Related papers: Analytical model of infiltration under constant su…
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…
Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
A new computational method is presented to resolve hydrodynamic interactions acting on solid particles immersed in incompressible host fluids. In this method, boundaries between solid particles and host fluids are replaced with a continuous…
In this study, a novel semi-implicit second-order temporal scheme combined with the finite element method for space discretization is proposed to solve the coupled system of infiltration and solute transport in unsaturated porous media. The…
Improving the accuracy of soil moisture estimation is required for advancing irrigation scheduling and water conservation efforts. Central to this task are soil hydraulic parameters, which govern moisture dynamics but are rarely known…
The spatiotemporal water flow dynamics in unsaturated soils can generally be modeled by the Richards equation. To overcome the computational challenges associated with solving this highly nonlinear partial differential equation (PDE), we…
A novel centrifuge set-up for the study of unsaturated flow characteristics in porous media is examined. In this set-up, simple boundary conditions can be used, but a free moving boundary between unsaturated-saturated flow arises. A precise…
The analytical solution of the equation describing diffusion of intrinsic point defects has been obtained for a one-dimensional finite-length domain. This solution is intended for investigating and modeling the changes in defect…
Irregular terrain has a pronounced effect on the propagation of seismic and acoustic wavefields but is not straightforwardly reconciled with structured finite-difference (FD) methods used to model such phenomena. Methods currently detailed…
Modeling unsaturated flow through soils with water uptake by plan root has many applications in agriculture and water resources management. In this study, our aim is to develop efficient numerical techniques for solving the Richards…
We develop a new approach to solve the nonlinear Richards equation based on the Kirchhoff transformation and localized radial basis function (LRBF) techniques. Our aim is to reduce the nonlinearity of the governing equation and apply LRBF…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…
This short note provides explicit solutions to the linearized Boussinesq equations around the stably stratified Couette flow posed on $\mathbb{T}\times\mathbb{R}$. We consider the long-time behavior of such solutions and prove inviscid…
In this paper, we focus on one-dimensional vertical infiltration, assuming constant diffusivity and a quadratic relationship between hydraulic conductivity and water content. Under these assumptions, Richards' equation reduces to Burgers'…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
The Richards equation is a nonlinear parabolic equation that is commonly used for modelling saturated/unsaturated flow in porous media. We assume that the medium occupies a bounded Lipschitz domain partitioned into two disjoint subdomains…
The inclination angle of the undrained shear slip surface in saturated soils is analyzed based on mixture theory. First, starting from the property that the bulk strain of soil skeleton is equal to the flow ratio of water discharged from…
An analytical linear solution of the fully compressible Euler equations is found, in the particular case of a stationary two dimensional flow that passes over an orographic feature with small height-width ratio. A method based on the…
Richards equation is often used to represent two-phase fluid flow in an unsaturated porous medium when one phase is much heavier and more viscous than the other. However, it cannot describe the fully saturated flow for some capillary…