Stability analysis of traveling wave solution for gravity-driven flow

Surfactant effects on unsaturated flow in porous media with hysteresis: horizontal column experiments and numerical modeling

Numerical solution of Richards’ equation of water flow by generalized finite differences

Temporal and spatial (down profile) variability of unsaturated soil hydraulic properties determined from a combination of repeated field experiments and inverse modeling

Fully discrete IPDG–HMM for multiscale Richards equation of unsaturated flow in porous media

Boltzmann variable is introduced as an intermediate variable in differential transform method (DTM), and an approximate analytical solution is presented about the Brooks-Corey model in Richards equation, which governs the problem of unsaturated flow in porous media. Compared with experimental data of Hall's mortar and finite element method (FEM), the results show highly accuracy in intermediate variable method.

This work proposes an inverse analysis methodology for estimating soil physical-hydraulic parameters, based on the coupling between a Genetic Algorithm and the Finite Difference Method for solving the Richards equation. The Richards equation models water flow in unsaturated porous media, being in this work discretized by the Finite Difference Method with an implicit scheme (Picard), thus ensuring stability and consistency in the presence of strong nonlinearities. The inverse problem is formulated as an optimization problem, in which hydraulic parameters are adjusted to maximize the coefficient of determination between simulated and observed moisture profiles. Numerical simulations were performed for a one-dimensional vertical infiltration problem in a 40 cm deep soil column, using the Haverkamp model to describe the soil constitutive relations. The Genetic Algorithm is configured with a fixed population, tournament selection operators, arithmetic crossover, mutation and elitism. Different scenarios are investigated, considering the simultaneous identification of four and five parameters. Results indicate efficient convergence of the inverse process, with determination coefficients greater than R^2 > 0.98 in most tests, demonstrating the robustness of the proposed coupling.

SummaryNumerical modeling of large deformations in fluid‐infiltrated porous media must accurately describe not only geometrically nonlinear kinematics but also fluid flow in heterogeneously deforming pore structure. Accurate simulation of fluid flow in heterogeneous porous media often requires a numerical method that features the local (elementwise) conservation property. Here, we introduce a new finite element framework for locally mass conservative solution of coupled poromechanical problems at large strains. At the core of our approach is the enriched Galerkin discretization of the fluid mass balance equation, whereby elementwise constant functions are augmented to the standard continuous Galerkin discretization. The resulting numerical method provides local mass conservation by construction with a usually affordable cost added to the continuous Galerkin counterpart. Two equivalent formulations are developed using total Lagrangian and updated Lagrangian approaches. The local mass conservation property of the proposed method is verified through numerical examples involving saturated and unsaturated flow in porous media at finite strains. The numerical examples also demonstrate that local mass conservation can be a critical element of accurate simulation of both fluid flow and large deformation in porous media.

A simplified model of nitrate ion transport (and other nonadsorbing solutes) in unsteady, unsaturated flow in porous media has been developed. The model represents nitrate flow in infiltration and drainage in sand quite well and can be applied to unsaturated flow in other homogeneous media with only minimum extra experimental data needed to describe the medium.

Random porous media flow on large 3-D grids: Numerics, performance, and application to homogenization.- Modeling transport phenomena in porous media.- Modelling of compositional flow in naturally fractured reservoirs.- A particle-grid air quality modeling approach.- On the equilibrium equations of poro-elasticity.- Eulerian-Lagrangian localized adjoint methods for reactive transport in groundwater.- Stochastic modeling of rainfall.- Incorporating model uncertainty into spatial predictions.- Models for flow and transport through porous Media derived by homogenization.- Global surface temperature changes since the 1850s.- A multicomponent self-similar characterization of rainfall fluctuations.- Estimation of kinetic rate coefficients for 2,4-D biodegradation during transport in soil columns.- Modeling in nuclear waste isolation: Approximate solutions for flow in unsaturated porous media.- Similarity solutions for gravity-dominated spreading of a lens of organic contaminant.- Application of optimal data assimilation techniques in oceanography.- Mathematical physics of infiltration on flat and sloping topography.- A note concerning multivariate total positivity on the simplex.- Spatial analysis for environmental studies.- On diagonalization of coupled hydrologic transport and geochemical reaction equations.

The water penetration in soil is investigated numerically using the finite element method (FEM) in a novel way. In the suggested method, new spherical Hankel shape functions are used and the finite element method is reformulated based on them. These new functions are obtained from the first and second kind of Bessel functions. The properties of Hankel shape functions lead to having more accuracy and robustness for the proposed method with low number of elements. To validate the suggested approach, at first, a boundary value problem is solved and the results are compared with the available analytical solution. Then, in order to prove the efficiency and applicability of the present model in the seepage problems, five examples including saturated and unsaturated flow in porous media are studied and the hydraulic head is calculated. Afterward, the results obtained from the classical and new method are compared together. The comparisons indicate that the suggested method with the low number of elements is more precise than the classic FEM with the same mesh.

Head-based isogeometric analysis of transient flow in unsaturated soils

For a point or a spherical source in infinite space the steady state potential is simply a constant over the distance from the source. Flow of soil gases was studied by comparing results for other cavity shapes for sources (or sinks) to the spherical solution. Cavity shapes included a vertical line source of finite length, a prolate spheroid with a vertical axis of rotation, and a vertical well also of finite length and radius. Questions addressed include the distance over which the differences between a sphere and the alternatives become negligible and what radius of spherical source at a given pressure results in the same flow rate as from the other shapes. For a vertical line source the pressure is within 5% of the pressure for the spherical source at a distance of 2.5 times the vertical line and within 1% beyond 6 times the vertical line. Similar results were expressed for the other shapes relative to a spherical source. Travel times are presented in a generalized relationship illustrated for spherical and finite line sources. The results are relevant to other potential problems as well, for example, steady water flow in saturated porous media, steady water flow in unsaturated porous media without gravity, heat conduction, diffusion, and electrostatics.

A Numerical Experiment to Determine the Soil Water Contents in the Unsaturated Zone and the Water Table Response under Transient Ponding Conditions

Galerkin finite-element program for stimulating unsaturated flow in porous media : Khaleel, R; Yeh, T C GroundwaterV23, N1, Jan-Feb 1985, P90–96

It is generally accepted that integrable partial differential time evolution equations possess Lie-Backlund symmetries of arbitrarily high finite order. It has already been established that in (1+1) dimensions the full class of nonlinear Fokker-Planck (convection-diffusion) equations having this property consists of the known integrable examples. These are closely related either to the Burgers equations or to the Fokas-Yortsos-Rosen equation, both of which have been applied to unsaturated flow in porous media. Here the author shows that higher-order Lie-Backlund symmetries do not exist for any examples of the nonlinear Fokker-Planck equation in (1+2) (one time and two space) dimensions.