An Explicit Mass-Conservative Method for Modelling 1-D Variably Saturated Flow

This study presents an explicit mixed-form finite-volume (EFV) solver for the one-dimensional Richards equation and evaluates its performance across a broad range of unsaturated and saturated flow conditions. Within the van Genuchten–Mualem framework, the numerical scheme computes water content (θ) through a conservative flux balance and evaluates intercell fluxes from pressure head gradients, while a simple saturated zone treatment allows positive heads (ψ) to be represented without altering the conservative balance in θ. A Fourier-based adaptive time step approach is derived from local hydraulic conductivity and storage terms, and its relation to the classical explicit diffusion restriction is established through a local linearised stability analysis. The resulting criterion supports the use of r max = 1/2 for the benchmark regimes considered. Ten benchmark tests with diverse initial and boundary conditions are used to assess profile reproduction, mass balance, time step behaviour, and computational cost. The results show that the EFV formulation reproduces the reference solutions, maintains conservative behaviour, and remains computationally feasible for the 1-D column problems examined.