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 Eu lerian-Lagrangian approach to separate the governing flow equation int o ''convection'' and ''diffusion'' parts, which are solved with the me thod of characteristics and the conventional finite element method, re spectively. The method of characteristics combines a single-step rever se particle tracking technique with a correction strategy to ensure ac curate mass balances. The correction process is implemented by weighin g the calculated convective contribution to the pressure head at each node with the pressure head values of two upstream nodes, using an ada ptive weighing factor lambda. The value of lambda is automatically adj usted by considering the global mass balance at each time step. Numeri cal experiments for ponded infiltration are presented to illustrate th e scheme's performance for situations involving highly nonlinear soil hydraulic properties and extremely dry initial conditions. Results ind icate that the proposed method is mass-conservative, virtually oscilla tion-free, and computationally quite efficient. The method is especial ly effective for simulating highly nonlinear flow scenarios for which traditional finite difference and finite element numerical methods oft en fail to converge.