Consider the steady$-$state two$-$dimensional groundwater flow in a homogeneous, isotropic

aquifer. This rectangular aquifer has dimensions $100$ m $($x$-$direction$)$ by $80$ m $($y$-$direction$).$

Groundwater divide exist at the top and bottom boundaries. The head along the left boundary is

$12$ m$,$ while the head along the right boundary is $10$ m$.$

$1.(40$pts$)$ Draw the mesh$-$centered finite$-$difference grid for this aquifer. Use a grid with $5$

columns and $4$ rows $($recall that node $1,1$ occurs at the top, left corner$).$ Label all nodes in the

computational grid, grid spacing and boundary conditions. This should be a scaled figure

$($use graph or engineering paper, a scale, or a computer tool$).$

$2.(10$pts$)$ Write the general finite$-$difference approximation for the head at generic node $($i$,$ j$),$

based on the steady$-$state groundwater flow equation.

$3.(50$pts$)$ For each of the following nodes, apply the finite$-$difference approximation from

Question $2$ and simplify the resulting equations: $(1,1,(2,1),(2,2),$ and $(5,2).$