孔隙介质中渗流团分形维数的模拟计算方法

Numerical Simulation Method of Fractal Dimension of Percolation Cluster in Porous Mediums

详细介绍了在二维情况下孔隙介质逾渗流的基本理论、重正化群方法的原理及其在逾渗研究中的应用。采用了计算机数值模拟试验的方法,证明了渗流团的分形性质,并拟合逾渗团所包含的孔隙数M[L]与L之间的曲线和曲线方程:M(L)=0.353 8L1.937 9(座逾渗),M(L)=0.711 2L1.905 4(键逾渗)。求出渗流团的分形维数D=1.937 9(座逾渗),D=1.905 4(键逾渗)。比较了数值模拟结果与精确值,说明误差产生的原因。在本文中具体地说明了编制计算机程序的方法和数值试验的步骤。为以后的研究做了些基本的准备性工作。

The basic theory of porous mediums in 2D condition is introduced and the theory of Renormalization method is applied to research the percolation. Based on numerical simulation experiment, this paper demonstrates the fractal characteristic of percolation duster and drew the relationship curve between the number of percolation cluster： M（L） and L. deduced the function： M（L） = 0.353 8L^1.9379 （site percolation） ,M（L） = 0.711 2L^1.9054 （bond percolation） .the fractal dimension of percolation is D = 1.937 9（site percolation）. D = 1.905 4 （bond percolation）. We compared the result of numerical simulation experiment with accurate value, and analyzed the reason for the error. At the same time this paper explicated how to write the program in detail, how to experiment by using numerical simulation step by step. The essential preparative is order to our research in the future.