Determination of Consistent Performance of Lax-Friedrichs Method in Solving Seepage Problem

We developed a consistent Lax-Friedrichs method for numerical solution of the seepage problem subject to some initial and boundary conditions. We also compared the result obtained using numerical method (Lax-Friedrichs) with the result obtained using Alternating Direction Implicit finite difference method (ADIS). The scheme developed was found to be stable for φ < 1, and unstable for φ ≥ 1. Since the model used in this work was evaluated at a selected discrete point with the region of integration, the surface of the plots becomes naturally not smooth. We also deduced from our result that for any given value of x, the solution u(x,t) increases to almost one as t →∞. Also, for a given value of t, the solution u(x,t) decreases indefinitely as x → ∞, and we observed that the seepage gradually goes to null as the mesh size becomes smaller, which shows that the fluid flow seepage problem may eventually stop.