Finite Element Analysis in Porous Media for Incompressible Flow of Contamination from Nuclear Waste

A non-linear parabolic system is used to describe incompressible nuclear waste disposal contamination in porous media, in which both molecular diffusion and dispersion are considered. The Galerkin method is applied for the pressure equation. For the brine, radionuclide and heat, a kind of partial upwind finite element scheme is constructed. Examples are included to demonstrate certain aspects of the theory and illustrate the capabilities of the kind of partial upwind finite element approach

Adomian and Adomian-Padé Technique for Solving Variable Coefficient Variant Boussinesq System

In this paper, Adomian and Adomian-Padé Technique are used to find approximate solutions for the Variable-Coefficient Variant Boussinesq System, and using Adomian-Padé Technique for Debug (Remove) The Gap (Complex Root)

An Approximate Solution to The Newell-Whitehead Equation by Adomian Decomposition Method

ABSTRACT In this paper, we solved the Newell-Whitehead equation approximately using Adomain Decomposition method and we have compared this solution with the exact solution; we found that the solution of this method is so close to the exact solution and this solution is slower to converge to the exact solution when we increase t however, this method is effective for this kind of problems

Numerical Solution and Stability Analysis of Huxley Equation

ABSTRACT The numerical solution of Huxley equation by the use of two finite difference methods is done. The first one is the explicit scheme and the second one is the Crank-Nicholson scheme. The comparison between the two methods showed that the explicit scheme is easier and has faster convergence while the Crank-Nicholson scheme is more accurate. In addition, the stability analysis using Fourier (von Neumann) method of two schemes is investigated. The resulting analysis showed that the first scheme is conditionally stable if, ( ) Introduction It is probably not an overstatement to say that almost all partial differential equations (PDEs) that arise in a practical setting are solved numerically on a computer. Since the development of high-speed computing devices the numerical solution of PDEs has been in active state with the invention of new algorithms and the examination of the underlying theory. This is one of the most active areas in applied mathematics and it has a great impact on science and engineering because of the ease and efficiency it has shown in solving even the most complicated problems. The basic idea of the method of finite differences is to cast the continuous problem described by the PDE and auxiliary conditions into a discrete problem that can be solved by a computer in finitely many steps. The discretization is accomplished by restricting the problem to a set of discrete points. By systematic procedure, we then calculate the unknown function at those discrete points. Consequently, a finite difference technique yields a solution only at discrete points in the domain of interest rather than, as we expect for an analytical calculation, a formula or closed-form solution valid at all points of the domain and 1. Manoranjan [13] studied in detail the solutions bifurcating from the equilibrium state a u = . Eilbeck and Manoranjan [3] considered different types of basis functions for the pseudo-spectral method applied to the nonlinear reaction-diffusion equation in 1-and 2-space dimensions. Eilbeck [4] extended the pseudo-spectral method to follow steady state solutions as a function of the problem parameter, using path-following techniques. Fath and Domanski [6] studied the cellular differentiation in a developing organism via a discrete bistable reaction-diffusion model and they used the numerical simulation to support their expectations of the qualitative behavior of the system. Lewis and Keener [10] studied the propagation failure using the one -dimensional scalar bistable equation by a passive gap and they used the numerical simulation in their study. Binczak et a

A kind of Upwind Finite Element Approximations for Compressible Flow of Contamination from Nuclear Waste in Porous Media

ABSTRACT A non-linear parabolic system is derived to describe compressible nuclear waste disposal contamination in porous media . Galerkin method is applied for the pressure equation . For the concentration of the brine of the fluid, a kind of partial upwind finite element scheme is constructed. A numerical application is included to demonstrate certain aspects of the theory and illustrate the capabilities of the kind of partial upwind finite element approach