求解弹性波解耦方程的一种优化拟解析方法

常规伪谱方法二阶时间差分格式时间精度较低,且对于大步长时间采样间隔,常规伪谱方法不稳定.拟解析方法对于速度变化剧烈的模型,在时间和空间上均有较大误差.本文提出了一种基于解耦的二阶位移弹性波方程波场模拟及矢量波场分解的优化拟解析方法,将归一化的拟拉普拉斯算子分别应用于P波和S波波场延拓,延拓矢量波场的同时,可分解并延拓纯纵波和纯横波波场.利用弹性波优化拟微分算子表示拟拉普拉斯算子,该拟微分算子不仅包括原始微分算子的谱估计,而且还包含一个时间补偿项,其可在波数-空间域精确地补偿波动方程在时间方向上采用二阶有限差分引起的误差.利用低秩分解近似求解弹性波优化拟微分算子,可有效提高计算效率.2D均匀模型、层状模型以及部分盐丘模型数值正演模拟结果表明:相比较于常规的伪谱法和拟解析法,本文方法在时间和空间上均有很高的精度,并且稳定性条件比较宽松.     

基于非结构混合网格求解二维浅水方程的一种数值方法

复杂边界下的流场数值模拟常基于非结构化网格进行求解,建立一种在非结构混合网格上求解水深平均的二维浅水方程的模型,以便精确模拟复杂边界、提高计算效率。该模型时间项离散采用隐格式使得模型具有较好的稳定性,对流项和扩散项分别采用总变差减小(Total Variation Diminishing,TVD)格式和构造辅助点的方法来离散,同时采用水深平均的标准k-ε模型来封闭湍流模型。选用两个经典验证算例检验模型,计算结果表明,基于非结构混合网格开发的模型具有较高的精度,且收敛性能较好。     

A theoretical and numerical framework for modeling gypsum cavity dissolution

In this paper, a large‐scale diffuse interface model is used to describe the evolution of a gypsum cavity formation induced by dissolution. The method is based upon the assumption of a pseudo‐component dissolving with a thermodynamic equilibrium boundary condition. A methodology is proposed based on numerical computations with fixed boundaries in order to choose suitable parameters for the diffuse interface model, and hence predict the correct dissolution fluxes and surface recession velocity. Additional simulations were performed to check which type of momentum balance equation should be used. The numerical results did not show a strong impact of this choice for the typical initial boundary value problems under consideration. Calculations with a variable density and Boussinesq approximation were also performed to evaluate the potential for natural convection. The results showed that the impact of density driven flows was negligible in the cases under investigation. The potential of the methodology is illustrated on two large‐scale configurations: one corresponding to a gypsum lens located strictly within a porous rock formation and the other to an isolated pillar in a flooded gypsum room and pillar quarry. Copyright © 2016 John Wiley & Sons, Ltd.     

Time–space fractional governing equations of one‐dimensional unsteady open channel flow process: Numerical solution and exploration

Although fractional integration and differentiation have found many applications in various fields of science, such as physics, finance, bioengineering, continuum mechanics, and hydrology, their engineering applications, especially in the field of fluid flow processes, are rather limited. In this study, a finite difference numerical approach is proposed to solve the time–space fractional governing equations of 1‐dimensional unsteady/non‐uniform open channel flow process. By numerical simulations, results of the proposed fractional governing equations of the open channel flow process were compared with those of the standard Saint‐Venant equations. Numerical simulations showed that flow discharge and water depth can exhibit heavier tails in downstream locations as space and time fractional derivative powers decrease from 1. The fractional governing equations under consideration are generalizations of the well‐known Saint‐Venant equations, which are written in the integer differentiation framework. The new governing equations in the fractional‐order differentiation framework have the capability of modelling nonlocal flow processes both in time and in space by taking the global correlations into consideration. Furthermore, the generalized flow process may possibly shed light on understanding the theory of the anomalous transport processes and observed heavy‐tailed distributions of particle displacements in transport processes.     

Allometry in the pliocene bivalveAstarte omalii: A new look at an old data set

The relationships between ontogeny and phylogeny have been studied for the bivalve Astarte omaliifrom the Lower, Middle, and Upper Pliocene of Belgium using canonical variates analysis, principal components in the form of multivariate allometry, and bivariate power functions or allometric equations. The results indicate that the three samples represent segments of a single evolutionary lineage which is characterized mainly by paedomorphosis where adult descendants are similar to juvenile ancestors. Recapitulation or peramorphosis is only observed for a single parameter. The Lower and Middle Pliocene samples are considered as Astarte omalii omalii,whereas the Upper Pliocene specimens are placed in A. omalii basteroti.The evolutionary trends most likely reflect changes in the living positions of the bivalves.     

含裂隙双相各向异性介质中的地震波传播

基于各向异性介质和含裂隙双相介质中的地震波传播理论,导出了具有四阶对称轴的含裂隙双相各向异性介质的本构关系与波传播的运动方程．指出在含裂隙双相各向异性介质中可能传播６种类型的准纵横波,即快纵波ＱＰ１,慢纵波ＱＰ２,两个分裂的快横波ＱＳＶ１,ＱＳＨ１和两个分裂的慢横波ＱＳＶ２,ＱＳＨ２．并以平面波传播为例作了进一步分析     

湿大气方程组解的渐近性质

研究无穷维Ｈｉｌｂｅｒｔ空间中,湿大气运动系统解的长期行为,在导得了湿大气运动方程是Ｈｉｌｂｅｒｔ空间中一个非常特殊的算子方程之后,利用算子的性质讨论了全局吸收集和全局吸引子的存在性,揭示出系统解的渐近行为表现在吸引子的结构上及系统向非绝热加热的非线性适应过程。最后指出了几个简化方程组与原方程组在解的长期行为上的根本不同,从而给出长期天气或气候研究中简化方程组必须遵循的原则。     

The Internal Energy of a PV = RT Gas: A Univariable or Multivariable Function

Historically, the characterization of the internal energy of a simple gas is based on free expansion experiments and imprecise use of the word function, which is rigorously defined in mathematics. Univariable equations of state show that the internal energy of simple monatomic, diatomic, and polyatomic gases can be expressed as a function of temperature only. However, multivariable equations of state derived from composite functions confirm that the internal energy of these gases can in each situation also be expressed as a function of pressure and volume only. It is essential that the mathematical definition of the word function be adhered to in science because it is fundamental for the formulation of the calculus, a mathematical tool essential for solving a variety of thermodynamics problems.     

数值微分插值及其应用

以平面区域内偏微分方程定解问题的离散代数方程组为基础,给出了由平面区域内任意分布点上的值求整个区域中值的一种新播值方法──数值微分插值．该方法可直接推广到一维和高维空间的区域中,有较广的应用背景。     

共转换点道集的迭代算法及应用

对转换波共转换点道集选取进行了详细的研究,对水平层状和倾斜情况下共转换点的选取建立了统一的迭代公式,分析了影响共转换点选取的因素,给出了共转换面元的一般原则,最后给出了实际处理结果。