The velocity, shear-rate, variable viscosity, and variable power-law index profiles are calculated for non-Newtonian fluids using the finite difference method. The calculations are carried out for an actual viscosity function obtained by a cilrve fit through measured data and for the corresponding power law model, the simplest and most often used form for non­ Newtonian viscosity function appro...

Models for multiphase-multicomponent flow in porous media are described in systems of PDEs. Solving them using finite difference discretization method can be of three ways; explicit, semi-implicit, and fully implicit. In this study, we present the implementation of an adaptive Newton-Raphson method in the context of IMPECS (Implicit Pressures Explicit Concentrations and Saturations) method of s...

In this paper, we consider the Darboux problem for a (1+1)dimensional cubic nonlinear Klein-Gordon equation with an external source. Stable finite difference scheme is constructed on a four-point stencil, which does not require additional iterations for passing from one level to another. It is proved, that the finite difference scheme converges with the rate O(h2), when the exact solution belon...

We propose a finite difference scheme for the Heisenberg equation and the LandauLifshitz equation. These equations have a length-preserving property and energy conservation or dissipation property. Our proposed scheme inherits both characteristic properties. We also show that the boundedness of finite difference solutions and an unique solvability of our scheme. Finally, we show some numerical ...

Abstract—This paper presents the heat and mass driven natural convection succession in a Darcy thermally stratified porous medium that embeds a vertical semi-infinite impermeable wall of constant heat flux and concentration. The scale analysis of the system determines the two possible maps of the heat and mass driven natural convection sequence along the wall as a function of the process parame...

Abstract: Complex diffusion is a common and broadly used denoising procedure in image processing. The method is based on an explicit finite difference scheme applied to a diffusion equation with a proper complex diffusion parameter in order to preserve edges and the main features of the image, while eliminating noise. In this paper we present a rigorous proof for the stability condition of comp...

Cheng Wang, Jian-Guo Liu, Hans Johnston 1 Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA; e-mail: [email protected] 2 Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, MD 20742, USA; e-mail: [email protected] 3 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA; e-mail: hansjo...

A class of singularly perturbed two point boundary value problems (BVPs) for third order ordinary differential equations is considered. The BVP is reduced to a weakly coupled system of one first order Ordinary Differential Equation (ODE) with a suitable initial condition and one second order singularly perturbed ODE subject to boundary conditions. In order to solve this system, a computational ...

A summary of the Lebedev finite-difference timedomain method, which is designed for modelling anisotropic problems in a simple and accurate manner, is provided. The basics of the method are presented, as well as augmentations to allow for coupling the Lebedev grid to standard Yee grid for more efficient use of memory; and implementation of conducting surfaces, and corners of 90◦ or 270◦.

A new mimetic finite difference scheme for solving the acoustic wave equation is presented. It combines a novel second order tensor mimetic discretizations in space and a leapfrog approximation in time to produce an explicit multidimensional scheme. Convergence analysis of the new scheme on a staggered grid shows that it can take larger time steps than standard finite difference schemes based o...