具有非局部源的反应扩散方程中解的消失行为

本文主要研究低维情形中具有非线性非局部源项和非线性内部吸收项的反应扩散方程的初边值问题,并利用积分模估计的方法得到其非负弱解的消失、非消失现象及其衰减估计。结果发现,在低维情形下非负弱解消失的临界指数不变,并且衰减估计值依赖于初始值、系数及区域的选取。     

广义Birkhoff方程的积分方法

场方法和最终乘子法是求解运动微分方程的基本方法. 本文将这两种方法应用于广义Birkhoff系统,求出了场方法的基本偏微分方程和该方程的完全积分; 根据Jacobi最终乘子定理求出了广义Birkhoff方程的解. 并举例说明结果的应用.     

解Burgers方程的迎风加权交替分块显-隐方法

利用迎风加权格式对二维Burgers方程的对流项进行处理,构造求解二维Burgers方程的一类交替分块显隐的有限差分格式,该方法具有并行本性,且绝对稳定.数值实验表明方法还具有较好的精度.     

不同时空格式在求解污染物对流扩散方程中的应用

为了研究污染物对流扩散方程中不同时空格式的适用性,针对对流扩散方程的一维﹑二维和三维3种情况,分别建立了预报-校正的有限差分数值模型。在时间步进格式上分别采用了Crank-Nicolson格式或混合4阶Adams-Bashforth-Moulton格式,对对流项分别采用2阶精度或4阶精度,对扩散项采用了2阶精度。利用建立的数值模型求解了经典的污染物浓度场对流扩散,通过数值解与解析解的比较讨论了不同时空格式对数值模型计算结果的影响。结果表明:对空间一次导数采用4阶精度可以避免采用2阶精度带来的误差。采用混合4阶Adams-Bashforth-Moulton格式或Crank-Nicolson格式数值计算结果均与解析解吻合程度较好,但对于数组为[40,40,40]的三维对流扩散问题,前者比后者省时20.7%。     

对流扩散方程迎风差分格式的稳定性分析

此文应用Fourier方法和能量不等式研究了常系数和变系数的对流扩散方程在迎风差分格式的情形下数值解的稳定性,所得结果对实际计算有着重要的意义。     

基于一维扩散方程反演温度垂直扩散系数的变分方法

Diapycnal mixing is important in oceanic circulation. An inverse method in which a semi-explicit scheme is applied to discretize the one-dimensional temperature diffusion equation is established to estimate the vertical temperature diffusion coefficient based on the observed temperature profiles. The sensitivity of the inverse model in the idealized and actual conditions is tested in detail. It can be found that this inverse model has high feasibility under multiple situations ensuring the stability of the inverse model, and can be considered as an efficient way to estimate the temperature diffusion coefficient in the weak current regions of the ocean. Here, the hydrographic profiles from Argo floats are used to estimate the temporal and spatial distribution of the vertical mixing in the north central Pacific based on this inverse method. It is further found that the vertical mixing in the upper ocean displays a distinct seasonal variation with the amplitude decreasing with depth, and the vertical mixing over rough topography is stronger than that over smooth topography It is suggested that the high-resolution profiles from Argo floats and a more reasonable design of the inverse scheme will serve to understand mixing processes.     

求解代数Riccati方程的一些数值方法评述

在过去的三十多年中 ,代数 Riccati方程的数值求解一直是数值代数界和控制论界关注的重要课题。作者简要评述几种用于求解代数 Riccati方程的有代表性的数值方法。     

非结构化网格下椭圆型缓坡方程的数值求解

椭圆型缓坡方程是一种用线性波浪理论研究近岸波浪传播变形的有效波浪数学模型。非结构化网格下的有限容积法不仅对复杂边界的适应性好,还能保证迭代求解过程的守恒性。建立了非结构化网格下的椭圆型缓坡方程数值模型。在模型中采用非结构化网格下的有限容积法对椭圆型缓坡方程进行了数值离散,结合GPBiCG(m,n)算法求解离散方程。数值计算结果表明,该数值模型可有效地用于模拟近岸缓坡区域复杂边界下波浪的传播。     

基于广义扩散方程海工混凝土结构耐久寿命概率评估方法

针对国内现有的氯离子侵蚀寿命预测模型存在的问题,提出了基于广义扩散方程(GDF)的海洋环境下混凝土结构耐久寿命预测的概率方法.以某海上混凝土工程原位取粉测试及室内快速试验为手段,获得不同环境分区的时变模型参数统计值.采用随机抽样方法,实现结构各部位混凝土使用寿命的概率预测.通过对模型参数的敏感性分析讨论了该模型的优点.最后,提出了周期性检测,不断更新模型参数的动态寿命评估思路.     

一维扩散方程整体观测资料下的初值变分同化反演

本文考虑一维扩散方程的反问题,利用变分同化方法通过观测资料来确定方程中的未知初值,通过分析观测误差对于初值误差的影响,证明变分同化初值收敛于原问题的真实参数,并得到了参数的收敛精度。同时将得到的初值代入预报模式中,得到预报解,并分析了预报解的收敛性和预报误差。     

A Three-Dimensional Prediction Method for Thermal Diffusion

A three-dimensional,first order turbulence closure,thermal diffusion model is described inthis paper.The governing equations consist of an equation of continuity,three components of momentum,conservation equations for salt,temperature and subgridscale energy,and an equation of state.In the mod-el,according to the hypothesis of Kolmogorov and Prandtl,the viscosity coefficient of turbulent flow ofhomogeneous fluid is related to the local turbulent energy,and the horizontal and vertical exchangecoefficients of mass,heat and momentum are computed with the introduction of subgridscale turbulenceenergy.The governing equations are solved by finite difference techniques.This model is applied to theJiaozhou bay to predict thermal pollution by the Huangdao power plant.An instantaneous tidal currentfield is computed,then the distribution of temperature increment is predicted,and finally the effect of windstress on thermal discharge is discussed.     

二维各向异性介质中三分量波动方程有限元法模拟

利用六面体单元和三线性插值函数 ,推导出在任意弹性各向异性介质中三维三分量波动方程所满足的有限元方程 ,同时给出也适用于矩形单元和双线性插值的二维三分量各向异性介质中的波动方程模拟的一般性公式 ,最后讨论两个数值模拟的结果。     

Evaluation of the Risk of Marine Slope Instability: A Pseudo-3D Approach for Application to Large Areas

Abstract

This article presents a methodology developed to evaluate the instability of submarine slopes that extend over a large area. Special attention was paid to (1) the complex geometry (bathymetry) and the expanse of the slope, (2) the heterogeneity of the sediment, and (3) the distribution of the pore pressure. The safety factor was considered as a spatially varying quantity. The General Formulation (GLE, Fredlund and Krahn 1977), which fully satisfies equilibrium conditions, was used for evaluating the stability of the marine slope. The submarine slope failure, which occurred on 16 October 1979 during the construction of the new Nice airport, was studied in order to test the developed model. Geotechnical parameters were taken from experimental tests carried out by IFREMER on 19 cores extracted at different depths (from 27 m to 1300 m) (Cochonat, Bourillet, and Savoye, 1993; Mulder et al., 1994). Many scenarios were proposed in order to explain the cause of the Nice slope failure (Habib, 1994). In this article, two of those scenarios were tested. Simulation results are presented and discussed.