Numerical Solutions for Nonequilibrium Solute Transport with First-Order Decay and Zero-Order Production

Abstract

Solute transport in the subsurface is often considered to be a nonequilibrium process. Nonequilibrium during transport of solutes in porous medium has been categorized as either transport-related or sorption-related. For steady state flow in a homogeneous soil and assuming a linear sorption process, we will consider advection-diffusion adsorption equations. In this paper, numerical methods are considered for the mathematical model for steady state flow in a homogeneous soil with a linear sorption process. The modified upwind finite difference method is adopted to approximate the concentration in mobile regions and immobile regions. Optimal order $l^2$-error estimate is derived. Numerical results are supplied to justify the theoretical work.