Transformation approaches for simulating flow in variably saturated porous media

Sharp fronts with rapid changes in quid saturations over short distance and timescales often exist in multiphase flow in subsurface systems. Such highly nonlinear problems are notoriously difficult to solve, and standard solution approaches are often inefficient 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 range of medium properties and simulation conditions. The new IT2 transform is defined as a linear combination of volumetric water fraction of the aqueous phase and integrated hydraulic conductivity terms. We show that transformation methods can significantly improve solution efficiency and robustness compared to standard solution approaches; optimal transformation parameters depend upon auxiliary conditions, medium properties, and spatial and temporal discretization and are difficult to evaluate a priori; and IT2 compares favorably with existing transforms.