The numerical solution of the Advection-Dispersion Equation: A review of some basic principles

The simulation of solute transport in rivers is frequently based on numerical models of the Advection-Dispersion Equation. The construction of reliable computational schemes, however, is not necessarily easy. The paper reviews some of the most important issues in this regard, taking the finite volume method as the basis of the simulation, and compares the performance of several types of scheme for a simple case of the transport of a patch of solute along a uniform river. The results illustrate some typical (and well known) deficiencies of explicit schemes and compare the contrasting performance of implicit and semi-Lagrangian versions of the same schemes. It is concluded that the latter have several benefits over the other types of scheme.     

基于累积相似度表面的空间权重矩阵构建方法

将地理要素相似度定义为属性相似度与空间相似度,提出累积相似度表面的概念,引入曲线演化理论和快速行进方法生成累积相似度表面,构建空间权重矩阵。通过趋势面模拟数据与ASTER GDEM数字高程模型数据的实验分析证明,相比于利用欧氏距离等距离测度方法,通过累积相似度表面构建的空间权重矩阵综合考虑了地理要素的属性相似度与空间相似度,体现了地理要素的局部空间特征,能够更为准确地描述地理要素空间特征变化趋势。     

三维复杂山地多级次群推进迎风混合法多波型走时计算

三维复杂山地条件下的各种地震波型的走时计算技术,可以直接用于复杂山地区域地震波运动学特性的分析、地震数据采集观测系统的设计以及直接基于三维复杂地表的地震数据处理技术的研发.为了在三维复杂地表条件下准确、灵活且稳定地计算各种地震波型的走时,提出一种多级次群推进迎风混合法.该算法利用不等距迎风差分法简洁稳定地处理三维复杂地表及附近的局部走时计算问题,利用计算精度不错的迎风双线性插值法处理绝大部分均匀正方体网格中的局部走时计算问题,利用群推进法模拟三维复杂地表条件下地震波前的扩展问题,利用多级次算法处理各种类型的地震波的走时计算问题.算法分析和计算实例表明:新方法具有很好的计算精度与效率,且能灵活稳定地处理三维复杂地表复杂介质条件下的多波型走时计算问题.     

A semianalytical approach for solving first-order perturbation equations of dissolution-timescale reactive infiltration instability problems in fluid-saturated rocks

This paper presents a semianalytical approach for solving first-order perturbation (FOP) equations, which are used to describe dissolution-timescale reactive infiltration instability (RII) problems in fluid-saturated rocks. The proposed approach contains two parts because the chemical dissolution reaction divides the whole problem domain into two subdomains. In the first part, the interface-condition substitution strategy is used to derive the analytical expressions of purely mathematical solutions for the FOP equations in the upstream subdomain, where the dissolution chemical reaction is ceased and the FOP equations are weakly coupled. In the second part, the finite element method (FEM) is used to derive the analytical expressions of numerical solutions for the FOP equations in the downstream subdomain, where the dissolution chemical reaction needs to be considered and the FOP equations are strongly coupled so that it is impossible to derive purely mathematical solutions for them. Particular attention is paid to the development of the element-by-element forward marching strategy, which is associated with the use of the FEM for solving this new kind of scientific problem. The related analytical results demonstrated that (1) both the dynamic characteristic of a reactive infiltration system and the dimensionless wavenumber can have pronounced influences on the distribution of the FOP dimensionless acid concentration within the entire domain of the dissolution-timescale RII problems in fluid-saturated rocks and (2) the FOP dimensionless acid concentration distribution exhibits two significantly different patterns in the upstream and downstream subdomains of the dissolution-timescale RII system.     

3D P‐wave traveltime computation in transversely isotropic media using layer‐by‐layer wavefront marching

Subsurface rocks (e.g. shale) may induce seismic anisotropy, such as transverse isotropy. Traveltime computation is an essential component of depth imaging and tomography in transversely isotropic media. It is natural to compute the traveltime using the wavefront marching method. However, tracking the 3D wavefront is expensive, especially in anisotropic media. Besides, the wavefront marching method usually computes the traveltime using the eikonal equation. However, the anisotropic eikonal equation is highly non‐linear and it is challenging to solve. To address these issues, we present a layer‐by‐layer wavefront marching method to compute the P‐wave traveltime in 3D transversely isotropic media. To simplify the wavefront tracking, it uses the traveltime of the previous depth as the boundary condition to compute that of the next depth based on the wavefront marching. A strategy of traveltime computation is designed to guarantee the causality of wave propagation. To avoid solving the non‐linear eikonal equation, it updates traveltime along the expanding wavefront by Fermat's principle. To compute the traveltime using Fermat's principle, an approximate group velocity with high accuracy in transversely isotropic media is adopted to describe the ray propagation. Numerical examples on 3D vertical transverse isotropy and tilted transverse isotropy models show that the proposed method computes the traveltime with high accuracy. It can find applications in modelling and depth migration.     

A fast marching method for reservoir simulation

We present a fast marching level set method for reservoir simulation based on a fractional flow formulation of two-phase, incompressible, immiscible flow in two or three space dimensions. The method uses a fast marching approach and is therefore considerably faster than conventional finite difference methods. The fast marching approach compares favorably with a front tracking method as regards both efficiency and accuracy. In addition, it maintains the advantage of being able to handle changing topologies of the front structure. This revised version was published online in July 2006 with corrections to the Cover Date.     

基于完全三叉树的快速推进法地震波走时计算

快速推进法(简称FMM)在地震波走时计算中有着精度高、效率高的特点,但窄带扩展每次都要寻找最小走时。当网格节点较多时,寻找最小走时非常耗时。在保证精度的前提下,为了提高计算效率,笔者对堆排序的排序方式做了改进,将完全三叉树排序方法引入到快速推进法地震波走时计算中。模型试算结果表明,基于完全三叉树快速推进法计算出的地震波走时与用完全二叉树方法的精度一致,且前者比后者效率提高约10%。     

复杂层状模型中多次波快速追踪——一种基于非规则网格的最短路径算法

使用不规则网格单元划分下的最短路径算法,结合分区多步计算技术实现了二维和三维复杂层状起伏介质中的多次透射、反射及转换波的追踪计算.其原理是将模型按速度界面分成若干个独立的计算区域(在速度界面和起伏地表处采用一种不规则网格单元划分),采用分步计算技术进行多次波的追踪计算.通过与有限差分下快速行进法的比较,表明无论是计算精度还是CPU时间,不规则最短路径算法均好于快速行进法算法.最后,实例模拟中给出了二维、三维复杂层状模型(包括Marmousi模型及含低速体的模型)中的多次透射、反射及转换波的追踪计算,验证了不规则最短路径算法的功能.     

曲线坐标系程函方程的求解方法研究

笛卡尔坐标系中经典的程函方程在静校正、叠前偏移、走时反演、地震定位、层析成像等许多地球物理工作都有应用,然而用其计算起伏地表的地震波走时时却比较困难.我们通过把曲线坐标系中的矩形网格映射到笛卡尔坐标系的贴体网格推导出了曲线坐标中的程函方程,此时,曲线坐标系的程函方程呈现为各向异性的程函方程(尽管在笛卡尔坐标系中介质是各向同同性的).然后尝试用求解各向同性程函方程的快速推进法和Lax-Friedrichs快速扫描算法来分别求解该方程.数值试验表明未加考虑各向异性程函方程与各向同性程函方程的差别而把求解各向同性程函方程的快速推进法直接拓展到曲线坐标中的程函方程的做法是错误的,而Lax-Friedrichs快速扫描算法总能稳定地求解曲线坐标系的程函方程,进而有效地处理了地表起伏的情况,得到稳定准确的计算结果.