The Richards’-equation is widely used for modeling complex soil water dynamics in the vadose zone. Usually, the Richards’-equation is simulated with the Finite Element Method, the Finite Difference Method, or the Finite Volume Method. In...
A stable explicit difference scheme, which is based on forward Euler format, is proposed for the Richards equation. To avoid the degeneracy of the Richards equation, we add a perturbation to the functional coefficient of the parabolic term. In additi...
Soil moisture distribution plays a significant role in soil erosion, evapotranspiration, and overland flow. Infiltration is a main component of the hydrological cycle, and simulations of soil moisture can improve infiltration process modeling. Differ...
A time stepping quasilinearization approach to the mixed (or coupled) form of one and two dimensional Richards’ equations is developed. For numerical solution of the linear ordinary differential equation (ODE) for 1D case and elliptic for 2D ca...
In this paper, we introduce peridynamic theory and its application to Richards’ equation with a piecewise smooth initial condition. Peridynamic theory is a non-local continuum theory that models the deformation and failure of materials. Richard...
The accurate description of the flow of water in porous media is of the greatest importance due to its numerous applications in several areas (groundwater, soil mechanics, etc.). The nonlinear Richards equation is often used as the governing equation...
Research on seepage flow in the vadose zone has largely been driven by engineering and environmental problems affecting many fields of geotechnics, hydrology, and agricultural science. Mathematical modeling of the subsurface flow under unsaturated co...
The lookup table option, as an alternative to analytical calculation for evaluating the nonlinear heterogeneous soil characteristics, is introduced and compared for both the Picard and Newton iterative schemes in the numerical solution of Richards’ e...
P-band radar remote sensing applied during the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) mission has shown great potential for estimation of root zone soil moisture. When retrieving the soil moisture profile (SMP) from P-ba...
The Richards’ equation is widely used in the modeling soil water dynamics driven by the capillary and gravitational forces in the vadose zone. Its state and parameter estimation based on field soil moisture measurements is important and challen...
To model dynamic systems in various situations results in an ordinary differential equation of the form dydt=g(y,t,θ), where g denotes a function and θ stands for a parameter or vector of unknown parameters that require estimation from ob...
Water infiltration is simulated by obtaining the time infiltrated depth evolution and humidity profiles with the numerical solution of the two-dimensional Richards’ equation. The contact time hypothesis is accepted in this study and used to app...
The Richards equation plays an important role in the study of agro-hydrological systems. It models the water movement in soil in the vadose zone, which is driven by capillary and gravitational forces. Its states (capillary potential) and parameters (...
The North China Plain is a crucial agricultural region in China, but irregular precipitation patterns have led to significant water shortages. To address this, analyzing the high-resolution dynamics of root-zone soil moisture transport is essential f...
The aim of this study is the deduction of an analytic representation of the optimal irrigation flow depending on the border length, hydrodynamic properties, and soil moisture constants, with high values of the coefficient of uniformity. In order not...
Leaks from landfills to underlying soil layers are one of the main problems that endanger the sustainability of waste disposal in landfills. Indeed, the possible failing of in-situ equipment can give rise to serious pollution consequences or costly i...
In this article, the modeling of infiltration--induced landslides, in unsaturated soils using the radial basis function (RBF) method, is presented. A novel approach based on the RBF method is proposed to deal with the nonlinear hydrological process i...
The moving particle semi-implicit method (MPS) has been employed to numerically simulate fluid flows. Further, some studies have used the MPS method to solve the Darcy–Brinkman equation, which also expresses fluid flow in porous media. However,...
The structure of soils is often heterogeneous with layered strata having distinct permeabilities. An advanced mathematical and numerical coupled model of elastic wave propagation in poroelastic multi-layered soils subjected to subsoil water infiltrat...
Background/Objectives: In recent years, the discharge of antibiotics into rivers and irrigation canals has increased. However, few studies have addressed the impact of these compounds on agricultural fields that use such water to meet crop demands. M...
In this paper, a novel meshless method for the transient modeling of subsurface flow in unsaturated soils was developed. A linearization process for the nonlinear Richards equation using the Gardner exponential model to analyze the transient flow in...
Based on the Richards-Wolf (RW) formalism, we obtain two different exact expressions for the angular momentum (AM) density of light in the focus of an optical vortex with a topological charge n and right circular polarization. One expression for the...
The uncertainty in a hydrological model, due to its structure or implemented input parameters, affects the accuracy of simulations that are usually used for important applications such as drought predictions, flood risk assessment, irrigation schedul...
Subterranean termite activity can increase the hydraulic conductivity and water infiltration of filling soil, and therefore affects the stability of an earth embankment and subsequent safety. As a physical barrier for sustainable termite management,...
Numerical modeling has become an irreplaceable tool for the investigation of water flow and solute transport in the unsaturated zone. The use of this tool for real situations is often faced with lack of knowledge of hydraulic and soil transport param...
Finite element discretization of the pressure head form of the Richards equation leads to a nonlinear model, which yields numerical convergence difficulties. When the numerical solution to this problem has either an extremely sharp moving front, infi...
(1) Background: Simulation of soil water infiltration process and analysis of its influencing factors are important for water resources management. (2) Methods: In this study, the relative contributions of the soil water retention characteristics (SW...
In this paper, we present a multiscale model reduction technique for unsaturated filtration problem in fractured porous media using an Online Generalized Multiscale finite element method. The flow problem in unsaturated soils is described by the Rich...
Soil water movement is important in fields such as soil mechanics, irrigation, drainage, hydrology, and agriculture. The Richards equation describes the flow of water in an unsaturated porous medium, and analytical solutions exist only for simplified...
The computational cost of approximating the Richards equation for water flow in unsaturated porous media is a major challenge, especially for tasks that require repetitive simulations. Data-driven modeling offers a faster and more efficient way to es...
Landslide events are among natural hazards with many fatalities and financial losses. Studies demonstrate that natural factors such as rainfall and human activities such as deforestation are important causes of triggering a landslide. In this study,...
The phenomenological universalities (PU) approach is employed to derive the Richards growth function in the unknown hyperbolic representation. The formula derived can be applied in theoretical modeling of sigmoid and involuted growth of biological sy...
Accurate knowledge of individual tree ages is critical for forestry and ecological research. However, previous methods suffer from flaws such as tree damage, low efficiency, or ignoring autocorrelation among residuals. In this paper, an approach for...
Estimation of contaminant travel time through the vadose zone is needed for assessing groundwater vulnerability to pollution, planning monitoring and remediation activities or predicting the effect of land use change or climate change on groundwater...
This study focused on the estimation of groundwater recharge rates and travel time of conservative contaminants between ground surface and aquifer. Numerical simulations of transient water flow and solute transport were performed using the SWAP compu...
Individual tree growth and yield models precisely describe tree growth irrespective of stand complexity and are capable of simulating various silvicultural alternatives in the stands with diverse structure, species composition, and management history...
Competition indices may improve tree growth modelling in high-density stands, found often in new cork oak plantations. Distance-dependent competition indices have hardly been considered for juvenile cork oak plantations since existing models were dev...
The Richards equation has high plasticity and compatibility. Compared with other curve equations, it has higher applicability and accuracy in describing S-shaped curves. It can describe the changes in the initial growth stage, rapid growth stage, and...
Water storage and flow in shallow subsurface drives runoff generation, vegetation water use and nutrient cycling. Modelling these processes under non-steady state conditions is challenging, particularly in regions like the subtropics that experience...
Significant deviations from standard Boltzmann scaling, which corresponds to normal or Fickian diffusion, have been observed in the literature for water movement in porous media. However, as demonstrated by various researchers, the widely used conven...
Leak 2D is a new two-dimensional dual permeability mathematical model for the simulation of the preferential flow in the vadose zone. In this model, water flow in the soil matrix domain is described by the two-dimensional h-based Richards’ equa...
Matter grows and self-assembles to produce complex structures such as virus capsids, carbon fullerenes, proteins, glasses, etc. Due to its complexity, performing pen-and-paper calculations to explain and describe such assemblies is cumbersome. Many y...
Biometric systems are the basis of forest management and consist of a set of equations that describe the relationships between forest attributes and dendrometric variables. A systematic review of the state of the art of biometric systems in Mexico wa...
To account for the seasonal changes in the soil thermal and hydrological dynamics, the soil moisture state physical process defined by the Richards Equation is integrated with the soil thermal state defined by the numerical model of phase change base...
Close-to-nature management (CTNM) is the most promising option for plantation silviculture and has received widespread attention in recent years. Stand density is a key variable in CTNM, as it directly influences growth and yield. Research for the op...
The paper argues that universal approaches to infiltration and drainage in permeable media pivoting around capillarity and leading to dual porosity, non-equilibrium, or preferential flow need to be replaced by a dual process approach. One process has...
The migration of hazardous substances in a bentonite barrier layer is a key issue for the safety of nuclear waste storage. This study develops a thermo-hydro-mechanical coupling model to simulate the contaminant migration in a bentonite barrier layer...
A hybrid interpolating meshless (HIM) method is established for dealing with three-dimensional (3D) advection–diffusion equations. To improve computational efficiency, a 3D equation is changed into correlative two-dimensional (2D) equations. Th...
In this study, a two-dimensional numerical landslide model was developed to investigate the effects of the amount of rainfall and lateral flow on induced slope failures. The Richard’s equation was used to evaluate pore water pressure distribution in...
Due to the high nonlinearity of the three-dimensional (3-D) unsaturated-saturated water flow equation, using a fully 3-D numerical model is computationally expensive for large scale applications. A new unsaturated-saturated water flow model is develo...
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