An algebraic dynamic multilevel method for the simulation of contaminant transport and retention through vadose zones

Abstract

This study extends the Algebraic Dynamic Multilevel (ADM) method for simulating contaminant transport and retention in vadose zones. Building upon a fully implicit scheme that couples variably saturated flow and contaminant transport, the developed ADM framework effectively predicts contaminant plume migration across both unsaturated and saturated media under heterogeneous conditions. During the simulation, ADM dynamically adjusts grid resolution based on the spatial gradients of primary variables, applying fine-scale grids in regions with steep gradients and coarsening the mesh where fields remain smooth. These dynamic adjustments are achieved through prolongation and restriction operators that transfer solutions across multilevel grid systems. As both water content and contaminant concentration evolve spatiotemporally, dual coarsening criteria are introduced to simultaneously capture flow and transport dynamics. Results show that the developed model reproduces the contaminant migration obtained from the fully resolved solution using substantially fewer grids. Moreover, it offers the flexibility to trade off numerical accuracy against computational cost by selecting an appropriate coarsening criterion.