Error propagation in the Newton-based solution control of unsaturated flow

The Newton method represents the numerical core of the primary variable switching technique (PVST) which has been shown to be superior to conventional approaches in both unsaturated flow and multiphase flow modelling. In the context of PVST, empirically controlled strategies in time are rather common, where the Newton convergence is attempted for a possibly large step size. This technique is known as the target-based full Newton (TBFN) time stepping strategy. In comparison to adaptive techniques satisfying a predefined discretization error, the TBFN results can be inaccurate in spite of the convergence achieved in the Newton method. The present paper aims to analyse the cause of discrepancies in simulating unsaturated flows. This is done by comparison of analytical solutions which are based on exponential constitutive laws.