In this paper, a least squares group finite element method for solving coupled Burgers' problem in 2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved. The theoretical results show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the efficiency of the proposed method that are solved through implementation in MATLAB R2018a.
Determining the aerodynamic characteristics of iced airfoil is an important step in aircraft design. The goal of this work is to study experimentally and numerically an iced airfoil to assess the aerodynamic penalties associated with presence of ice on the airfoil surface. Three iced shapes were tested on NACA 0012 straight wing at zero and non-zero angles of attack, at Reynolds No. equal to (3.36*105). The 2-D steady state continuity and momentum equations have been solved utilizing finite volume method to analyze the turbulent flow over a clean and iced airfoil. The results show that the ice shapes affected the aerodynamic characteristics due to the change in airfoil shape. The experimental results show that the horn iced airfoil
... Show MoreThe Halabja earthquake occurred on 12/11/2017 in Iraq, with a magnitude of 7.3 Mw, which happened in the Iraqi-Iranian borders. This earthquake killed and injured many people in the Kurdish region in the north of the country. There is no natural disaster more dangerous than earthquake, especially it occurs without warning, great attention must be paid to the impact of earthquakes on the soil and preparing for a wave of earthquakes. Numerical modeling using specific elements is considered a powerful tool to investigate the required behavior of structures in Geotechnical engineering, and the main objective of this is to assess the response of the Al-Wand dam to the Halabja earthquake, as this dam is located in an area that has been su
... Show MoreIn this paper, we show that for the alternating group An, the class C of n- cycle, CC covers An for n when n = 4k + 1 > 5 and odd. This class splits into two classes of An denoted by C and C/, CC= C/C/ was found.
One of the unique properties of laser heating applications is its powerful ability for precise pouring of energy on the needed regions in heat treatment applications. The rapid rise in temperature at the irradiated region produces a high temperature gradient, which contributes in phase metallurgical changes, inside the volume of the irradiated material. This article presents a comprehensive numerical work for a model based on experimentally laser heated AISI 1110 steel samples. The numerical investigation is based on the finite element method (FEM) taking in consideration the temperature dependent material properties to predict the temperature distribution within the irradiated material volume. The finite element analysis (FEA) was carried
... Show MoreAn efficient modification and a novel technique combining the homotopy concept with Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced in this paper . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.
The discussion in this paper gives several theorems and lemmas on the Sums of Squares of consecutive Carol Numbers. These theorems are proved by using the definition of carol numbers and mathematical induction method. Here the matrix form and the recursive form of sum of squares of consecutive Carol numbers is also given. The properties of the Carol numbers are also derived.
The rotor dynamics generally deals with vibration of rotating structures. For designing rotors of a high speeds, basically its important to take into account the rotor dynamics characteristics. The modeling features for rotor and bearings support flexibility are described in this paper, by taking these characteristics of rotor dynamics features into standard Finite Element Approach (FEA) model. Transient and harmonic analysis procedures have been found by ANSYS, the idea has been presented to deal with critical speed calculation. This papers shows how elements BEAM188 and COMBI214 are used to represent the shaft and bearings, the dynamic stiffness and damping coefficients of journal bearings as a matrices have been found
... Show MoreThis paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient