Title:  非结构网格上并行差分格式及在油藏模拟中的应用研究 
Author:  高家全

Issued Date:  2002

Major:  计算机软件与理论

Degree Grantor:  中国科学院软件研究所

Place of Degree Grantor:  中国科学院软件研究所

Degree Level:  博士

Keyword:  并行差分格式
; 有限体积元方法
; 抛物型方程
; （非）结构网格
; 隐显格式
; 油藏数值模拟

Alternative Title:  The application of parallel difference schemes on unstructured grids in reservoir numerical simulation

Abstract:  中科院软件所并行中心研制的并行油藏模拟器PRIS_1.0已成功地运行于各种并行环境下,而且其线性解法器的性能已达到国际先进水平.此PRIS_1.0的解法器是基于结构网格上的,为能更好地描述区域的性质,以便能够比较容易实现并行计算.该文主要做了以下创新工作：●首先该文从简单的抛物型方程出发,对非结构网格上的并行差分格式进行了一些研究.在第二章里把结构网格上的一类并行差分格式推广到非结构网格上;在此格式实现时,边界节点的选取是关键.●从线性或非线性抛物型方程本身出发,使用有限体积元方法进行空间离散,系数进行分裂,其中一部分使用显式格式离散,其它部分使用隐式格式离散.时间层上使用线性多步法进行离散,从而可得到高阶精度格式.●从简单的热传导方程出发,研究了结构网格上的并行差分格式.在第五章里提出了一个超时间步的显隐并行差分格式.此格式基于在子区域边界上用显式格式,子区域内部使用隐式格式.●通过对一维径向单相流、二维单相流、二维油水两相流的数值模拟实验验证了该文方法的可行性.●针对黑油模型方程,给出了非结构网格上黑油数值模拟程序的实现技术.包括在非结构网格上差分黑油模型方程的技术、边界条件的处理、井的处理、传导率的处理、及一些系数的处理方法等. 
English Abstract:  Since 1970, numerical analyst all high on research work about finite difference methods with appearance and vigorous development of vector computer and parallel computer. Some new parallel algorithms come out along with Evans and Abdullah's work. However, it is rather difficult to generate appropriate structured grids when computing domains are much more complicated domains, such as reservoir numerical simulation domains. So we may quit inner structure of structured grids, and take complete unstructured grids. Unstructured grids, whose positions of nodes are flexible, can more accurately describe geometric shape, and can overcome some localizations which exist in rightangle numerical simulation. But unstructured grids are more complicated, how to develop parallel algorithms on them is concerned generally. RDCPS(R & D Center for Parallel Software, Institute of Software, Chinese Academy of Sciences) had developed a parallel reservoir simulator named PRIS_1.0, and it has running on all kinds of parallel platforms. However, the linear solver in PRISA.Q is based on structured grids. In order to much more describe property of domains, professor Sun wishes to be able to use unstructured grids to computing domains, and intrinsically divide computing domains into many independent subdomains after we make difference to reservoir numerical simulation equations (systems), so that it is much more convenient to parallel computing. Under professor Sun's instructions, author makes main contributions as follows: author starts from simple parabolic model equations, and makes some research to parallel difference schemes on unstructured grids. In chapter two, a parallel difference scheme on unstructured grids is constructed, which is an extend to par allel difference scheme on structured grids. When implemented, it is key to select boundary nodes. Starting from the linear or nonlinear parabolic equations, in space we discretize it by the finite volume element methods. The discretization in time is based on linear multistep schemes. One part of the equations is discretized implicitly and the other explicitly. Starting from the simple linear parabolic equations , we make some research on structured grids. In chapter five, we construct an explicitimplicit parallel difference scheme with suppertimestepping, which is based on an implicit scheme inside boundary layers and an explicit scheme on them. In order to reduce the restrictive timestep limits that exists, we present the suppertimestepping algorithm. In chapter seven, two unconditionally stable parallel difference schemes are presented. Its main ideas are as follows: to decompose the computing domain some overlapping subdomains, take values of the last time layer as Dirichlet boundary conditions (flux of the last time layer as Neumann boundary conditions to scheme(II)) for the time layer on inner boundary points of subdomains to scheme(I), solve it with the fully implicit scheme on each subdomain, then take correspondent values of its neighbor subdomains as its values for inner boundary points of each subdomain, and mean its neighbor subdomain and itself at overlapping points. o The feasibility of the proposed methods is proved by numerical simulation to one dimensional singlephase fluids, two dimensional singlephase fluids, two dimen sional oil water twophase fluids. aiming to model equations of black oils, we give the technique of implement about numerical simulation programs of black oils on unstructured grids, including how to make difference to model equations of black oils, disposal of boundary conditions, disposal of wells, disposal of conductivity, and disposal of some coefficients etc. 
Language:  中文

Content Type:  学位论文

URI:  http://ir.iscas.ac.cn/handle/311060/7558

Appears in Collections:  中科院软件所

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Recommended Citation: 
高家全. 非结构网格上并行差分格式及在油藏模拟中的应用研究[D]. 中国科学院软件研究所. 中国科学院软件研究所. 20020101.


