Mixed formulation for an easy and robust numerical computation of sorptivity

Sorptivity is one of the most important parameters for the quantification of water infiltration into soils. Parlange (1975) proposed a specific formulation to derive sorptivity as a function of the soil water retention and hydraulic conductivity functions, as well as initial and final soil water contents. However, this formulation requires the integration of a function involving the hydraulic diffusivity, which may be undefined or present numerical difficulties that cause numerical misestimations. In this study, we propose a mixed formulation that scales sorptivity and splits the integrals into two parts: the first term involves the scaled degree of saturation while the second involves the scaled water pressure head. The new mixed formulation is shown to be robust and well-suited to any type of hydraulic functions - even with infinite hydraulic diffusivity or positive air-entry water pressure heads - and any boundary condition, including infinite initial water pressure head, h → −∞.

A MIXED FORMULATION FOR A BENDING DOMINATED KOITER SHELL WITH OBSTACLE

In this paper, we present a mixed formulation for a bending dominated Koiter shell with obstacle in order to avoid numerical locking or the deterioration of the convergence when the small parameter the thickness goes to zero. This formulation is a combination between the free locking mixed formulation presented in [1,10] and the Koiter’s model with obstacle for flexural shell proposed in [6].