Mass conservative numerical solutions of the head‐based Richards equation

Abstract

Numerical procedures for efficient mass conservative solutions of the head‐based form of the Richards equation are presented. Mass conservative solutions are shown to result when the capacity coefficient, C, is formulated by equating the storage term and its chain rule expansion in their discretized forms. Equivalence in the storage term expansion is maintained in finite difference models when C is evaluated with a standard chord slope approximation. This scheme is shown to produce excellent global mass balance accuracy in simulations of vertical moisture infiltration. An analogous approach to the expansion of the storage term using finite elements results in element dependent expressions of C. Application of this approach produces mass balance accuracy with errors less than 1%, but also exhibits slow convergence in the consistent form. A nontraditional finite element procedure is presented which maintains equivalence in the storage term expansion when C is evaluated with the standard chord slope approximation. This scheme exhibits excellent mass balance accuracy, in either the consistent or lumped forms, without significant loss in computational efficiency.