MASS CONSERVATIVE NUMERICAL-SOLUTIONS OF THE HEAD-BASED RICHARDS EQUATION

Numerical procedures for efficient mass conservative solutions of the head-based form of the Richards equation are presented. Mass conservat ive 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 s tandard chord slope approximation. This scheme is shown to produce exc ellent global mass balance accuracy in simulations of vertical moistur e 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 e rrors less than 1%, but also exhibits slow convergence in the consiste nt form. A nontraditional finite element procedure is presented which maintains equivalence in the storage term expansion when C is evaluate d with the standard chord slope approximation. This scheme exhibits ex cellent mass balance accuracy, in either the consistent or lumped form s, without significant loss in computational efficiency.