Moving Multi-Front (MMF): A generalized Green-Ampt approach for vertical unsaturated flows

Abstract

A Moving Multi-Front (MMF) method is developed and tested for solving the Richards equation governing unsaturated flow in vertical homogeneous porous columns. The MMF model is a gridless method. It can be viewed as a generalization of the Green-Ampt piston flow approach, which models flow as a single abrupt moving front separating saturated and dry regions during infiltration. The MMF model further generalizes this concept, using a parametrization of unsaturated water retention and conductivity-pressure curves. It reduces the Richards PDE to an ODE system governing “M” moving front positions. Different tests are developed to validate this approach for 1D transient downwards/upwards flows submitted to constant and time-varying pressure boundary conditions. They include: (i)infiltration to deep water tables; (ii) infiltration to shallow water tables; (iii) capillary rise from fixed water tables; (iv) gradual water table rise (partially saturated column with evolving pressure condition at bottom). The MMF results are compared favorably to finely discretized fixed grid solutions of Richards PDE. Analyses of error and accuracy show satisfactory results in terms of water content profiles and boundary fluxes (e.g. infiltration rate).