د.انس محمد علي الحبوبي

In this paper, we mainly focus on the development of the Taylor-Galerkin/Pressure-Correction method (TG/PC) method to solve the flow of a compressible Newtonian fluid under nonisothermal conditions. The process of development needs applying the two-step Lax–Wendroff method on the energy equation, after which two new steps for energy equations will be obtained within the TG/PC algorithm. In addition, for the density component, the Tait equation of state is adopted to relate density to pressure, which also yields a new step within the novel method to give the correction formula of compressible pressure. To perform the analysis of the new algorithm, Poiseuille flow through axisymmetric rectangular channel for the Newtonian thermal flow is utilized as a simple problem test. The effect of nondimensional factors such as Reynolds number (Re) and Prandtl number (Pr) is discussed in this study. The influence of thermal conductivity (k) and viscosity (μ) on the solution components is presented as well. Also, comparison for both compressible and incompressible flows is provided in addition to a comparison between both cases’ convergence, as it turns out that the convergence of the incompressible case is better than the compressible case. All the results of the effects presented in this study agree well with the approved physical trend.

This paper applies Modifed Decomposition Method (MDM) as numerical analysis linear second-order FredholmIntegro-differential Equations. The calculation of the approximate solutions are computed by mathematical package. The main aim of this paper is to demonstrate how effective this method minimizes the size of calculations and reaching the final solution in the shortest time and best result. When com paring the results with the (ADM) and with the exact solution, we will note how effective this method minimizes the size of calculations of the solution and reaches the exact solution. Accordingly, the (MDM) is the best method to be used to solve linear second-order FredholmIntegro-Differential equation. The convertion to the exact solution is notably fast and also a time saver, as it requires less computational work in solving equations. This is why the (MDM) is more efficient in solving this kind of equations.

In this study, we have studied the multi-order differential equations. The model we have followed agrees with initial value problem which, in its turn, has a group of linear ordinary differential equations. This paper's aim is programming a Variational Iteration Method (VIM) using Wolfram's Mathematica. Variational Iteration Method offers a study that introduce approximated solutions of the multi-order ordinary differential equations. Several examples of different order have been resolved.

In this work, we propose a numerical method based on the generalized sine-cosine wavelets for solving multi-order fractional differential equations. After introducing generalized sine-cosine wavelets, the operational matrix of Riemann-Liouville fractional integration is constructed using the properties of the block-pulse functions. The fractional derivative in the problem is considered in the Caputo sense. This method reduces the considered problem to the problem of solving a system of nonlinear algebraic equations. Finally, some examples are included to demonstrate the applicability of the new approach.

In this study, we present a novel algorithm designed to address the computational challenges posed by the governing equations of incompressible Newtonian fluid flow, particularly of bluff bodies of circular and square in a channel. This a significant innovation algorithm is developed based on the Taylor–Galerkin/Pressure-Correction finite element method. Notably, a pivotal element of this approach involves the implementation of the two-step Lax–Wendroff scheme to resolve the momentum equation. To assess the efficacy of our novel algorithm, we conducted a comprehensive analysis using a standard benchmark scenario; the initiation of Poiseuille flow through an axisymmetric rectangular channel encompassing bluff bodies. In this context, our investigation centered on the influence of the Reynolds number (

In this study, three main problems in fluid flow have been discussed. First, the derivation of the energy equation is conducted within cylindrical coordinates, which has not been addressed by the researchers before. Secondly, we develop a new algorithm for solving the governing equations that describe incompressible Newtonian flows under thermal condition. This algorithm is constructed based on the so- called Taylor-Galerkin/Pressure-Correction finite element method with the help of the two-step Lax-Wendroff scheme. Finally, we study the effect of non-dimensional numbers, such as the Reynolds number (Re) and the Prandtl number (Pr), on the velocity, pressure, and temperature. The results show that the developed method is consistent with established physical phenomena and other studies.