基于相平均方法的折射绕射联合波浪模型

近岸带波浪运动的研究具有很重要的工程意义，近年来已获得了较丰硕的研 究成果并发展了许多波浪模型，而基于不同理论的波浪模型往往具有特定的适用性. 在海岸 工程中应用比较广泛的一类波浪模型以波能(波作用量)守恒为基本依据，如SWAN模型. 该 类模型在实际工程中已经得到了大量的应用，但该类模型未计及波浪绕射效应，成为其突出 的缺陷之一. 如何对模型做适当的改进，使之适用于波浪绕射的模拟，从而在原有基础上拓 广模型的应用范围是一项具有实际意义的研究工作. 该文采用波能(波作用量)守恒方程描 述近岸带波浪运动，通过引入绕射因子，得到折射、绕射联合波浪模型，从而拓广了模型的 应用范围. 通过实际算例验证，表明所建立的模型计及了波浪折射、绕射作用，对相平 均波浪模型在波浪绕射效应模拟方面的改进具有一定的意义.     

利用非结构化网格方法对翼型绕流的数值研究

利用同位非结构化网格上的压力加权修正算法 ,对翼型湍流绕流进行了数值分析。详细地给出了一孤立翼型在不同攻角下的分离流结构及翼型表面压力分布 ,为了显示非结构化网格方法在求解多连通流动区域的优越性 ,对双翼型绕流进行了数值计算。在数值分析中 ,对阵面推进法进行改进来生成三角形网格 ,采用有限控制体方法直接在物理空间中的非结构化网格单元上离散 Navier- Stokes方程及 k- ε方程 ,形成的代数方程组通过预条件矩阵共轭梯度平方法求解。计算结果表明 :当流动为附着流时 ,计算结果与实验值吻合程度令人相当满意 ;而在分离区内 ,计算结果与实验值存在一定的误差 ,需对分离区内的湍流模型做进一步的改进。     

随机波浪作用下近岸波流场的数值模拟

结合近岸波浪抛物型缓坡模型和近岸波流场模型,对近岸不规则波浪及其破碎后所产生的流场进行了数值模拟. 在不规则波浪场的模拟中,采用JONSWAP波浪谱对入射单向不规则波浪要素按等分频率法进行离散,应用考虑波浪不规则性和破碎效应的抛物型缓坡方程对波浪场进行数值模拟,并基于抛物型缓坡方程中的波浪势函数等参数计算波浪辐射应力,以波浪辐射应力为主要动力因素基于近岸流数学模型对近岸波浪破碎所产生的近岸流场进行数值模拟,并对数值模拟结果进行了验证. 模拟结果表明该模型可有效地用于研究波浪破碎产生的近岸波流场.      

基于VPM-THINC/QQ模型的波浪高保真模拟

为实现波浪传播的高保真数值模拟,采用包含单元均值和点值(volume-average/point-value method,VPM)的有限体积法求解纳维-斯托克斯方程和具有二次曲面性质和高斯积分的双曲正切函数(THINC method with quadratic surface representation and Gaussian quadrature,THINC/QQ)方法来重构自由面,建立以开源求解库OpenFOAM底层函数库为基础的VPM-THINC/QQ模型. 在本模型中添加推板造波法实现波浪的产生功能,采用松弛法实现消波功能,构建高精度黏性流数值波浪水槽. 分别采用VPM-THINC/QQ模型和InterFoam求解器(OpenFOAM软件包中广泛使用的多相流求解器)开展规则波的数值模拟,重点探究网格大小和时间步长等因素对波浪传播过程的影响,定量地分析波高衰减程度;为验证本模型的适应性,对长短波进行模拟. 结果表明,在相同网格大小或时间步长条件下,VPM-THINC/QQ模型的预测结果与参考值吻合较好,波高衰减较少,且无相位差,在波浪传播过程的模拟中呈现出良好的保真性. 本文工作 为波浪传播的模拟研究提供了一种高精度的黏性数值波浪水槽模型.      

波浪破碎的一种混合湍流模拟模式

近岸波浪的变形与破碎,一方面影响水体与泥沙运输,另一方面对消波护岸具有指导意义.本文提出一种三维混合湍流模拟模式方法,将求解区域分为造波区、波浪传播区和消波区.造波区采用层流模式,通过基于Fluent的二次开发的UDF方法在边界进行速度造波.这种方法在给定入口速度的条件下,根据已知波高进行精准插值,从而控制水的体积分数.在波浪传播区域,采用大涡模拟进行模拟研究,在消波区,采用RANS模型并利用多孔介质消波法进行消波.模型通过VOF方法捕捉波浪破碎过程中的自由面变化.本文对波高为5.5 cm的规则波(M1)、波高为13.5cm的规则波(M3)、有效波高为7.75cm的TMA谱单向不规则波(U1)和有效波高为19cm的TMA谱多向不规则波(B5)展开了模拟研究,并与前人的相关实验结果作比较,各条件下模拟结果与实验结果吻合.模拟结果说明本文提出的模型能够准确模拟出波浪传播过程中的折射和绕射现象,并且能够捕捉的波浪破碎过程中的自由面变化,为三维波浪的传播与破碎的数值模拟提供一种模拟方法.     

基于VPM-THINC/QQ模型的波浪高保真模拟

为实现波浪传播的高保真数值模拟,采用包含单元均值和点值(volume-average/point-value method,VPM)的有限体积法求解纳维-斯托克斯方程和具有二次曲面性质和高斯积分的双曲正切函数(THINC method with quadratic surface representation and Gaussian quadrature,THINC/QQ)方法来重构自由面,建立以开源求解库OpenFOAM底层函数库为基础的VPM-THINC/QQ模型.在本模型中添加推板造波法实现波浪的产生功能,采用松弛法实现消波功能,构建高精度黏性流数值波浪水槽.分别采用VPM-THINC/QQ模型和InterFoam求解器(OpenFOAM软件包中广泛使用的多相流求解器)开展规则波的数值模拟,重点探究网格大小和时间步长等因素对波浪传播过程的影响,定量地分析波高衰减程度;为验证本模型的适应性,对长短波进行模拟.结果表明,在相同网格大小或时间步长条件下,VPM-THINC/QQ模型的预测结果与参考值吻合较好,波高衰减较少,且无相位差,在波浪传播过程的模拟中呈现出良好的保真性.本文工作为波浪传播的模拟研究提供了一种高精度的黏性数值波浪水槽模型.     

多尺度嵌入式离散裂缝模型模拟方法

天然裂缝性油藏和人工压裂油藏内裂缝形态多样,分布复杂,传统的离散裂缝模型将裂缝作为基岩网格的边界,采用非结构化网格进行网格划分,其划分过程复杂,计算量大。嵌入式离散裂缝模型划分网格时不需要考虑油藏内的裂缝形态,只需对基岩系统进行简单的网格剖分,可以大大降低网格划分的复杂度,从而提高计算效率。然而,在油藏级别的数值模拟和人工压裂裂缝下的产能分析中,仍然存在计算量巨大、模拟时间过长的问题。本文提出嵌入式离散裂缝模型的多尺度数值计算格式,使用多尺度模拟有限差分法研究嵌入式离散裂缝模型渗流问题。通过在粗网格上求解局部流动问题计算多尺度基函数,多尺度基函数可以捕捉裂缝与基岩间的相互关系,反映单元内的非均质性,因此该方法既有传统尺度升级法的计算效率,又可以保证计算精度,数值结果表明这是一种有效的裂缝性油藏数值模拟方法。     

多尺度嵌入式离散裂缝模型模拟方法

天然裂缝性油藏和人工压裂油藏内裂缝形态多样,分布复杂,传统的离散裂缝模型将裂缝作为基岩网格的边界,采用非结构化网格进行网格划分,其划分过程复杂,计算量大。嵌入式离散裂缝模型划分网格时不需要考虑油藏内的裂缝形态,只需对基岩系统进行简单的网格剖分,可以大大降低网格划分的复杂度,从而提高计算效率。然而,在油藏级别的数值模拟和人工压裂裂缝下的产能分析中,仍然存在计算量巨大、模拟时间过长的问题。本文提出嵌入式离散裂缝模型的多尺度数值计算格式,使用多尺度模拟有限差分法研究嵌入式离散裂缝模型渗流问题。通过在粗网格上求解局部流动问题计算多尺度基函数,多尺度基函数可以捕捉裂缝与基岩间的相互关系,反映单元内的非均质性,因此该方法既有传统尺度升级法的计算效率,又可以保证计算精度,数值结果表明这是一种有效的裂缝性油藏数值模拟方法。     

破碎带波浪的数值模拟

基于一组色散关系得到改进的完全非线性Boussinesq方程建立了一个波浪模型可以模拟近岸水域的波浪变浅、破碎以及在海滩上的爬高等多种变形。波浪破碎引起的能量衰减是在动量方程中引入一个在空间和时间上都只作用于波前的涡粘项来模拟。动海岸线边界用窄缝法处理。波浪爬高用非线性浅水方程推导的非破碎波浪在斜坡上爬高的解析解来验证。本模型还模拟了波浪在斜坡上不同类型的破碎变形过程,并将其波高和平均水位的沿程变化和物理模型实验的结果比较,两者符合良好。     

翼型冰增长和结冰影响的数值模拟研究

翼面结冰是威胁飞行安全的重要因素之一.本文对于霜状结冰,在给定的结冰气候条件下,采用数值方法,预测整个结冰过程,建立冰增长模型,求解水滴轨迹运动方程,分析结冰过程中翼型绕流流场的变化,以及冰层的发展和形成过程.针对给定的三种不同冰型,即钝头型、尖头型和双角型,进一步采用结构化网格生成技术,结合中心有限体积法和LU-SGS隐式算法,利用B-L代数湍流模型,完成了绕流流场的N-S方程数值模拟,分析不同形状的冰型对翼型绕流及气动特性的影响.计算结果与试验数据进行了对比,表明采用的方法是正确、可行的.     

Numerical simulation of H2/air detonation using unstructured mesh

To explore the capability of unstructured mesh to simulate detonation wave propagation phenomena, numerical simulation of H₂/air detonation using unstructured mesh was conducted. The unstructured mesh has several adv- antages such as easy mesh adaptation and flexibility to the complicated configurations. To examine the resolution dependency of the unstructured mesh, several simulations varying the mesh size were conducted and compared with a computed result using a structured mesh. The results show that the unstructured mesh solution captures the detailed structure of detonation wave, as well as the structured mesh solution. To capture the detailed detonation cell structure, the unstructured mesh simulations required at least twice, ideally 5times the resolution of structured mesh solution.      

近岸非平整海底上耗散动力系统的广义波作用量守恒方程

为刻划近岸波-流-海底相互作用耗散动力系统的多种复杂作用机制，着眼于波浪对近岸大尺度变化环境流作用和考虑多变海底地形(可典型地刻划为由慢变水深和快变水深构成)的影响，由基于黏性流体Navie-Stokes方程的平均流方程，建立了近岸耗散动力系统的广义波作用量守恒方程，从中提出垂向速度波作用量和耗散波作用量这两种新概念，使得它们和经典的波作用量相互间达成了一种互补、协调而又主次分明的更为广泛的守恒形式．从而把波作用量这一经典概念从理想的平均流守恒系统引申到实际的平均流耗散系统(即广义守恒系统)中去，为解释沿岸过程和应用于近海、海岸工程提供了一个理论基础．     

A new numerical model for simulations of wave transformation,breaking and long‐shore currents in complex coastal regions

In this paper, we propose a model based on a new contravariant integral form of the fully nonlinear Boussinesq equations in order to simulate wave transformation phenomena, wave breaking, and nearshore currents in computational domains representing the complex morphology of real coastal regions. The aforementioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. A procedure developed in order to correct errors related to the difficulties of numerically satisfying the metric identities in the numerical integration of fully nonlinear Boussinesq equation on generalized boundary‐conforming grids is presented. The Boussinesq equation system is numerically solved by a hybrid finite volume–finite difference scheme. The proposed high‐order upwind weighted essentially non‐oscillatory finite volume scheme involves an exact Riemann solver and is based on a genuinely two‐dimensional reconstruction procedure, which uses a convex combination of biquadratic polynomials. The wave breaking is represented by discontinuities of the weak solution of the integral form of the nonlinear shallow water equations. The capacity of the proposed model to correctly represent wave propagation, wave breaking, and wave‐induced currents is verified against test cases present in the literature. The results obtained are compared with experimental measures, analytical solutions, or alternative numerical solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

A gas‐kinetic scheme for the simulation of turbulent flows on unstructured meshes

This paper presents a numerical method for simulating turbulent flows via coupling the Boltzmann BGK equation with Spalart–Allmaras one equation turbulence model. Both the Boltzmann BGK equation and the turbulence model equation are carried out using the finite volume method on unstructured meshes, which is different from previous works on structured grid. The application of the gas‐kinetic scheme is extended to the simulation of turbulent flows with arbitrary geometries. The adaptive mesh refinement technique is also adopted to reduce the computational cost and improve the efficiency of meshes. To organize the unstructured mesh data structure efficiently, a non‐manifold hybrid mesh data structure is extended for polygonal cells. Numerical experiments are performed on incompressible flow over a smooth flat plate and compressible turbulent flows around a NACA 0012 airfoil using unstructured hybrid meshes. These numerical results are found to be in good agreement with experimental data and/or other numerical solutions, demonstrating the applicability of the proposed method to simulate both subsonic and transonic turbulent flows. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical simulation of pollutant transport acted by wave for a shallow water sea bay

A numerical model of pollutant transport acted by water waves on a shallow‐water mild‐slope beach is established in this study. The numerical model is combined with a wave propagation model, a multiple wave‐breaking model, a wave‐induced current model and a pollutant convection–dispersion model. The wave propagation model is based on the higher‐order approximation of parabolic mild‐slope equation which can be used to simulate the wave refraction, diffraction and breaking in a large area of near‐shore zone combined with the wave‐breaking model. The wave‐induced current model is established using the concept of the radiation stress and considering the effect of bottom resistance caused by waves. The numerical model is verified by laboratory experiment results of regular and irregular waves over two mild beaches with different slopes. The numerical results agree well with experimental results. The numerical model has been applied in the near‐shore zone of Bohai bay in China. It is concluded that pollutant transport parallel to the shoreline due to the action of waves, which will induce serious pollution on the beach. Copyright © 2005 John Wiley & Sons, Ltd.     

非均匀介质散射问题的体积分方程数值解法

将非均匀介质视为某一均匀背景介质中的扰动，可建立用均匀背景介质格林函数作基本解的体积分方程．给出了配置法求解体积分方程的数值方法，首先解得扰动域内各点以速度扰动为权的波场函数，然后回代计算得到观测面上各接收点的散射波场．与边界元法和Ｂｏｒｎ近似法计算结果比较表明该方法具有很高的精度，可得到穿过非     

A compact numerical algorithm for solving the time‐dependent mild slope equation

The mild slope equation has been widely used to describe combined wave refraction and diffraction. In this study, a new numerical algorithm is developed to solve the time‐dependent mild slope equation in a second‐order hyperbolic form. The numerical algorithm is based on a compact and explicit finite difference method that is second‐order accurate in both time and space. The algorithm has the similar structure to the leap‐frog method but is constructed on three time levels for the second‐order time derivative term. The numerical model has the capability of simulating transient wave motion by correctly predicting the speed of wave energy propagation, which is important for the real‐time forecast of the arrival time of storm waves generated in the far field. The model is validated against analytical solution for wave shoaling and experimental data for combined wave refraction and diffraction over a submerged elliptic shoal on a slope (Coastal Eng. 1982; 6 :255). Lastly, the realistic scale Homma's island (Geophys. Mag. 1950; 21 :199) is studied with the use of various wave periods of T = 720s, T = 120 s, and T = 24 s. These wave periods correspond to long, intermediate, and short waves for the given topography, respectively. Comparisons are made between numerical results and existing analytical solutions in terms of the wave amplification around the island, which serves as the indicator for the potential wave runup. Excellent agreements are obtained. The model runs on a PC (Pentium IV 1.8GHz) and the computer capacity allows the computation of a mesh system up to 3000 × 3000, which is equivalent to about 150 × 150 waves or a large area of 540km × 540km for a wave train with the period of T = 60 s. Copyright 2004 John Wiley & Sons, Ltd.     

An unstructured-grid numerical model for interfacial multiphase fluids based on multi-moment finite volume formulation and THINC method

We present a practical numerical framework for incompressible interfacial multiphase flows on unstructured grids with arbitrary and hybrid elements. The numerical framework is constructed by combining VPM (volume-average/point-value multi-moment) and UMTHINC (unstructured multi-dimensional tangent of hyperbola interface capturing) schemes. To facilitate accurate and reliable simulations for interfacial multiphase flows on arbitrary and hybrid unstructured grids, we have made the following major new efforts in this work. (1) UMTHINC scheme on prismatic and pyramidal elements to facilitate computations on hybrid arbitrary unstructured grids; (2) Consistent numerical formulation for mass and momentum transports to simulate multiphase flows of large density ratio; (3) Combined FVM-FEM for accurate solution to diffusion equation; (4) Pressure-projection formulation in consistent with the balanced-force model. Integrating all these numerical techniques effectively enhances the accuracy and robustness in interface capturing and numerical solution of multiphase fluid dynamics, which results in a numerical framework of great significance for practical applications. Numerical verifications have been carried out through benchmark tests ranging from surface tension dominant flows of small scale to large scale flows with violently-changing interfaces. Numerical results demonstrate that the present framework is robust with adequate accuracy for simulating multiphase flows in complex geometries.     

An improved depth-averaged nonhydrostatic shallow water model with quadratic pressure approximation

Phase-resolved information is necessary for many coastal wave problems, for example, for the wave conditions in the vicinity of harbor structures. Two-dimensional (2D) depth-averaging shallow water models are commonly used to obtain a phase-resolved solution near the coast. These models are in general more computationally effective compared with computational fluid dynamics software and will be even more capable if equipped with a parallelized code. In the current article, a 2D wave model solving the depth-averaged continuity equation and the Euler equations is implemented in the open-source hydrodynamic code REEF3D. The model is based on a nonhydrostatic extension and a quadratic vertical pressure profile assumption, which provides a better approximation of the frequency dispersion. It is the first model of its kind to employ high-order discretization schemes and to be fully parallelized following the domain decomposition strategy. Wave generation and absorption are achieved with a relaxation method. The simulations of nonlinear long wave propagations and transformations over nonconstant bathymetries are presented. The results are compared with benchmark wave propagation cases. A large-scale wave propagation simulation over realistic irregular topography is shown to demonstrate the model's capability of solving operational large-scale problems.     

A multi‐energy‐level lattice Boltzmann model for two‐dimensional wave equation

A lattice Boltzmann model for two‐dimensional wave equation is presented. In this model, we used higher‐order moment method, multi‐scale technique and Chapman–Enskog expansion, and multi‐energy‐level to obtain wave equation and energy conservation equation. As numerical examples, the interference and diffraction of wave are simulated. The numerical results show this model can be used to simulate two‐dimensional wave propagation. Copyright © 2009 John Wiley & Sons, Ltd.