Modeling Groundwater Flow in Unconfined Conditions: Numerical Model and Solvers’ Efficiency

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

“…Another important property of the scheme is its similarity to finite volume schemes, which results from the same assignation of mesh unknowns and the same approximation of divergence operator. This ensures local conservativity and allows for easy incorporation into existing finite volume framework, including some constitutive relationships and procedures designed specifically for finite volume paradigm [9].…”

“…Previous work [14] studied Newton and Picard solvers as well as their combination. Experiments showed that the use of mixed solver may help to complete the nonlinearity continuation procedure in 1 step for simpler constitutive model from [9], but requires setting parameters, such as initial number of Picard iterations and initial relaxation coefficient. For the VGM model, the mixed solver gave no clear advantage.…”

Comparison of nonlinear solvers within continuation method for steady-state variably saturated groundwater flow modeling

“…A much simpler model, so-called unconfined flow model uses piecewise linear dependencies proposed in [10] and is designed specifically for numerical solution with the finite volume method. These functions depend on spatial discretization, possibly varying from cell to cell.…”

“…The first problem is a model problem describing groundwater flow in a square dam (taken from [33]). The dam problem is used as a verification test for the unconfined flow model and as a performance benchmark [8,10]. In this paper, that problem is slightly modified to exclude seepage boundary condition and make it more challenging for spatial discretization.…”

“…This paper focuses on steady-state case and, more precisely, on a special solution technique applied recently for these problems -the nonlinearity continuation method [8]. Unlike commonly used pseudo-transient method [5,9,10], in which the system evolves in time until reaching steady-state, the nonlinearity continuation works directly with the steady-state equation. As it has been reported [5,11], straightforward application of standard nonlinear solvers such as Newton method may fail due to lack of good initial guess.…”