An Evaluation of Linearly Implicit Time Discretization Methods For Approximating Richards' Equation

The solution of Richards' equation and two-phase air/water models for flow in porous media continues to be a challenge for many problems of interest. Typically, fully implicit time discretizations are preferred due to the strong, potentially degenerate nonlinearities that result from standard constitutive relationships. Recently however, there has been renewed interest in linearly implicit methods, since they avoid the solution of full nonlinear problems, while retaining desirable stability properties over explicit discretizations. In this work, we consider modern implicit and linearly implicit temporal approximations for Richards' equation and two-phase air/water models. We evaluate their performance in terms of robustness and efficiency for different levels of accuracy under a range of conditions that reflect many of the difficulties often found in simulating flow in the vadose zone.