Novel Implicit Automated Time Stepping Algorithm for Contaminant Transport through Soil

Accurate estimation of mass transport parameters of chemical contaminants through a soil system is a prerequisite for realistic inverse modeling. In this situation, a mathematical model of the transport process is solved numerically to optimize the design parameters. As the stability and convergence requirements of the numerical procedures limit the usage of large numerical time steps, these time-integral numerical methods either become computationally expensive or yield inaccurate solutions. A detailed convergence and error analyses of different numerical methods is performed in this paper. Further, an automated time stepping implicit algorithm is proposed by smartly adjusting the numerical time step for implicit time-integral numerical procedure using the numerical time step of the explicit schemes obtained by stability and convergence criteria. Thus, the procedure to estimate the numerical solution is rapid due to the implicit nature of the solution yet accurate as it satisfies stability and convergence requirements.