A multiple domain algorithm for modeling one-dimensional transient contaminant transport flows

Solving numerically the transient one-dimensional advection dispersion equation by using an explicit scheme is limited by the choice of time step size according to the Courant-Friedrich-Levy (CFL) stability condition. For transient simulations over large domains, a small time step would require a very large computational time. To address this issue, we investigate the performance of coupling an explicit solution with a multiple domain methodology for modeling transient phenomena. In this approach, at a constant time period the numerical solution is computed over a series of spatial domains that are characterized by varying grid spacing. This facilitates spreading the effect of the boundary condition across a wider interior domain with reduced computational effort. Emphasis has been equally distributed in testing the effect of this coupling on both the accuracy of the end solution and on the associated computational savings. Two improvements that reflect on the accuracy of the solution are discussed and their performance analyzed. A two-dimensional application is presented in the following paper.