Robust Newton Solver Based on Variable Switch for a Finite Volume Discretization of Richards Equation

Abstract

We propose an efficient nonlinear solver for the resolution of the Richards equation. It is based on variable switching and is easily implemented thanks to a fictitious variable allowing to describe both the saturation and the pressure. Numerical experiments show that our method enables to use Newton's method with large time steps, reasonable number of iterations and in regions where the pressure-saturation relationship is given by a graph.

Richards’ Equation: Transition Between Constitutive Equations and the Mechanics of Water Flow in Unsaturated Soil

“…(10) and (11) to have a better curve-fitting ability than Eqs. 7and (8). Figure 2(b) has proven the effectiveness of this method which was able to recreate the center of the water infiltration front, possible beyond 34.7 days.…”

“…Richards' equation consists of a governing equation that is used to describe water flow in subsurface porous media such as soil [1]. It is continuously subjected to numerical investigation [2][3][4][5][6][7][8][9].The modeling of water distribution using the equation has important application in climate science, agriculture and also ecosystem management [10]. Among many applications, Zeide [11] has reported the use of Richards' equation in the tree growth modeling prediction.…”

A Gravity Current Model with Capillary Trapping for Oil Migration in Multilayer Geological Basins

“…The Darcean model is approximated thanks to a fully implicit finite volume scheme with upstream mobility and parametrization of the monotone relation (56). We refer to [5] for details on the numerical method. The viscosity of each phases are given in centipoise (cPo) where 1 cPo corresponds to 10 −3 Pa s. The viscosity of the oil phase set to µ o = 11.78 cPo while the viscosity of the water phase is set to µ w = 0.548 cPo.…”

“…This choice is known to be suitable for such vertically integrated models, see for instance [1,2] since it allows to transpose the stability of the continuous model to the discrete one. The strong stability of the numerical scheme allows to show that the corresponding nonlinear system admits solutions, which are computed thanks to a parametrization based robust Newton solver [5] allowing for large time steps. All in all, the numerical procedure appears to be very efficient to compute the long-time behavior of the model in which we are interested.…”

Transition Between Constitutive Equations and the Mechanics of Water Flow in Unsaturated Soil: Numerical Simulations

“…Richards' equation consists of a governing equation that is used to describe the water flow in subsurface porous media such as soil in unsaturated conditions [1]. It is continuously subjected to numerical investigation [2][3][4][5][6][7][8][9][10][11]. The modeling of water distribution using the equation has essential applications in climate science, agriculture and also ecosystem management [12].…”