非规则网格下二维浅水流动的数值模拟

建立了一种在非规则结构化网格上求解平面二维浅水流动的有限体积方法。通过采用地形在离散网格内双线性变化及离散网格界面间地形连续的地形逼近方法和应用可以有效处理间断问题的Roe格式来离散浅水方程中的对流项,并通过VanLeer提出的状态插值法提高格式精度。在计算原始变量在网格内的插值梯度时,采用最小二乘方法求变量的最优梯度代替差分计算梯度,从而可采用任意形状的不规则四边形网格离散计算域。计算实例表明,该方法能够计算间断问题并能够处理各种复杂流态的过渡,具有较好适应性和计算精度,能够满足不同实际问题的计算要求。     

天然河道一维不恒定流计算的守恒格式

本文从数值计算的角度分析和讨论了天然河道一维不恒定流方程组的各种形式及其差分格式的守恒性。据此,本文总结了建立守恒差分格式的途径和应遵循的原则,并就差分格式如何达到准确或近似守恒提出了实际的处理方法。     

近岸波浪传播的非静压数值模型

基于均匀网格,建立了沿水深积分的非静压波浪传播数值模型,模型的求解分静压步和动压步两部分。静压步的控制方程为全非线性浅水方程,采用有限体积格式求解,通过采用线性重构技术和全隐式离散底摩阻项,保证了格式的和谐性、守恒性和水深非负性,有效处理了海岸动边界问题。动压步通过应用有限差分方法求解泊松方程考虑动压力,使得模型具备模拟色散性波浪传播的能力。引入波浪破碎指标,波浪破碎后模型退化为静压模型,破碎波自动捕捉为间断。通过算例对所建立模型进行了验证。     

通量差分裂方法在一维河网模型中的应用

以通量差分裂格式离散非守恒型圣维南方程组,为保证河网整体离散形式的一致性,采用特征线方法离散边界节点,并引入限制器和熵修正使离散模型具有TVD（Total Variation Diminishing）特性,在线性隐式化的基础上最终构建基于隐式TVD类方法的一维河网水流模型。通过实例验证,表明提出的方法能处理跨临界流变化,而且在实际复杂河网中对水位及主、支河道分流比都能较好地模拟,具有一定实用性。     

伴随数据同化法反演涌潮河口开边界

构造了非线性守恒型浅水方程的伴随方程,并给出无结构三角网格的开边界校正表达式,利用Godunov格式和Riemann间断解Roe通量格式的设计思想,建立了无结构三角网格有限体积法的伴随开边界反演模型。进行了概化涌潮河口和钱塘江涌潮河口M2分潮开边界反演的数值实验,经过同化得到开边界上振幅的平均误差分别为0.000 6 m和0.053 3 m,证实了本文构造有限体积伴随模型的可行性,也表明本模型能够适应间断解问题。     

一维浅水流动方程的Godunov格式求解

以准确Riemann解为基础,建立了求解一维非平底浅水流动方程的Godunov格式,用"水位方程法(WaterLevel Formulation,WLF)"求解Riemann解,结合中心差分和Riemann解离散底坡项,保证了计算格式的和谐性.经算例验证,方法健全、通用,且分辨率高.     

浅水方程数值计算方法的研究

求解以水位为变量的连续方程,并根据Navier-Stokes方程压力修正算法的基本思想,建立了浅水方程的水位修正算法,放宽了对离散时间步长的限制.通过对离散方程系数矩阵的重新构造,建立了高分辨率有限元格式,该格式既具有较高的离散精度又避免了数值解的伪振荡.对动量方程的阻力项做负坡线性化处理,提高了露滩计算的稳定性.数值模拟结果与解析解吻合良好,表明所建立的数值计算方法是正确的和可靠的.     

Runge-Kutta间断有限元格式在一维浅水方程中的应用

针对一维浅水方程组建立了考虑源项离散的Runge-Kutta间断有限元格式,该格式具有通量与源项的和谐性,可以用于求解任意非棱柱体明渠浅水流动问题。所建立的数值模式分别应用于复杂地形下非棱柱体明渠跨临界流浅水流动算例和水跃问题,模拟结果表明,数值解与解析解以及实测值吻合良好,数值格式具有捕捉间断问题中锐利波形的能力。     

钱塘江口涌潮的二维数值模拟

应用二维有限体积法、Osher格式及间断拟合法,计算了钱塘江河口涌潮产生、发展到消亡的全过程。该算法能保证水量和动量守恒,且能适应水深巨大变化和动边界。根据钱塘江涌潮的特点,可将其合理概化为一线潮。在网格尺寸较大情况下,计算的一线潮仍保持高分辨率,能准确满足水力学间断条件,且计算量小,可以在微机上实现。在对某实测半日小潮进行率定后,对随后的大潮进行了验证计算,涌潮的主要特征(如涌潮高度、移速、水位和流场等)与实测资料符合良好,证实了模型的合理性和模拟能力。     

有限差分法精确计算地震走时

快速精确计算走时在层析成像反演中起重要作用，本文采用有限差分法来计算。首先通过变换，将程函方程化成一守恒形式；然后再差分离散，得到一阶和二阶精度的差分格式，并证明了差分格式条件稳定。模型试算表明：本文算法简明稳定，能快速高精度地计算地震走时，是一种值得注意和采用的走时计算方法。     

Unsplit Variables Perfectly Matched Layers for the Shallow Water Equations with Coriolis Forces

The paper presents an analytical and numerical study of two perfectly matched layer (PML) formulations for the shallow water equations in terms of the unsplit physical variables. A perturbation method followed by a change of dependent variable allows us to extend the methods to include the Coriolis forces. The PML equations, usually given in terms of the primitive variables, are also presented here in terms of the conservative variables, which facilitates their use in flows containing discontinuities. The performance of the two methods on a set of test cases is investigated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Short Communication: A numerical method for diffusive transport with moving boundaries and discontinuous material properties

A method for the numerical simulation of diffusive transport with moving boundaries is developed and tested. The variable domain is mapped onto a fixed region, which introduces a term of convective form to the transformed governing equation. The resulting convection/diffusion equation is solved by a finite-difference method. An ‘Immersed Interface’ Method (IIM) is introduced in order to retain second-order accuracy near discontinuities in material properties, where the solution is not smooth. The method performs well in benchmark calculations against an analytical solution. The IIM scheme is capable of treating a strong discontinuity in the gradient, and it is readily extended to two or three dimensions. The methods are illustrated through a calculation for the temperature profile in a growing continental ice sheet, in which the thermal properties are discontinuous at the rock/ice interface. © 1997 by John Wiley & Sons, Ltd.     

Godunov格式下高精度二维水流-输运耦合模型

针对复杂流体运动中物质输运方程的数值求解面临地形复杂、数值阻尼过大以及数值振荡等难题,建立了Godunov格式下求解二维水流-输运方程的高精度耦合数学模型,提出了集成输运对流项的HLLC (Harten-Lax-van Leer-Contact)型近似黎曼算子,可同时计算水流通量及输运通量,不仅有效模拟了复杂地形上水流运动,而且解决了输运方程中对流项产生的数值阻尼过大和不稳定振荡等难题。采用水深-水位加权重构技术和Minmod限制器,提高了模型处理复杂混合流态的能力,同时结合Hancock预测-校正方法,使模型具有时空二阶精度。算例结果表明,模型精度高、稳定性好,能有效抑制数值阻尼,适合模拟实际复杂流体运动中物质的输运过程,具有较好的推广应用价值。     

不连续面在双重介质热-水-力三维耦合分析中的有限元数值实现

在建立双重介质热-水-力耦合微分控制方程的基础上,提出了裂隙岩体热-水-力耦合的三维力学模型,对不同介质分别建立以节点位移、水压力和温度为求解量的三维有限元格式,开发了双重介质热-水-力耦合分析的的三维有限元计算程序,在有限元数值分析中不连续面应力计算采用等厚度空间8节点节理单元进行离散,而不连续面渗流和热能计算时采用平面4节点等参单元进行离散,这样保证了不同介质之间的水量、热量交换和两类模型接触处节点水头、温度和位移相等。通过高温岩体地热开发算例,揭示了在热-水-力耦合作用下不连续面处于低应力区,其张开度随运行时间的延长呈非线性增加,非稳定渗流阶段不连续面显著地控制着渗流场的整体分布,它的水头远高于拟连续岩体介质的水头,而进入稳定渗流阶段不连续面的控渗作用不明显,由于高温岩体地热开发系统中存在大规模的热量补给,不连续面对岩体温度场分布的影响并不显著。     

应变局部化弹黏塑性分析的内嵌局部软化带模型

针对岩土介质结构在破坏过程中局部化变形的问题,结合位移不连续的思想,提出内嵌局部软化带模型来捕捉结构中的局部化带。通过虚功原理建立了含局部化带影响的弹黏塑性的有限元计算模式,其中分叉理论作为局部化判断条件。模型将局部化带的形成视为一个黏塑性屈服流动过程,从而能够连续地描述局部化变形前后的力学性质。特点是计算量小、物理意义明确,可以方便地整合到传统有限元分析程序中。算例表明,计算模型是合理和有效的。     

等效水力隙宽和水力梯度对岩体裂隙网络非线性渗流特性的影响

等效水力隙宽和水力梯度是影响岩体裂隙网络渗流特性的重要因素。制作裂隙网络试验模型,建立高精度渗流试验系统;求解纳维-斯托克斯方程,模拟流体在裂隙网络内的流动状态,研究等效水力隙宽和水力梯度对非线性渗流特性的影响。结果表明,当水力梯度较小时,等效渗透系数保持恒定的常数,流体流动属于达西流动区域,流量与压力具有线性关系,可采用立方定律计算流体流动;当水力梯度较大时,等效渗透系数随着水力梯度的增加而急剧减少,流体流动进入强惯性效应流动区域,流量与压力具有强烈的非线性关系,可采用Forchheimer方程计算流体流动。随着等效水力隙宽的增加,区别线性和非线性流动区域的临界水力梯度呈幂函数关系递减。当水力梯度小于临界水力梯度时,控制方程可选立方定律;当水力梯度大于临界水力梯度时,控制方程可选Forchheimer方程,其参数A和B可根据经验公式计算得到。其研究结果可为临界水力梯度的确定及流体流动控制方程的选取提供借鉴意义。     

OpenMP and CUDA simulations of Sella Zerbino Dam break on unstructured grids

This paper presents two 2D dam break parallelized models based on shallow water equations (SWE) written in conservative form. The models were implemented exploiting multicore PC systems and graphics processor unit (GPU) architectures under the OpenMP and the NVIDIA?’s compute unified device architecture (CUDA) frameworks. The mathematical model is solved using a finite-volume technique on an unstructured grid, with Roe’s approximate Riemann solver, a first-order upwind scheme. The upwind treatment of the source terms is implemented. A technique to cope with a wetting-drying advance front is adopted, together with the inclusion of the influence of source terms in the stability constraint in order to prevent negative water depths at the dry fronts. The proposed model is first applied to a laboratory test and then to a real dam break that occurred in Italy in 1935. Results on different grid sizes are compared to show the computing efficiency between the original sequential model and the parallelized models.     

对MPS法在溃坝模拟中数值压力振荡问题的改进

为探索模拟大变形自由面流体运动的高精度数值计算方法,以溃坝水流运动为例,基于MPS法(Moving Particle Semi-implicit method,移动粒子半隐式法)建立了一个垂向二维改良MPS法数值计算模型。首先,为了改善传统MPS法中存在的自由表面粒子误判以及数值能量耗散问题,提出新的自由表面粒子识别方法和高精度的压力梯度模型。在此基础上,以Lobovsky'等的溃坝物理模型实验为例,探讨不同形式压力泊松方程源项对溃坝冲击压计算精度的影响,提出一个新的源项形式。数值结果分析表明,新自由表面粒子识别方法和高精度压力梯度模型可以有效地减少自由面粒子的误判概率,抑制水流运动计算中的数值能量耗散。而压力计算结果与实验结果的对比表明,所提出的压力泊松方程源项可以有效地减少数值压力震荡的幅度。     

An improved return‐map stress update algorithm for finite deformation analysis of general isotropic elastoplastic geomaterials

This paper develops a novel return mapping algorithm for the numerical integration of general isotropic finite strain elastoplastic constitutive models for geomaterials. The constitutive formulation is founded on multiplicative decomposition of the deformation gradient. The logarithmic strain measure as well as the exponential approximation of the plastic flow rule is utilized to restore the standard infinitesimal format return mapping algorithm. Central to the algorithm is the exploitation of a set of three mutually orthogonal unit base tensors for the representation of constitutive relations and the corresponding integration of the rate form of the constitutive equations. The base tensors constitute a local cylindrical coordinate system in the principal space, which allows to formulate the return mapping algorithm in the three‐dimensional space and reduce the dimension of the problem to be analyzed from six down to three. With the proposed approach, direct determination of the principal axes and the transformation procedure between the general space and the principal space, as required in traditional spectral decomposition, are avoided. Furthermore, the matrices that are involved in the inversion evaluation take simple forms, leading to extremely easy inverse computation. As a result, the consistent tangent operator can be streamlined into a form simpler and more compact than those by conventional integration methods. Following the formulation of the integration procedure, a numerical experiment is performed to assess the accuracy and efficiency of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.