This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

Abstract\

In this research, estimated the reliability of water system network in Baghdad was done. to assess its performance during a specific period. a fault tree through static and dynamic gates was belt and these gates represent logical relationships between the main events in the network and analyzed using dynamic Bayesian networks . As it has been applied Dynamic Bayesian networks estimate reliability by translating dynamic fault tree to Dynamic Bayesian networks and reliability of the system appreciated. As was the potential for the expense of each phase of the network for each gate . Because there are two parts to the Dynamic Bayesian networks and two part of gate (AND), which includes the three basic units of the

In the present paper, an eco-epidemiological model consisting of diseased prey consumed by a predator with fear cost, and hunting cooperation property is formulated and studied. It is assumed that the predator doesn’t distinguish between the healthy prey and sick prey and hence it consumed both. The solution’s properties such as existence, uniqueness, positivity, and bounded are discussed. The existence and stability conditions of all possible equilibrium points are studied. The persistence requirements of the proposed system are established. The bifurcation analysis near the non-hyperbolic equilibrium points is investigated. Numerically, some simulations are carried out to validate the main findings and obtain the critical values of th

This paper presents a numerical analysis using ANSYS finite element program to simulate the reinforced concrete slabs with spherical voids. Six full-scale one way bubbled slabs of (3000mm) length with rectangular cross-sectional area of (460mm) width and (150mm) depth are tested as simply supported under two-concentrated load. The results of the finite element model are presented and compared with the experimental data of the tested slabs. Material nonlinearities due to cracking and crushing of concrete and yielding of reinforcement are considered. The general behavior of the finite element models represented by the load-deflection curves at midspan, crack pattern, ultimate load, load-concrete strain curves and failure m

In the present research, the chemical washing method has been selected using three chelating agents: citric acid, acetic acid and Ethylene Diamine Tetraacetic Acid (EDTA) to remove 137Cs from two different contaminated soil samples were classified as fine and coarse grained. The factors that affecting removal efficiency such as type of soil, mixing ratio and molarity have been investigated. The results revealed that no correlation relation was found between removal efficiency and the studied factors. The results also showed that conventional chemical washing method was not effective in removing 137Cs and that there are further studies still need to achieve this objective.