An Eulerian-Lagrangian approach with an adaptively corrected method of characteristics to simulate variably saturated water flow

A relatively simple method of characteristics is developed to simulate one-dimensional variably saturated water flow. The method uses the Eulerian-Lagrangian approach to separate the governing flow equation into "convection" and "diffusion" parts, which are solved with the method of characteristics and the conventional finite element method, respectively. The method of characteristics combines a single-step reverse particle tracking technique with a correction strategy to ensure accurate mass balances. The correction process is implemented by weighing the calculated convective contribution to the pressure head at each node with the pressure head values of two upstream nodes, using an adaptive weighing factor λ. The value of λ is automatically adjusted by considering the global mass balance at each time step. Numerical experiments for ponded infiltration are presented to illustrate the scheme's performance for situations involving highly nonlinear soil hydraulic properties and extremely dry initial conditions. Results indicate that the proposed method is mass-conservative, virtually oscillation-free, and computationally quite efficient. The method is especially effective for simulating highly nonlinear flow scenarios for which traditional finite difference and finite element numerical methods often fail to converge.