Nonlinearity continuation method for steady-state groundwater flow modeling in variably saturated conditions

First-order continuation method for steady-state variably saturated groundwater flow modeling

“…A more powerful approach is the nonlinearity continuation method [13]. The relative permeability function K r (h), which makes the equation nonlinear, is parametrized with a continuation parameter q ∈ [0; 1] such that the resulting function, K(h, q), has the following properties:…”

“…These are techniques for discretization of diffusion-type operators and have been employed in various applications such as simulation of groundwater flow or multiphase flow in porous media. While finite volume schemes have been already employed in earlier work [13,14], the mimetic scheme is considered for the first time within the nonlinearity continuation method and is included in order to test the solution strategy for discretization other than finite volume.…”

“…This paper focuses on improvement of a special solution approach for boundary value problems for the steady-state Richards equation, namely, the nonlinearity continuation method [13]. In this procedure, the governing Richards equation in original problem is parametrized in a way that its "degree of nonlinearity" can be controlled.…”

Surface runoff model in Gera Software: parallel implementation and surface-subsurface coupling

“…. (12) This definition means that water flow cannot have a downward direction (from surface to subsurface) when there is no water on the surface. Equation ( 12) is discontinuous with respect to both arguments for 0, 0 sg hh  .…”

“…Recently, a large number of different highly efficient computational codes for groundwater modelling have appeared [6] [7][8] [9] and parallelization of different aspects of this process remains challenging [10], [11], [12], [13]. The GeRa software was developed taking into account the necessity of massive parallel calculations [14].…”