MASS TYPES, ELEMENT ORDERS AND SOLUTION-SCHEMES FOR THE RICHARDS EQUATION

The Richards equation for water movement in unsaturated soils is highl y nonlinear and generally cannot be solved analytically. An alternativ e is to solve the equation numerically with finite-element methods. Co nventionally, it has been accepted that the consistent mass scheme wit h higher-order elements is superior for solving complex nonlinear phys ical problems. However, results from other studies indicate that a fin ite-element model based on the consistent mass with higher-order eleme nts would cause numerical oscillation problems. In this study, lumped mass, consistent mass, linear elements, and quadratic/cubic elements w ere evaluated to determine the most efficient method to solve the Rich ards equation with finite-element models. Results demonstrated that, w hen using consistent mass schemes or quadratic/cubic elements, the tim e step cannot be arbitrarily reduced to achieve the convergence; the m esh size must first be reduced in order to avoid numerical oscillation s. In a time-dependent problem with large and complex domain, the mini mum mesh size allowed is often unknown a priori. As a result, the intr insic necessity of constantly adjusting the mesh size and hence rearra nging the mesh structure is not efficient. On the other hand, in the l umped mass scheme with linear elements, one can arbitrarily reduce the time step at any time during the simulation to obtain a stable and co nsistent solution without changing the mesh structure. For nonlinear a nd time-dependent problems with large mesh domain, most of the compute r time is used in algorithms to solve the linearized matrix equations. Results from this study indicate that, to solve the Richards equation , the conjugate-gradient methods are more efficient than the sky-line decomposition method. The three preconditioning schemes investigated d o not have any significant difference in computer memory and time requ ired. (C) 1997 Elsevier Science Ltd.