On the primary variable switching technique for simulating unsaturated±saturated ̄ows

Primary variable switching appears as a promising numerical technique for variably saturated ̄ows. While the standard pressurebased form of the Richards equation can su€er from poor mass balance accuracy, the mixed form with its improved conservative properties can possess convergence diculties 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 ®nite 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 di€erent behaviors with respect to accuracy and solution e€ort. Additionally, a simpli®ed 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 dicult-to-solve problems (in®ltration, drainage, perched water table, capillary barrier), where comparable results are available. It is shown that the TBFN iteration is an e€ective but error-prone procedure. TBFN sacri®ces temporal accuracy in favor of accelerated convergence if aggressive time step sizes are chosen. Ó 1999 Elsevier Science Ltd. All rights reserved.