自仿射Sierpinski地毯中的粘滞指进

VISCOUS FINGERING IN SELF AFFINE SIERPINSKI CARPET 

构造了自仿射Ｓｉｅｒｐｉｎｓｋｉ地毯．在自仿射Ｓｉｅｒｐｉｎｓｋｉ地毯中，认为喉管半径服从截断瑞利分布，采用逐次超松弛技术，模拟了自仿射Ｓｉｅｒｐｉｎｓｋｉ地毯中的粘滞指进．计算了粘滞指进分维，结果表明，当粘滞比Ｍ→∞时，指进图样与在自仿射Ｓｉｅｒｐｉｎｓｋｉ地毯中ＤＬＡ模拟的结果类似：当Ｍ＝１时，驱替流体在长标度范围内具有紧凑的结构，且具有稳定的位移．

Abstract In this paper, the self affine Sierpinski carpet is constructed. The viscous fingering (VF) in self affine Sierpinski carpet, based on the assumption that bond radii are truncated Rayleigh distribution, is simulated by means of successive over relaxation techniques. The fractal dimension of VF is calculated. The results show that the VF pattern of self affine Sierpinski carpet in the limit viscosity ratio M →∞ is found to be similar to the DLA pattern. When M=1 , the interior of the cluster of the displacing fluid is compact and the displacement process is stable for long length scales.