We consider the Richards equation on a domain that is decomposed into nonoverlapping layers, i.e., the decomposition has no cross points. We assume that the saturation and permeability functions are space-independent on each subdomain. Kirchhoff transformation of each subdomain problem separately then leads to a set of semi-linear equations, which can each be solved efficiently using monotone m...

*Correspondence: [email protected] 2School of Aerospace Engineering and Applied Mechanicas, Tongji University, Shanghai, China Full list of author information is available at the end of the article Abstract We apply a series expansion technique to estimate the water content distribution and front position in finite boundary conditions. We derive an approximate analytical solution of the Richard...

In this work, we present a two-dimensional mixed-hybrid finite element model of variably saturated flow on unstructured triangular meshes. Velocities are approximated using lowest order Raviart-Thomas (RT0) elements with piecewise constant pressure. The resulting nonlinear systems of algebraic equations are solved using Picard or Newton iterations in combination with ad hoc preconditioning tech...

Professionalism has been generally linked to nations’ economic, industrial, and technological developments. Therefore, having a professionally and ethically competent workforce is a necessity in today's changing world. More specifically, L2 teacher professionalism plays a crucial role in economic development too.  Given its utmost importance in language teaching, this study intended to investig...

Preconditioners for the Conjugate Gradient method are studied to solve the Newton system with symmetric positive definite (SPD) Jacobian. Following the theoretical work in [1] we start from a given approximation of the inverse of the initial Jacobian, and we construct a sequence of preconditioners by means of a low rank update, for the linearized systems arising in the Picard-Newton solution of...

Several sigmoidal functions (logistic, Gompertz, Richards, Schnute, and Stannard) were compared to describe a bacterial growth curve. They were compared statistically by using the model of Schnute, which is a comprehensive model, encompassing all other models. The t test and the F test were used. With the t test, confidence intervals for parameters can be calculated and can be used to distingui...

In this note, the existing porousMultiphaseFoam toolbox, developed initially for any two-phase flow in porous media is extended to the specific case of the Richards’ equation which neglect the pressure gradient of the non-wetting phase. This model is typically used for saturated and unsaturated groundwater flows. A Picard’s algorithm is implemented to linearize and solve the Richards’ equation ...

[1] This paper presents analytical solutions for one-dimensional radial transient flow through a horizontal, unsaturated fractured rock formation. In these solutions, unsaturated flow through fractured media is described by a linearized Richards’ equation, while fracture-matrix interaction is handled using the dual-continuum concept. Although linearizing Richards’ equation requires a specially ...

We prove a substructuring result for a variational inequality concerning — but not restricted to — the Richards equation in homogeneous soil and including boundary conditions of Signorini’s type. This generalizes existing results for the linear case and leads to interface conditions known from linear variational equalities: continuity of Dirichlet and flux values in a weak sense. In case of the...

[1] Inverse solutions of the Richards equation, either for evaluating soil hydraulic parameters from experimental data or for optimizing irrigation parameters, require considerable numerical effort. We present an alternative methodology based on self-organizing maps (SOM) which was further developed in order to include multiple input-output (MIO) relationships. The resulting SOM-MIO network app...