ACCURATE AND ECONOMICAL SOLUTION OF THE PRESSURE-HEAD FORM OF RICHARDS EQUATION BY THE METHOD OF LINES

The pressure-head form of Richards' equation (RE) is difficult to solv e accurately using standard time integration methods. For example, mas s balance errors grow as the integration progresses unless very small time steps are taken. Further, RE may be solved for many problems more economically and robustly with variable-size time steps rather than w ith a constant time-step size, but variable step-size methods applied to date have relied upon empirical approaches to control step size, wh ich do not explicitly control temporal truncation error of the solutio n. We show how a differential algebraic equation implementation of the method of lines can give solutions to RE that are accurate, have good mass balance properties, explicitly control temporal truncation error , and are more economical than standard approaches for a wide range of solution accuracy. We detail changes to a standard integrator, DASPK, that improves efficiency for the test problems considered, and we adv ocate the use of this approach for both RE and other problems involvin g subsurface flow and transport phenomena. Copyright (C) 1996 Elsevier Science Ltd