相关论文: An analytical solution for vertical infiltration i…
This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form…
We develop numerical methods to simulate the fluid-mechanical erosion of many bodies in two-dimensional Stokes flow. The broad aim is to simulate the erosion of a porous medium (e.g. groundwater flow) with grain-scale resolution. Our fluid…
The dynamical boundary value problem for viscoelastic half-space with cut in the form of a strip is considered. The problem is reduced to the singular integral equation of first kind. Using the method of orthogonal polynomials, the integral…
A broad class of inverse problems deals with determining certain parameters, from measurement data, in models which are associated to certain partial differential equations. In this work we focus on the heat equation on a finite interval…
In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation…
Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by…
In this paper, we are interested to an inverse Cauchy problem governed by the Stokes equation, called the data completion problem. It consists in determining the unspecified fluid velocity, or one of its components over a part of its…
Considered here is an efficient technique to compute approximate profiles of solitary wave solutions of fractional Korteweg-de Vries equations. The numerical method is based on a fixed-point iterative algorithm along with extrapolation…
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…
We obtain new integral representations, expressed as contour integrals in the complex Fourier plane, for the solution of fully nonhomogeneous interface problems for the linearized Cahn-Hilliard equation with arbitrary initial data on the…
To design a method to solve the issues of handling 'dirty' and highly complex geometries, the topology-free method combined with the immersed boundary method is presented for viscous and incompressible flows at a high Reynolds number. The…
We present an immersed boundary projection method formulated in a body-fixed frame of reference for flow-structure interaction (FSI) problems involving rigid bodies with complex geometries. The body-fixed formulation is aimed at maximizing…
Interfacial Stokes flow can be efficiently computed using the Boundary Integral Equation method. In 3D, the fluid velocity at a target point is given by a 2D surface integral over all interfaces, thus reducing the dimension of the problem.…
Forecasting water content dynamics in heterogeneous porous media has significant interest in hydrological applications; in particular, the treatment of infiltration when in presence of cracks and fractures can be accomplished resorting to…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply-connected fluid domain that includes…
We derive the extension of the classical d'Alembert formula for the wave equation, which provides the analytical solution for the direct scattering problem for a medium with constant refractive index; this is achieved by employing results…
Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…
We revisited the analytical solutions for the tidal circulation in an idealized, frictional, elongated, rotating, and enclosed basin. The parameters in the tidal model with a single vertical layer and two vertical layers, including the…
This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits both nonlocal and nonlinear behaviour making the numerical…