APPLICATION OF THE MULTIGRID METHOD IN NUMERICAL SIMULATION OF SEDIMENT TRANSPORT

IINTRODUCTIONThemultigridmethod(Brandt,1988)iswidelyusedinmanydisciplinesandengineeringsubjects,especiallyintheareaofComputationalFluidMechanicsbecauseofitshighefficiencyincomputation.Themultigridmethodhasbeenprovenintheorytobeoneofbestnumericalmethodsforsolvinglinearellipticproblemsbecausetheloadofcomplltationisindirectproportiontothenumberofgridnodes;theconvergentspeedofmultigridmethodisirrelevanttothesizeofgird.Soitissuitableforthenumericalsimulationoffullscaleengineeringprojects.The…     

大规模三维大地电磁各向异性正演的非均匀网格外推多重网格法

大地电磁正演线性方程组求解的主要加速手段有并行技术和多重网格技术.传统的几何多重网格（GMG）方法依赖于均匀嵌套的正交网格,处理带跃变系数的问题时存在一定缺陷,且对各向异性问题需采用半粗化、线/面磨光等策略特殊处理,限制了GMG方法的应用.本文提出一种基于非均匀网格的外推瀑布式多重网格方法（EXCMG）,快速求解三维大地电磁各向异性有限元正演形成的大型复线性方程组.首先,对库仑规范下电磁耦合势满足的向量Helmholtz方程,由Galerkin加权余量法推导有限元离散系统,得到大规模、稀疏、复线性方程组.然后,从最密的非均匀正交网格出发,逐层粗化得到一系列嵌套网格;借助Richardson外推及Lagrange二次插值技术,设计非均匀正交网格下全新的多网格延拓算子;利用前两层网格上的数值解,构造下层密网上有限元解的高精度逼近,作为多网格磨光算子——复数域不完全LU分解预处理稳定双共轭梯度算法（BiCGStab）的迭代初值,加速收敛.最后,通过典型地电模型验证算法的精度和效率.数值实验表明,本文提出的算法适用于较宽频带,加速效果明显,相较于预条件BiCGStab方法,求解效率提升数十倍.本文算法能够求解上亿自由度的超大规模、强各向异性问题,且求解问题的规模越大,算法效率优势越明显.EXCMG算法有望在其他地球物理领域得到应用.

     

基于多重网格预条件求解平均导数法离散的Helmholtz方程

有限差分法求解Helmholtz方程,依赖于两点：1差分格式的构造;2高效的求解算法.本文采用平均导数法离散Helmholtz方程.该差分格式有三点好处：1能适用于横纵不等间距采样;2在完全匹配层区域（PML）,差分方程与微分方程逐点相容;3能将一个波长内的采样点数减少至少于4.求解离散的Helmholtz方程的算法一般分为直接法和迭代算法.直接法由于内存需求太大而无法适用于大规模问题;基于Krylov子空间的迭代方法结合多重网格预条件算法是一种快速高效求解方法,然而对于横纵不等间距采样（在多重网格中称为各向异性问题）,经典的多重网格方法失效.本文分析了经典多重网格的三个重要组成部分：完全加权限制算子,点松弛技术以及双线性延拓算子,进而采用了半粗化技术代替全粗化技术,线松弛技术代替点松弛技术以及依赖差分算子的延拓算子代替双线性延拓算子,使得各向异性问题变得收敛;而且对于非均匀介质中-低频率的迭代问题,我们获得了较为满意的收敛速度.

     

盆地模拟水动力油气二次运移隐式多重网格法

本文提出一种高效率求解油气二次运移的方法,以水动力为油气运移模型,采用多重网格加速方法．典型油气二次运移的计算表明：该多重网格加速方法极大地提高了求解油气二次运移的偏微分方程速度,其计算工作量为O（N）（N为网格节点数）,解的收敛速度与网格尺度无关,当网格密度增加时,仍能保证偏微分方程解的稳定性．本文在数值模拟之后,对东营凹陷的实际资料进行了处理,其计算结果表明本文提出的多重网格方法对油气运移的计算有良好的实用意义．     

盆地模拟水动力油气二次运移隐式多重网格法

本文提出一种高效率求解油气二次运移的方法,以水动力为油气运移模型,采用多重网格加速方法．典型油气二次运移的计算表明：该多重网格加速方法极大地提高了求解油气二次运移的偏微分方程速度,其计算工作量为O（N）（N为网格节点数）,解的收敛速度与网格尺度无关,当网格密度增加时,仍能保证偏微分方程解的稳定性．本文在数值模拟之后,对东营凹陷的实际资料进行了处理,其计算结果表明本文提出的多重网格方法对油气运移的计算有良好的实用意义．     

Integration of linear programming and GIS for land-use modelling

Abstract

Geographical Information Systems (GIS) are becoming basic tools for a wide variety of earth science and land-use applications. This article presents linear programming (LP) as a promising tool for spatial modelling within a GIS. Although LP is not properly a spatial technique, it may be used to optimize spatial distributions or to guide the integration of variables. An example of the use of LP in land-use planning is described, with minimizing rural unemployment as the main goal. Technical, financial and ecological constraints are established to show the influence of several limitations on achieving the optimal solution. LP makes it possible to achieve optimal land-use, where the objective is maximized and the constraints respected. LP can also be used to simulate different planning scenarios, by modifying both the objective function coefficients and the constraints. The integration of LP and GIS is presented in two phases: (i) acquisition of attribute data for the LP model, and (ii) modelling and mapping the results.     

Numerical simulation of three-dimensional saltwater–freshwater fingering instabilities observed in a porous medium

We consider saltwater–freshwater fingering instabilities in a saturated porous medium. In the first part, we present three-dimensional results obtained from a laboratory experiment using non-invasive imaging. In the second part, we define a set of model problems in which the performed laboratory experiments can be ranged in. Due to its highly non-linear behavior and inevitable modeling errors, a detailed numerical reproduction of the physical concentration measurements cannot be expected. Nevertheless, four criteria have been identified, two quantitative and two qualitative, which facilitate a substantiated comparison of the physical experiment and the numerical simulation. With respect to these criteria a high degree of similarity could be observed. The use of these features allows a deeper understanding of the physical processes and the influence of the initial conditions.     

A discretization and multigrid solver for a Darcy–Stokes system of three dimensional vuggy porous media

We develop a finite element discretization and multigrid solver for a Darcy–Stokes system of three-dimensional vuggy porous media, i.e., porous media with cavities. The finite element method uses low-order mixed finite elements in the Darcy and Stokes domains and special transition elements near the Darcy–Stokes interface to allow for tangential discontinuities implied by the Beavers–Joseph boundary condition. We design a multigrid method to solve the resulting saddle point linear system. The intertwining of the Darcy and Stokes subdomains makes the resulting matrix highly ill-conditioned. The velocity field is very irregular, and its discontinuous tangential component at the Darcy–Stokes interface makes it difficult to define intergrid transfer operators. Our definition is based on mass conservation and the analysis of the orders of magnitude of the solution. The coarser grid equations are defined using the Galerkin method. A new smoother of Uzawa type is developed based on taking an optimal step in a good search direction. Our algorithm has a measured convergence factor independent of the size of the system, at least when there are no disconnected vugs. We study the macroscopic effective permeability of a vuggy medium, showing that the influence of vug orientation; shape; and, most importantly, interconnectivity determine the macroscopic flow properties of the medium. This work was supported by the U.S. National Science Foundation under grants DMS-0074310 and DMS-0417431.     

A mixed-dimensional finite volume method for two-phase flow in fractured porous media

We present a vertex-centered finite volume method for the fully coupled, fully implicit discretization of two-phase flow in fractured porous media. Fractures are discretely modeled as lower dimensional elements. The method works on unstructured, locally refined grids and on parallel computers with distributed memory. An implicit time discretization is employed and the nonlinear systems of equations are solved with a parallel Newton-multigrid method. Results from two-dimensional and three-dimensional simulations are presented.     

2009-18年西北太平洋区域海洋再分析CORA1.0产品研制及检验

在51年(1958-2008)西北太平洋区域海洋再分析CORA1.0产品的基础上,改进了模式配置和同化方法,研制了2009-18年的CORA产品并对其进行以下检验:(1)温盐和海表高度异常均方根误差分布检验;(2)35°N处温度断面分布检验;(3)再分析流场和表漂浮标轨迹对比检验.结果显示,2009-18年的CORA产品可以再现海洋要素长时间序列,时空多尺度的变化特征,为研究特征海洋现象和过程提供背景信息.