Takeo Taniguchi

Numerical experiments for 3-dimensional flow analysis in a fractured rock with porous matrix

Groundwater flow in a 3-D domain with fracture planes is numerically investigated using the finite element method. A flexible mesh generation method for discretization is proposed in this paper. The method, based on Delaunay triangulation, divides the whole domain into subdomains separated by fracture planes. It then triangulates each subdomain independently into tetrahedra which are further subdivided into hexahedra. By putting together all of the meshes of the subdomain, a finite element mesh of the whole domain is obtained. The appropriateness of the mesh generation method is topologically proved. Several applications of the proposed method are given, and the numerical solutions are in good agreement with those obtained with a structured grid. It is concluded that the proposed mesh generation method can replace the structured grid.

New renumbering algorithm for minimizing the bandwidth of sparse matrices

Abstract The minimum bandwidth of a sparse matrix is proved to be a kind of the width of a graph which is obtained from the matrix in question, and by using this result we not only clarify the reasons of the complexity to obtain the minimum bandwidth by digital computer but also, on the contrary, that we can design effective renumbering algorithm only for systems having a kind of topological structure. Under this restriction new renumbering algorithm which can reduce the bandwidth to the minimum or near minimum value is presented.

Flexible mesh generator for triangular and quadrilateral areas

Abstract The object of this paper is to propose a new method to generate the topological properties among the input data necessary for the user of the Finite Element Method. The method can generate the element-node relation for triangular and quadrilateral areas which are required to subdivide into different numbers of segments on their edges. This flexibility can largely remove the complexity of the mesh generation of two-dimensional area. The algorithm of the proposed method is so simple as to be used on a microcomputer. The main part of program listing written in BASIC is attached to this paper.

Hexahedral Mesh Generation and Its Application to the Analysis of Groundwater Flow and Transport Phenomena in 3D Fractured Rock

The development of underground space necessarily requires the analysis of the groundwater flow and transport problems through 3D fractured rock, and recent advances of the numerical analysis enable us to solve them using FEM. But there still exists a serious problem of how to model 3D rock with a set of fracture planes.

Complexities of the design of the bandwidth and profile minimisation algorithms

Abstract This paper treats theoretically the minimum bandwidth and profile problems which are required to be solved for the design of the efficient renumbering algorithms for minimising the bandwidth and profile of a sparse matrix, and it clarifies what decides the minimum values. From the relations between the theoretical results and the assumed input-data the possibility of the design of the renumbering algorithms is also investigated.

Profile minimisation algorithm for sparse matrix

Abstract In this paper a new renumbering method for minimising the profile of sparse matrices is proposed and its efficiency is surveyed through a number of numerical experiments. The characteristics of the new method are (1) it is effective only for the purpose of the profile minimisation; (2) it does not order nodes in accordance with the level structure constructes from the starting node; and (3) it is applicable for any kind of two-dimensional system.

ANALYTICAL STUDY FOR STRESS CONCENTRATION NEAR SUPPORTS FOR REPLACEMENT OF STEEL BRIGDE BEARINGS

阪神・淡路大震災以降，鋼橋の支承をゴム形式に取り替える施工が行われてきているが，支承が鋼形式からゴム形式に変更になった際には，支点近傍の応力集中が懸念される．鋼形式からゴム形式に変更した場合の支点近傍の応力集中をFEM解析により求めた．また，支点付近に取り付けられた小型の補強リブについて，その効果を鋼製支承，ゴム支承の場合で調べた．ゴム支承は鋼製支承と比較して，常時，地震時ともに支点近傍に発生する応力は低く，支承取替えには有効であると言える．小型の補強リブについては，ゴム支承の場合には効果が確認できたが，鋼製支承の場合には必要性を確認することができなかった．

Parallel Finite Element Method for Orographic Wind Flow and Rainfall

Abstract. This paper presents a parallel finite element method for the analysis of orographic wind flow and rainfall. The Kessler model, which is the model for warm rain, was used for the governing equation. For the governing equation of wind flow, the unsteady Navier -Stokes equation based on Boussinesq approximation was used. The SUPG and PSPG methods were uemployed for the stabilization method. Parallel implementation based on domain decomposition method and MPI was carried out on a PC cluster. The present method was applied to the analysis of orographic wind flow and rainfall past a semicircular hill and an actual mountain area. The effect of parallelization on the efficiency of the computation was also examined.

Coupled Geometric Modelling for the Analysis of Groundwater Flow and Transport in Fractured Rock

A strategy is proposed for preparing quadrilateral and hexahedral finite elements for the numerical analysis of groundwater flow and transport in three-dimensional fractured rock. We present three methods for the local discretization of fractured media (hexahedral elementsfor volumes and quadrilateral elements for fracture planes). These methods are based on the Delaunay triangulation. Therefore they can be applied to arbitrary convex domains consisting of a set of convex subdomains surrounded by fracture planes.

Estimation of optimum relaxation factor for the successive overrelaxation method

Abstract A new estimation method of the optimum relaxation factor for the successive overrelaxation method is proposed, and its efficiency is surveyed through a number of numerical experiments. The characteristics of the new method are that (1) it can a priori determine the value of the factor by using only the topological properties in the linear systems, and (2) it is valid not only for the linear system obtained by the finite difference method but also for the one led from the finite element method.