Some Numerical Experiments on the Variably-Saturated Flow Equation

Abstract

The variably-saturated flow equation (VSFE) is a special form of the well known Richards’ equation for unsaturated flow in which the elastic storage arguments are used to define the specific storativity (which is useful for saturated flow simulation). The Richards’ equation, under transient conditions, is highly nonlinear. Traditionally, numerical techniques have been used in solving this equation. The moisture-content form of Richards’ equation requires less computer time and is subject to low mass balance errors while simulating transient infiltration into very dry soils. However, this form of Richards’ equation is limited to complete unsaturated conditions and cannot handle positive pressure upper boundary or layered soil profiles. For this reason, while simulating water movement in variably saturated soils, the pressure-based form of Richards’ equation is used. The pressure-based form is prone to mass balance errors and requires large amounts of computer time due to the iterative nature of solution. A recently reported mixed form of Richards’ equation is used in this investigation for its mass conservative property. The computer time requirement for the mixed form Richards’ equation is similar to the pressure-based form. A series of numerical experiments were conducted using the VSFE which contained the mass-conservative form of the Richards’ equation. The Galerkin finite element technique was used to solve the equation numerically. The effects of the type of mass lumping (matrix diagonalization), initial and boundary conditions on the accuracy, stability, and the rate of convergence of this equation are presented. The influences of time varying top boundary conditions and layered heterogeneity on water movement are also presented. In addition,“tricks” for efficient time step control and steady-state simulation using this mass conservative formulation are shown. Finally, simulation results indicate that this mixed-form equation is superior to the pressure-based form.KeywordsPressure HeadMixed FormUnsaturated FlowMoisture ProfileTime Derivative TermThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.