Constants of integration were eliminated by specifying head at the left and right boundaries, and then requiring continuity of head and flux across each of the two internal boundaries. Solution derivations are included at the end of this notebook.
All variables are dimensionless.
The width of the fault relative to the problem domain is 0.05. The solid line shows the calculated hydraulic head profile across the fault, and the dashed line shows the unperturbed hydraulic gradient that would have existed without the fault. Now, add some explanatory information and a background to highlight the location of the fault. The governing equation for steady-state 1D flow in each of the three subdomains is . DSolve can also be used to solve the entire system of differential equations and boundary conditions, and it is included as an alternative at the end of this notebook.