Related papers: An analytical solution for vertical infiltration i…
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'…
Originating from the mathematical modelling of rainfall infiltration, we derive the solution of an initial-boundary value problem of a linear evolution partial differential equation, by using the Fokas method. We present numerical examples…
We present the numerical solution of two-point boundary value problems for a third order linear PDE, representing a linear evolution in one space dimension. The difficulty of this problem is in the numerical imposition of the boundary…
We obtain solution representation formulas for some linear initial boundary value problems posed on the half space that involve mixed spatial derivative terms via the unified transform method (UTM), also known as the Fokas method. We first…
An analytical solution of the nonlinear Richards equation is presented, for one-dimensional infiltration into a soil of uniform initial moisture content subject to a constant depth of surface ponded water. Adopted mathematical forms of the…
We implement the Unified Transform Method of Fokas as a numerical method to solve linear partial differential equations on the half-line. The method computes the solution at any x and t without spatial discretization or time stepping. With…
The Richards equation, a nonlinear elliptic parabolic equation, is widely used to model infiltration in porous media. We develop a finite element method for solving the Richards equation by introducing a new bounded auxiliary variable to…
We examine the analytic extension of solutions of linear, constant-coefficient initial-boundary value problems outside their spatial domain of definition. We use the Unified Transform Method or Method of Fokas, which gives a representation…
A new method for the solution of initial-boundary value problems for evolution PDEs recently introduced by Fokas is generalised to multidimensions. Also the relation of this method with the method of images and with the classical integral…
Considered here is a class of Boussinesq systems of Nwogu type. Such systems describe propagation of nonlinear and dispersive water waves of significant interest such as solitary and tsunami waves. The initial-boundary value problem on a…
We employ the Ablowitz-Ladik system as an illustrative example in order to demonstrate how to analyze initial-boundary value problems for integrable nonlinear differential-difference equations via the unified transform (Fokas method). In…
In this study, we focus on the modelling of infiltration process in porous media. We use the meshless techniques for efficiently solving the Richards equation which describes unsaturated water flow through soils. The design of approximate…
In this short communication, we announce an algorithmic procedure for constructing non-uniqueness counter-examples of classical solutions to initial-boundary-value problems for a wide class of linear evolution partial differential…
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…
A method for solving linear initial boundary value problems was recently reimplemented as a true spectral transform method. As part of this reformulation, the precise sense in which the spectral transforms diagonalize the underlying spatial…
We study a semidiscrete analogue of the Unified Transform Method introduced by A. S. Fokas, to solve initial-boundary-value problems for linear evolution partial differential equations with constant coefficients on the finite interval $x…
A numerical framework for rigorous linear stability analysis of two-phase stratified flows of two immiscible fluids in horizontal circular pipes is presented. For the first time, three-dimensional disturbances, including those at the…
We present an hybrid VOF/embedded boundary method allowing to model two-phase flows in presence of solids with arbitrary shapes. The method relies on the coupling of existing methods: a geometric Volume of fluid (VOF) method to tackle the…
The work presents an integral solution of the time-fractional subdiffusion through a preliminary defined profile with unknown coefficients and the concept of penetration layer well known from the heat diffusion The profile satisfies the…
The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…