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

Primary variable switching appears as a promising numerical technique for v ariably saturated flows. While the standard pressure-based form of the Rich ards equation can suffer from poor mass balance accuracy, the mixed form wi th its improved conservative properties can possess convergence difficultie s for dry initial conditions. On the other hand, variable switching can ove rcome 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 t o accuracy and solution effort. Additionally, a simplified upstream weighti ng technique is used. Compared with conventional approaches the primary var iable switching technique represents a fast and robust strategy for unsatur ated problems with dry initial conditions. The impact of the primary variab le 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 tha t the TBFN iteration is an effective but error-prone procedure. TBFN sacrif ices temporal accuracy in favor of accelerated convergence if aggressive ti me step sizes are chosen. (C) 1999 Elsevier Science Ltd. All rights reserve d.