Transformation Approaches for Simulating Flow in

Sharp fronts with rapid changes in uid saturations over short distance and time scales often exist in multiphase ow in subsurface systems. Such highly nonlinear problems are notoriously diicult to solve, and standard solution approaches are often ineecient and unreliable. We summarize four existing and one new transformation method (IT2) for solving Richards' equation within a common framework and compare performance for a wide range of media properties. We show that: transformation methods can signiicantly improve solution eeciency and robustness compared to standard solution approaches; transformation parameters depend upon auxiliary conditions, media properties, and spatial and temporal discretization; and IT2 compares favorably with existing transforms. 3