Analysis of eigenvalues for vadose-zone models

In this work, we address computational issues associated with using two-phase, air-water models and Richards' equation for vadose-zone simulations. Despite significant effort devoted to identifying efficient numerical approaches for these models, simulation of realistic three-dimensional problems remains challenging. While ongoing research continues to assess the validity of the physical assumptions underlying standard two-phase models and Richards' equation, we focus here on computational reasons for preferring one model over the other in cases where each is physically valid. To this end, we consider eigenvalue spectra for Jacobians associated with standard spatial discretizations within fully implicit temporal approximations for both Richards' equation and two-phase, air-water models. As part of our analysis, we further illustrate the impact of eigenvalue spectra on nonlinear convergence and overall computational efficiency for a test set of three-dimensional flow problems with heterogeneous material properties and a variety of boundary and initial conditions.