Accurate and economical solution of the pressure-head form of Richards' equation by the method of lines

• Published in: Advances in water resources 1997, Vol.20 (1), p.1-14
• Main Authors: Tocci, Michael D., Kelley, C.T., Miller, Cass T.
• Format: Article
• Language: English
• Subjects: Earth sciences; Earth, ocean, space; equations; Exact sciences and technology; Hydrology; Hydrology. Hydrogeology; ordinary differential equations; unsaturated flow; wetting front pressure head
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/S0309-1708(96)00008-5

The pressure-head form of Richards' equation (RE) is difficult to solve accurately using standard time integration methods. For example, mass 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 with a constant time-step size, but variable step-size methods applied to date have relied upon empirical approaches to control step size, which do not explicitly control temporal truncation error of the solution. We show how a differential algebrain 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 advocate the use of this approach for both RE and other problems involving subsurface flow and transport phenomena.