the computational domain are allowed to escape at the same time. The essence of its numerical implementation is to distinguish the inward and outward characteristics and to disconnect the incoming characteristic relation from the actual flow inside the domain. Compared with previous techniques, the present method includes extra terms in the derivation to account for the effects of the uneven bed, bottom friction and shape of the characteristic lines. A shock-capturing finite difference method is used to solve the shallow water equations in the deviatoric format, but the seaward boundary algorithms constructed herein are generic and applicable to other solvers. The necessity of these refinements is highlighted by simulating the tidal oscillation in the Persian/Arabian Gulf, periodic wave runup on the coastline and the wave resonance in a narrow harbour. It is found that neglecting the bed slope at the boundary may result in biased mean water levels in the prediction.     

一维全非线性Green-Naghdi水波方程数值模型

建立了求解一维全非线性Green-Naghdi水波方程的中心有限体积/有限差分混合数值格式。采用结构化网格对守恒形式的控制方程进行离散和积分,界面数值通量采用有限体积法计算,剩余项则采用中心有限差分格式求解。其中,采用中心迎风有限体积格式计算控制体界面数值通量,并结合界面变量的线性重构方法,使其在空间上具有四阶精度,通过引入静压重构技术和波浪破碎指标使模型具备处理海岸水-陆动边界及波浪破碎的能力。时间积分则采用具有总时间变差减小(Total Variation Diminishing,TVD)性质的三阶龙格-库塔法进行。应用该模型对孤立波在常水深和斜坡海岸上的传播过程及规则波跨越潜堤传播的实验进行了数值模型研究,数值计算同解析解及实验数据吻合良好。     

Isogeometric analysis for unsaturated flow problems

Unsaturated flow problems in porous media often described by Richards’ equation are of great importance in many engineering applications. In this contribution, we propose a new numerical flow approach based on isogeometric analysis (IGA) for modeling the unsaturated flow problems. The non-uniform rational B-spline (NURBS) basis is utilized for spatial discretization whereas the stable implicit backward Euler method for time discretization. The nonlinear Richards’ equation is iteratively solved with the aid of the Newton–Raphson scheme. Owing to some desirable features of an efficient numerical flow approach, major advantages of the present formulation involve: (a) numerical oscillation at the wetting front can be avoided or facilitated, simply by using either an h-refinement or a lumped mass matrix technique; (b) higher-order exactness can be obtained due to the nature of the IGA features; (c) the approach is straightforward to implement and it does not need any transformation, e.g., Kirchhoff transformation or filter algorithm; and (d) in contrast to the Picard iteration scheme, which forms linear convergences, the proposed approach can however yield quadratic convergences by using the Newton–Raphson method for solving resultant nonlinear equations. Numerical model validation is analyzed by solving a three-dimensional unsaturated flow problem in soil, and its derived results are verified against analytical solutions. Numerical applications are then studied by considering three extensive examples with simple and complex configurations to further show the accuracy and applicability of the present IGA.     

施密特望远镜CCD BVRI测光系统的初步研究

本文利用Thomson CCD,在北京天文台兴隆站施密特望远镜上进行BVRI四色测光,得到了该测光系统的颜色转换方程,并对所得结果进行了分析探讨。同时论证了BAO-CCD系统在施密特望远镜上用于测光的可行性。     

改进的波流相互作用Boussinesq方程

对于波流相互作用的Boussinesq方程,为了考虑水流作用所引起的平均水面变化,通过引入新的计算速度,使方程色散关系中的水深为考虑水流影响后的实际水深,并使方程色散精度达到了Padé[4,4]。通过计算潜堤强水流和裂流两种背景水流流场情况下的波浪运动特征,验证了该模型和数值方法的正确性。     

Numerical solution of the asymmetric water impact of a wedge in three degrees of freedom

Impact problems associated with water entry have important applications in various aspects of naval architecture and ocean engineering. Estimation of hydrodynamic impact forces especially during the first instances after the impact is very important and is of interest. Since the estimation of hydrodynamic impact load plays an important role in safe design and also in evaluation of structural weight and costs, it is better to use a reliable and accurate prediction method instead of a simple estimation resulted by analyzing methods. In landing of flying boats, some phenomena such as weather conditions and strong winds can cause asymmetric instead of symmetric descent. In this paper, a numerical simulation of the asymmetric impact of a wedge, as the step of a flying boat, considering dynamic equations in two-phase flow is taken into account. The dynamic motion of the wedge in two-phase flow is solved based on finite volume method with volume of fluid (VOF) scheme considering dynamic equations. Then the effects of different angles of impact and water depth on the velocity change and slamming forces in an asymmetric impact are investigated. The comparison between the simulation results and experimental data verifies the accuracy of the method applied in the present study.     

Improved method to determine the molar volume and compositions of the NaCl-H<Subscript>2</Subscript>O-CO<Subscript>2</Subscript> system inclusion

On the basis of Parry’s method (1986), an improved method was established to determine the molar volume (Vm) and compositions (X) of the NaCl-H2O-CO2 (NHC) system inclusion. To use this method, the determination of Vm-X only requires three microthermometric data of a NHC inclusion: partial homog-enization temperature (Th ,CO2), salinity (S) and total homogenization temperature (Th). Theoretically, four associated equations are needed containing four unknown parameters: X CO2, XNaCl, Vm and F (volume fraction of CO2 phase in total inclusion when occurring partial homogenization). When they are released, the Vm-X are determined. The former three equations, only correlated with Th ,CO2, S and F, have simplified expressions:XCO2=f1(Th,CO2,S,F),XNaCl=f2(Th,CO2,S,F),Vm=f3(Th,CO2,S,F). The last one is the thermodynamic relationship of X CO2, XNaCl, Vm and Th:f4(XCO2,XNaCl,Vm,Th)=0.Since the above four associated equations are complicated, it is necessary to adopt iterative technique to release them. The technique can be described by:(i) Freely input a F value (0≤F≤1),with Th ,CO2 and S, into the former three equations. As a result,X CO 2,XNaCl and the molar volume value recorded as Vm1 are derived. (ii) Input the X CO2 and XNaCl gotten in the step above into the last equation, and another molar volume value recorded as Vm2 is determined. (iii) If Vm1 is unequal to Vm2, the calculation will be restarted from “(i)”. The iteration is completed until Vm1 is equal to Vm2, which means that the four associated equations are released. Compared to Parry’s (1986) solution method, the improved method is more convenient to use, as well as more accurate to determine X CO 2. It is available for a NHC inlusion whose partial homogenization temperature is higher than clatherate melting temperature and there are no solid salt crystals in the inclusion at parital homogenization.     

COHERENS模式在长江口赤潮源推测中的应用

在COHERENS基础上,建立了一个σ坐标下的三维渤海、黄海和东海海域夏季环流数值模式,较好地模拟了夏季渤海、黄海和东海海域的环流系统(黑潮、台湾暖流、对马暖流和长江冲淡水)。在此斜压流场的基础上,进行了拉格朗日颗粒追踪和欧拉输运数值模拟来推测长江口及其邻近海域赤潮高发区的可能赤潮源。提出台湾海峡、福建浙江近海和台湾东北海底存在赤潮的“种子”,它们很可能就是我国长江口赤潮高发区的赤潮源,这仍需现场的海洋调查去证实。数值模拟推测赤潮源是对流-扩散输运方法在海洋生态学领域中的一个新应用。     

孤立波与直墙式多孔介质结构相互作用数值分析

以连续性方程和雷诺平均方程为控制方程,用k-ε模型封闭方程组,采用VOF方法追踪自由面,建立了具有造波和消波功能的二维孤立波数值水槽。并基于改进的Darcy多孔介质模型研究了二维孤立波与直墙式多孔介质结构的相互作用问题。数值分析了孤立波与直墙式多孔结构相互作用引起的流场和波形变化特性,并与文献中的实验结果进行了比较,数值结果与实验结果吻合良好。