粘弹性多孔介质渗流方程严格解的数值分析及应用

1976年Brutsaert和Corapcioglu1]2]提出了粘弹性多孔介质渗流积微分方程的边值问题,并给出了近似解.在1980年至1981年凌镛镛,吴林高和吴林高分别依据线性常系数偏微分方程的基本解理论给出了方程的严格解。由于该严格解是不能用初等函数经有限步计算来表示的,所以难以用于生产实际。本文对严格解采用数值积分方法,得到了可用于生产实践的粘弹性多孔介质水位降深和地面沉降量的两个计算式,并用ALGOL语言编制了计算机程序.另外,本文还给出求参数的方法和计算实例。从实例可以看出;Brutsaert-Corapcioglu3]近似解计算的水位曲线偏离实测水位曲线较大,而根据本文的理论公式计算的水位曲线与实测水位曲线基本一致。

The Numerical Analysis of an Exact Analytic Solution of Fluid Equation in Porous Media with Viscoelastic Properties and Its Application

A boundary value problem for the integral-differential equation for fluids in porous media with viscoelastic properties was proposed by Brutsaert and Corapcioglu, and an approximate solution to that problem was given. According to the theory of elementary solution of linear constant coefficient partial differential equotion, an exact solution of the equation was obtained by Ling Yongyong-Wu Lingao (1980) and Wu Lingao (1981). It is difficult to apply this exact solution to practice, because it cannot be expressed in elementary functions with limited procedure of calculation. Numerical integral method is used for the exact solution in this paper. Two formulas are obtained for subsidence of ground surface and drawing, of water level in porous media with viscoelastic properties due to pumping. They can be used in practical engineering. A program has been worked out in ALGOL language for the computer. In addition, a method of finding the parameter and an example of calculation are also given. It has been seen from this example that the water level curve calculated by B.-C. approximate solution deviates much from the practical water level curve, while the water level curve calculated by the theoretical formula given in this paper practically coincides with the practical water level curve.