Sharif Digital Repository

In this paper, the numerical errors associated with the finite difference solutions of two-dimensional advection-dispersion equation with linear sorption are obtained from a Taylor analysis and are removed from numerical solution. The error expressions are based on a general form of the corresponding difference equation. The variation of these numerical truncation errors is presented as a function of Peclet and Courant numbers in X and Y direction, a Sink/Source dimensionless number and new form of Peclet and Courant numbers in X-Y plane. It is shown that the Crank-Nicolson method is the most accurate scheme based on the truncation error analysis. The effects of these truncation errors on... 

The numerical errors associated with explicit upstream finite difference solutions of two-dimensional advection - Dispersion equation with linear sorption are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation. The numerical truncation errors are defined using Peclet and Courant numbers in the X and Y direction, a sink/source dimensionless number and new Peclet and Courant numbers in the XY plane. The effects of these truncation errors on the explicit solution of a two-dimensional advection-dispersion equation with a first-order reaction or degradation are demonstrated by comparison with an analytical solution in... 

The transient heat transfer analysis of a layer has been studied much less than the steady state. However, transient temperature distribution resulted from including radiation and conduction simultaneously, is significantly different from those obtained by considering conduction alone. In order to include the effect of radiation heat transfer, we must insert the gradient of radiative flux in the energy equation. For this purpose, a variety of multi-flux methods have been suggested. A simplified procedure is the two-flux method, which is the one used in the present paper. This paper is focused on one-dimensional transient heat transfer of a layer using Finite Difference Method. To this end, a... 

Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with nondecaying power-law correlation functions, are considered. The study is motivated in part by a recent discovery that the elastic moduli of rock at large length scales may be characterized by long-range power-law correlation functions. Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in any dimension. We have numerically checked the RG results using the... 

In this paper a laminar flow of water on an ice layer subjected to a slip condition is considered numerically. The paper describes a parametric mathematical model to simulate the coupled heat and mass transfer events occurring in moving boundary problems associated with a quasi steady state steady flow process. The discretization technique of the elliptic governing differential equations of mass, momentum and energy is based on the control volume finite difference approach and enthalpy method, the results illustrate, the distribution of heat transfer coefficient, ice melting thickness, slip velocity at solid moving boundary and boundary layer thickness for some values of slip velocity... 

This paper gives details of the refinement and application of a two-dimensional horizontal model for rivers. An explicit finite-difference algorithm was used for solving the governing differential equations, which includes the conservation of mass and momentum to predict hydrodynamic parameters. The model includes different turbulence closure models - that is, constant eddy viscosity, Prandtl simple mixing length and Smagorinsky methods. An experimental programme was designed and carried out in a laboratory flume to measure the length of eddy produced at the entrance of the intake. Model predictions have been compared with experimental results for a lateral intake. The effect of different... 

The three-dimensional supersonic turbulent flows over wrap-around fin missiles have been computed using the Thin Layer Navier-Stokes (TLNS) equations to reduce the computational efforts compared to those of the Full Navier-Stokes (FNS) equations. In this research, the missile configuration is divided into multi regions to enable fluid flow simulation using Personal Computers (PC). It also makes it possible to use a different number of nodes and distribution of grids in each region to enhance the accuracy. The Thin Layer Navier-Stokes equations in the generalized coordinate system were solved using an efficient, implicit, finite-difference factored algorithm of the Beam and Warming. For the... 

The Finite Difference Time Domain (FDTD) method has been applied to the analysis of abruptly-ended dielectric waveguides. In these waveguides, incident propagating wave undergoes reflection in an interaction with the end-facet. As a result of the discontinuity, all possible propagating modes may be excited. The constituent propagating modes are extracted from the reflected wave by the least square method. Thus, we present a good estimation of the amplitudes of the reflected modes. This full wave analysis technique is also capable of analyzing any arbitrarily shaped facet. © 2004 IEEE  

This paper presents the mathematical modeling of single-phase natural circulation of the University of Genoa's rectangular loop (LOOP#1) by a computer program and using RELAP5 system code. The mass, momentum and energy conservation equations in transient form were solved numerically using the finite difference method. One-dimensional linear stability analysis was performed for the single-phase natural circulation loop and the numerical perturbation technique was used in this analysis. The Nyquist criterion was employed to find the stability map of the LOOP#1. The obtained transient results using the first order upwind scheme of the fluid temperatures in various sectors of the LOOP#1 are... 

Identification of existing instability modes from experimental pressure measurements of rocket engines is difficult, specially when steep waves are present. Actual pressure waves are often non-linear and include steep shocks followed by gradual expansions. It is generally believed that interaction of these non-linear waves is difficult to analyze. A method of mode identification is introduced. After presumption of constituent modes, they are superposed by using a standard finite difference scheme for solution of the classical wave equation. Waves are numerically produced at each end of the combustion tube with different wavelengths, amplitudes, and phases with respect to each other. Pressure...