Related papers: Modeling an Aquifer: Numerical Solution to the Gro…
Stable and accurate finite element methods are presented for Darcy flow in heterogeneous porous media with an interface of discontinuity of the hydraulic conductivity tensor. Accurate velocity fields are computed through global or local…
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…
The water circulation in the Soil-Plant-Atmosphere continuum and particularly the soil erosion induced by water are problems of main concern in the new era of climate change. The present paper aims to provide a mathematical tool to…
In this paper, we consider the complex flows when all three regimes pre-Darcy, Darcy and post-Darcy may be present in different portions of a same domain. We unify all three flow regimes under mathematics formulation. We describe the flow…
Active Flux is a third order accurate numerical method which evolves cell averages and point values at cell interfaces independently. It naturally uses a continuous reconstruction, but is stable when applied to hyperbolic problems. In this…
The aim of this paper is to discuss several aspects of connections between the p-Laplacian and mathematical models in hydrology. At first we present models of groundwater flow in phreatic aquifers and models of irrigation and drainage that…
Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume…
Accurate prediction of flow resistance in high-Froude-number aerated flows remains challenging due to air entrainment, which causes strong spatial variability in mixture density. Here, we introduce for the first time a density-weighted…
This paper presents a conforming finite element discretization of the streamfunction formulation of the one-layer stationary quasi-geostrophic equations, which are a commonly used model for the large scale wind- driven ocean circulation.…
The paper presents an open source software for numerical integration of an extended Saint-Venant model used as a mathematical tool to simulate the water flow from laboratory up to large-scale spatial domains applying physically-based…
Numerical modeling of the migration of three-phase immiscible fluid flow in variably saturated zones is challenging due to the different behavior of the system between unsaturated and saturated zones. This behavior results in the use of…
We investigate two common numerical techniques for integrating reversible moist processes in atmospheric flows in the context of solving the fully compressible Euler equations. The first is a one-step, coupled technique based on using…
We study numerical methods for the nonlinear partial differential equation that governs the motion of level sets by affine curvature. We show that standard finite difference schemes are nonlinearly unstable. We build convergent finite…
Numerical simulations of groundwater flow are used to analyze and predict the response of an aquifer system to its change in state by approximating the solution of the fundamental groundwater physical equations. The most used and classical…
Dealing with variational formulations of second order elliptic problems with discontinuous coefficients, we recall a single field minimization problem of an extended functional presented by Bevilacqua et al (1974), which we associate with…
The mathematical model describing the non-stationary natural pH-gradient arising under the action of an electric field in an aqueous solution of ampholytes (amino acids) is constructed and investigated. The model is part of a more general…
The moist shallow water equations offer a promising route for advancing understanding of the coupling of physical parametrisations and dynamics in numerical atmospheric models, an issue known as 'physics-dynamics coupling'. Without moist…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
The Richards' equation is a model for flow of water in unsaturated soils. The coefficients of this (nonlinear) partial differential equation describe the permeability of the medium. Insufficient or uncertain measurements are commonly…
The calculation of the solvation properties of a single water molecule in liquid water is carried out in two ways. In the first, the water molecule is placed in a cavity and the solvent is treated as a dielectric continuum. This model is…