On the primary variable switching technique for simulating unsaturated–saturated flows

Abstract

Primary variable switching appears as a promising numerical technique for variably saturated flows. While the standard pressure-based form of the Richards equation can suffer from poor mass balance accuracy, the mixed form with its improved conservative properties can possess convergence difficulties for dry initial conditions. On the other hand, variable switching can overcome most of the stated numerical problems. The paper deals with variable switching for finite elements in two and three dimensions. The technique is incorporated in both an adaptive error-controlled predictor–corrector one-step Newton (PCOSN) iteration strategy and a target-based full Newton (TBFN) iteration scheme. Both schemes provide different behaviors with respect to accuracy and solution effort. Additionally, a simplified upstream weighting technique is used. Compared with conventional approaches the primary variable switching technique represents a fast and robust strategy for unsaturated problems with dry initial conditions. The impact of the primary variable switching technique is studied over a wide range of mostly 2D and partly difficult-to-solve problems (infiltration, drainage, perched water table, capillary barrier), where comparable results are available. It is shown that the TBFN iteration is an effective but error-prone procedure. TBFN sacrifices temporal accuracy in favor of accelerated convergence if aggressive time step sizes are chosen.