Numerical Analysis and Simulation of Solute Transport in Heterogeneous Porous Medium via Crank-Nicolson Finite Difference Scheme

Abstract

A Numerical framework is developed to investigate one-dimensional solute migration in heterogeneous porous media under variable transport conditions. By employing the Crank- Nicolson finite difference strategy - noted for its second order accuracy and inherent stability - that quantifies concentration behavior influenced by fluctuating groundwater velocities and nonuniform dispersion coefficients. By utilizing this numerical strategy, the framework effectively characterizes solute dynamics for space-time dependent decay and production parameter that vary sinusoidally 1+ sin (λxt) and exponentially exp(−λxt) with position and time. The results of this work reveal the spatial-temporal evolution of the contaminant plume and demonstrate the profound effects of variable hydrodynamic dispersions on solute migration within the given heterogeneous porous domain.