Problem 1The ground flow equation for 1D heterogeneous, isotropic porous medium with a constant aquifer thickness is given by:Where h(x，t） is the hydraulic head， T(x） is the transmissivity， and S is the storativity. The boundary conditions imposed are constant head hL （15m) and hR (5m) at the left and right ends of soil column ， respectively. The initial condition is 0 or random number at each node. The length of aquifer is 1m （L=1m）. The storativity is 1 （S = 1）。Develop a MATLAB program which can handle a heterogeneous transmissivity field using the implicit method。1) Test the program for the case of homogenous parameters, and compare the results with the results generated from flow equation with homogenous transmissivity field (i.e., )2) Test the program for patch- heterogeneous T field， which comprises a two—zone T field with a fivefold difference in transmissivity (T1=5T2, T1=0.01m2s—1， T2=0.002m2s-1 ; or, T1=0。2T2, T1=0。002m2s—1, T2=0。01m2s-1) and an interface in the middle of the domain。Problem 1 解答1 理论推导非 均 质 一 维 地 下 水 运 动 方 程 为 ： 如右图，各个点的水头分别为，水头和之间水力传导系数为.将方程(1)进行离散化：设，则 设 则 所以: 设， 则， , 2 编码实现根据第一部分的理论推导编写代码2.1均质情况下一维地下水运动function plot_Data = oneDimGroudwaterFlowHom(hL，hR，L，S,T,method,dx，dt）%％ Finite difference method to solve 1—D flow equation％% Writed By Dongdong Kong, 2025—01—07% Sun Yat-Sen University， Guangzhou， China％ emal： kongdd＠mail2.sysu。edu.cn％ -—--—-————---——-—--—--—-——-—-——---—----————-—----—-——-% one dimension groundwater flow model script% which can handle a heterogeneous transmissivity field% ——-—--————----—-—--———-————-----——--—-——-———-——...
