Adaptive time stepping and error control in a mass conservative numerical solution of the mixed form of Richards equation

Adaptive time stepping with embedded error control is applied to the mixed form of Richards equation. It is the first mathematically based adaptive sc heme applied to this form of Richards equation. The key to the method is th e approximation of the local truncation error of the scheme in terms of the pressure head, although, to enforce mass conservation, the principal time approximation is based on the moisture content. The time stepping scheme is closely related to an implicit Thomas-Gladwell approximation and is uncond itionally stable and second-order accurate. Numerical trials demonstrate th at the new algorithm fully automates stepsize selection and robustly constr ains temporal discretisation errors given a user tolerance. The adaptive me chanism is shown to improve the performance of the non-linear solver, provi ding accurate initial solution estimates for the iterative process. Further more, the stepsize variation patterns reflect the adequacy of the spatial d iscretisation, here accomplished by linear finite elements. When sufficient ly dense spatial grids are used, the time step varies smoothly, while exces sively coarse grids induce stepsize oscillations. (C) 2001 Elsevier Science Ltd. All rights reserved.