Numerical Method for Seepage Flow Problems by the Finite Volume Method using Linear Potential Field

線形ポテンシャル場を用いた有限体積法による地下水浸透問題の解析法を提案する．有限体積法(FVM)は，非直交格子を用いた有限差分近似として流体力学や移動現象論などの分野において広く用いられている．特に，地盤環境の問題である地下水による汚染拡散のような水以外との連成問題を解く手法として利用されている．これらの方法は，主に，水頭場を一定として取り扱っている．しかし，FVMは非Galarkin重みを有する有限要素法(FEM)の特殊なケースと考えることができるため，水頭場の次数を高めることで，より精度の高い解析が可能となる．本研究では，FEMの四角形要素と同一の水頭場を仮定し，FEMの概念を導入した定式化を試みた．さらに，本手法によって得られる解の特性を検討するため，簡単な数値計算例によりFEM解との比較検討を行った結果を示す．
A numerical method of seepage flow problems by finite volume method using the linear potential field is proposed. Finite volume method (FVM) is widely used as a finite difference approximation using the non-orthogonality grids in fields such as fluid dynamics and transport phenomenon. Especially, it is used as the technique which solves the coupled problem like the pollution diffusion by the groundwater which is a problem of the ground environment. In these methods, there are many cases in which the water head field is handled as being constant. However, FVM can be considered to be a particular case of finite elements with a non-Galarkin weighting. Therefore, the analysis accuracy is improved by raising the degree of the water head field. In this paper, water head field which is identical with the quadrilateral element of FEM is assumed, and the formulation which introduced the concept of FEM is developed. In addition, the result of the comparison examination with the FEM solution according to the simple model for examining characteristics of the solution by this method is shown.