Search results for: finite%20difference%20method

Authors: Mohamed S. El-Asfoury, Ahmed Abdel-Moneim, Mohamed N. A. Nasr

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The current study uses finite element modeling to investigate and analyze a modified form of the from the conventional equal channel multi-angular pressing (ECMAP), using non-equal channels, on the workpiece material plastic deformation. The modified process non-equal channel multi-angular extrusion (NECMAE) is modeled using two-dimensional plane strain finite element model built using the commercial software ABAQUS. The workpiece material used is pure aluminum. The model was first validated by comparing its results to analytical solutions for single-pass equal channel angular extrusion (ECAP), as well as previously published data. After that, the model was used to examine the effects of different % of reductions of the area (for the second stage) on material plastic deformation, corner gap, and required the load. Three levels of reduction in the area were modeled; 10%, 30%, and 50%, and compared to single-pass and double-pass ECAP. Cases with a higher reduction in the area were found to have smaller corner gaps, higher and much uniform plastic deformation, as well as higher required loads. The current results are mainly attributed to the back pressure effects exerted by the second stage, as well as strain hardening effects experienced during the first stage.

Keywords: non-equal channel angular extrusion, multi-pass, sever plastic deformation, back pressure, Finite Element Modelling (FEM)

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Authors: Haoui Rabah

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The aim of this work is to analyze a viscous flow around the axisymmetric blunt body taken into account the mesh size both in the free stream and into the boundary layer. The resolution of the Navier-Stokes equations is realized by using the finite volume method to determine the flow parameters and detached shock position. The numerical technique uses the Flux Vector Splitting method of Van Leer. Here, adequate time stepping parameter, CFL coefficient and mesh size level are selected to ensure numerical convergence. The effect of the mesh size is significant on the shear stress and velocity profile. The best solution is obtained with using a very fine grid. This study enabled us to confirm that the determination of boundary layer thickness can be obtained only if the size of the mesh is lower than a certain value limits given by our calculations.

Keywords: supersonic flow, viscous flow, finite volume, blunt body

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Authors: H. Samadiyeh, R. Khajavi

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A new FD-based procedure, modal finite difference method (MFDM), is proposed for seismic wave propagation modeling, in which simulation is dealt with in the modal space. The method employs eigenvalues of a characteristic matrix formed by appropriate time-space FD stencils. Since MFD runs for different modes are totally independent of each other, MFDM can easily be parallelized while considerable simplicity in parallel-algorithm is also achieved. There is no requirement to any domain-decomposition procedure and inter-core data exchange. More important is the possibility to skip processing of less-significant modes, which enables one to adjust the procedure up to the level of accuracy needed. Thus, in addition to considerable ease of parallel programming, computation and storage costs are significantly reduced. The method is qualified for its efficiency by some numerical examples.

Keywords: Finite Difference Method, Graphics Processing Unit (GPU), Message Passing Interface (MPI), Modal, Wave propagation

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Authors: Nan Tang, Bin Wu, Cunfu He

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The trapezoid rods are widely used in civil engineering as load –carrying members. Ultrasonic guided wave is one of the most popular techniques in analyzing the propagation of elastic guided wave. The goal of this paper is to investigate the propagation of elastic waves in the isotropic bar with trapezoid cross-section. Dispersion curves that describe the relationship between the frequency and velocity provide the fundamental information to describe the propagation of elastic waves through a structure. Based on the SAFE (semi-analytical finite element) a linear algebraic system of equations is obtained. By using numerical methods, dispersion curves solved for the rods with the trapezoid cross-section. These fundamental information plays an important role in applying ultrasonic guided waves to NTD for structures with trapezoid cross section.

Keywords: guided wave, dispersion, finite element method, trapezoid rod

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Authors: Haw-Long Lee, Win-Jin Chang, Yu-Ching Yang

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In this study, we use the atomic-scale finite element method to investigate the vibrational behavior of the armchair- and zigzag-structured nanoporous graphene layers with different size under the SFSF and CFFF boundary conditions. The fundamental frequencies computed for the graphene layers without pore are compared with the results of previous studies. We observe very good correspondence of our results with that of the other studies in all the considered cases. For the armchair- and zigzag-structured nanoporous graphene layers under the SFSF and CFFF boundary conditions, the frequencies decrease as the size of the nanopore increase. When the positions of the pore are symmetric with respect to the center of the graphene, the frequency of the zigzag pore graphene is higher than that of the armchair one.

Keywords: atomic-scale finite element method, graphene, nanoporous, natural frequency

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Authors: Ismail Cengiz, Faruk Elaldi

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Within the scope of the study presented in this paper, load carrying capacity and buckling behavior of a stiffened aluminum panel designed by adopting current ‘buckle-resistant’ design application and ‘Post –Buckling’ design approach were investigated experimentally and numerically. The test specimen that is stabilized by Z-type stiffeners and manufactured from aluminum 2024 T3 Clad material was test under compression load. Buckling behavior was observed by means of 3 – dimensional digital image correlation (DIC) and strain gauge pairs. The experimental study was followed by developing an efficient and reliable finite element model whose ability to predict behavior of the stiffened panel used for compression test is verified by compering experimental and numerical results in terms of load – shortening curve, strain-load curves and buckling mode shapes. While finite element model was being constructed, non-linear behaviors associated with material and geometry was considered. Finally, applicability of aluminum stiffened panel in airframe design against to composite structures was evaluated thorough the concept of ‘Structural Efficiency’. This study reveals that considerable amount of weight saving could be gained if the concept of ‘post-buckling design’ is preferred to the already conventionally used ‘buckle resistant design’ concept in aircraft industry without scarifying any of structural integrity under load spectrum.

Keywords: post-buckling, stiffened panel, non-linear finite element method, aluminum, structural efficiency

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Authors: Hyeongbok Kim, Lingling Zhao, Xiaohong Su, Junjie Wang

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The Bernoulli filter is a precise Bayesian filter for single target tracking based on the random finite set theory. The standard Bernoulli filter often underestimates the number of targets. This study proposes a Gaussian particle flow (GPF) Bernoulli filter employing particle flow to migrate particles from prior to posterior positions to improve the performance of the standard Bernoulli filter. By employing the particle flow filter, the computational speed of the Bernoulli filters is significantly improved. In addition, the GPF Bernoulli filter provides a more accurate estimation compared with that of the standard Bernoulli filter. Simulation results confirm the improved tracking performance and computational speed in two- and three-dimensional scenarios compared with other algorithms.

Keywords: Bernoulli filter, particle filter, particle flow filter, random finite sets, target tracking

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Authors: Yu Luan

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The bone-conducted objective occlusion effect (OE) is characterized by a discomforting sensation of fullness experienced in an occluded ear. This phenomenon arises from various external stimuli, such as human speech, chewing, and walking, which generate vibrations transmitted through the body to the ear canal walls. The bone-conducted OE occurs due to the pressure build-up inside the occluded ear caused by sound radiating into the ear canal cavity from its walls. In the hearing aid industry, artificial ears are utilized as a tool for developing hearing aids. However, the currently available commercial artificial ears primarily focus on pure acoustics measurements, neglecting the bone-conducted vibration aspect. This research endeavors to develop an artificial ear specifically designed for bone-conducted occlusion measurements. Finite element analysis (FEA) modeling has been employed to gain insights into the behavior of the artificial ear.

Keywords: artificial ear, bone conducted vibration, occlusion measurement, finite element modeling

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Authors: Khoa Tan Nguyen, Tuan Anh Le, Kihak Lee

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This paper presents the flexural response of Reinforced Geopolymer Concrete (RGPC) beams. A commercial finite element (FE) software ABAQUS has been used to perform a structural behavior of RGPC beams. Using parameters such: stress, strain, Young’s modulus, and Poisson’s ratio obtained from experimental results, a beam model has been simulated in ABAQUS. The results from experimental tests and ABAQUS simulation were compared. Due to friction forces at the supports and loading rollers; slip occurring, the actual deflection of RGPC beam from experimental test results were slightly different from the results of ABAQUS. And there is good agreement between the crack patterns of fly ash-based geopolymer concrete generated by FE analysis using ABAQUS, and those in experimental data.

Keywords: geopolymer concrete beam, finite element mehod, stress strain relation, modulus elasticity

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Authors: Mohamed Mohamed, Philip Bonello, Peter Russhard

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Blade Tip Timing (BTT) is a technology concerned with the estimation of both frequency and amplitude of rotating blades. A BTT system comprises two main parts: (a) the arrival time measurement system, and (b) the analysis algorithms. Simulators play an important role in the development of the analysis algorithms since they generate blade tip displacement data from the simulated blade vibration under controlled conditions. This enables an assessment of the performance of the different algorithms with respect to their ability to accurately reproduce the original simulated vibration. Such an assessment is usually not possible with real engine data since there is no practical alternative to BTT for blade vibration measurement. Most simulators used in the literature are based on a simple spring-mass-damper model to determine the vibration. In this work, a more realistic experimentally validated simulator based on the Finite Element (FE) model of a bladed disc (blisk) is first presented. It is then used to generate the necessary data for the assessment of different BTT algorithms. The FE modelling is validated using both a hammer test and two firewire cameras for the mode shapes. A number of autoregressive methods, fitting methods and state-of-the-art inverse methods (i.e. Russhard) are compared. All methods are compared with respect to both synchronous and asynchronous excitations with both single and simultaneous frequencies. The study assesses the applicability of each method for different conditions of vibration, amount of sampling data, and testing facilities, according to its performance and efficiency under these conditions.

Keywords: blade tip timing, blisk, finite element, vibration measurement

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Authors: Javid Iqbal, Zhu Shifan

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The development in the construction of unconventional ships and the implementation of lightweight materials have shown a large impulse towards finite element (FE) method, making it a general tool for ship design. This paper briefly presents the modeling and analysis techniques of ship structures using FE method for complex boundary conditions which are difficult to analyze by existing Ship Classification Societies rules. During operation, all ships experience complex loading conditions. These loads are general categories into thermal loads, linear static, dynamic and non-linear loads. General strength of the ship structure is analyzed using static FE analysis. FE method is also suitable to consider the local loads generated by ballast tanks and cargo in addition to hydrostatic and hydrodynamic loads. Vibration analysis of a ship structure and its components can be performed using FE method which helps in obtaining the dynamic stability of the ship. FE method has developed better techniques for calculation of natural frequencies and different mode shapes of ship structure to avoid resonance both globally and locally. There is a lot of development towards the ideal design in ship industry over the past few years for solving complex engineering problems by employing the data stored in the FE model. This paper provides an overview of ship modeling methodology for FE analysis and its general application. Historical background, the basic concept of FE, advantages, and disadvantages of FE analysis are also reported along with examples related to hull strength and structural components.

Keywords: dynamic analysis, finite element methods, ship structure, vibration analysis

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Authors: Mahtab Makaremi Masouleh, Günter Wozniak

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This work is part of a major research project concerning the design of a light temporary installable textile flood control structure. The motivation for this work is the great need of applying light structures for the protection of coastal areas from detrimental effects of rapid water runoff. The prime objective of the study is the numerical analysis of the interaction among free surface water flow and slender shaped pliable structures, playing a key role in safety performance of the intended system. First, the behavior of down scale membrane is examined under hydrostatic pressure by the Abaqus explicit solver, which is part of the finite element based commercially available SIMULIA software. Then the procedure to achieve a stable and convergent solution for strongly coupled media including fluids and structures is explained. A partitioned strategy is imposed to make both structures and fluids be discretized and solved with appropriate formulations and solvers. In this regard, finite element method is again selected to analyze the structural domain. Moreover, computational fluid dynamics algorithms are introduced for solutions in flow domains by means of a commercial package of Star CCM+. Likewise, SIMULIA co-simulation engine and an implicit coupling algorithm, which are available communication tools in commercial package of the Star CCM+, enable powerful transmission of data between two applied codes. This approach is discussed for two different cases and compared with available experimental records. In one case, the down scale membrane interacts with open channel flow, where the flow velocity increases with time. The second case illustrates, how the full scale flexible flood barrier behaves when a massive flotsam is accelerated towards it.

Keywords: finite element formulation, finite volume algorithm, fluid-structure interaction, light pliable structure, VOF multiphase model

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Authors: Alireza Lohrasbi, Alireza Lavaei, Mohammadali M. Shahlaei

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The liquid flow and the free surface shape during the initial stage of dam breaking are investigated. A numerical scheme is developed to predict the wave of an unsteady, incompressible viscous flow with free surface. The method involves a two dimensional finite element (2D), in a vertical plan. The Naiver-Stokes equations for conservation of momentum and mass for Newtonian fluids, continuity equation, and full nonlinear kinematic free-surface equation were used as the governing equations. The mapping developed to solve highly deformed free surface problems common in waves formed during wave propagation, transforms the run up model from the physical domain to a computational domain with Arbitrary Lagrangian Eulerian (ALE) finite element modeling technique.

Keywords: dam break, Naiver-Stokes equations, free-surface flows, Arbitrary Lagrangian-Eulerian

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Authors: Sabrina Nouri, Abderahmane Ghezal, Said Abboudi, Pierre Spiteri

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This paper deals with the numerical study of heat and mass transfer of laminar flow transition at low Prandtl numbers. The model includes the two-directional momentum, the energy and mass transfer equations. These equations are discretized by the finite volume method and solved by a self-made simpler like Fortran code. The effect of governing parameters, namely the Lewis and Prandtl numbers, on the transition of the flow and solute distribution is studied for positive and negative thermal and solutal buoyancy forces ratio. Nusselt and Sherwood numbers are derived for of Prandtl [10⁻²-10¹] and Lewis numbers [1-10⁴]. The results show unicell and multi-cell flow. Solute and flow boundary layers appear for low Prandtl number.

Keywords: natural convection, low Prandtl number, heat and mass transfer, finite volume method

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Authors: Güneş Aydın, Razi Kalantari Osgouei, Murat Emre Öztürk, Ahmad Partovi Meran, Ekrem Tüfekçi

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Advanced lightweight laminated composite shells are increasingly being used in all types of modern structures, for enhancing their structural efficiency and performance. Such thin-walled structures are susceptible to buckling when subjected to various loading. This paper focuses on the buckling of cylindrical shells under axial compression and torsional loads. Effects of fiber orientation on the maximum buckling load of carbon fiber reinforced polymer (CFRP) shells are optimized. Optimum fiber angles have been calculated analytically by using MATLAB program. Numerical models have been carried out by using Finite Element Method program ABAQUS. Results from analytical and numerical analyses are also compared.

Keywords: buckling, composite, cylindrical shell, finite element, compression, torsion, MATLAB, optimization

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Authors: Surita Maini

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There are many perceived advantages of microwave ablation have driven researchers to develop innovative antennas to effectively treat deep-seated, non-resectable hepatic tumors. In this paper a coaxial antenna with a miniaturized sleeve choke has been discussed for microwave interstitial ablation therapy, in order to reduce backward heating effects irrespective of the insertion depth into the tissue. Two dimensional Finite Element Method (FEM) is used to simulate and measure the results of miniaturized sleeve choke antenna. This paper emphasizes the importance of factors that can affect simulation accuracy, which include mesh resolution, surface heating and reflection coefficient. Quarter wavelength choke effectiveness has been discussed by comparing it with the unchoked antenna with same dimensions.

Keywords: microwave ablation, tumor, finite element method, coaxial slot antenna, coaxial dipole antenna

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Authors: Mahmoud Y. Shokry, Rami M. El-Sherbiny

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This paper aims to highlight the role of some parameters that may be of a noticeable impact on numerical analysis/design of embankments. It presents the results of a three-dimensional (3-D) finite element analysis of a monitored earth embankment that was constructed on soft clay formation stabilized by cast in-situ piles using software PLAXIS 3D. A comparison between the predicted and the monitored responses is presented to assess the adequacy of the adopted numerical model. The model was used in the targeted parametric study. Moreover, a comparison was performed between the results of the 3-D analyses and the analytical solutions. This paper concluded that the effect of using mono pile caps led to decrease both the total and differential settlement and increased the efficiency of the piled embankment system. The study of using geogrids revealed that it can contribute in decreasing the settlement and maximizing the part of the embankment load transferred to piles. Moreover, it was found that increasing the stiffness of the geogrids provides higher values of tensile forces and hence has more effective influence on embankment load carried by piles rather than using multi-number of layers with low values of geogrid stiffness. The efficiency of the piled embankments system was also found to be greater when higher embankments are used rather than the low height embankments. The comparison between the numerical 3-D model and the theoretical design methods revealed that many analytical solutions are conservative and non-accurate rather than the 3-D finite element numerical models.

Keywords: efficiency, embankment, geogrids, soft clay

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Authors: Tunahan Sapmaz, Harun Etçi, İbrahim Şenol, Yasemin Öner

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Rotor bar dimensions have a great influence on the air-gap magnetic flux density. Therefore, poor selection of this parameter during the machine design phase causes the air-gap magnetic flux density to be distorted. Thus, it causes noise, torque fluctuation, and losses in the induction motor. On the other hand, the change in rotor bar dimensions will change the resistance of the conductor, so the current will be affected. Therefore, the increase and decrease of rotor bar current affect operation, starting torque, and efficiency. The aim of this study is to examine the effect of rotor bar dimensions on the electromagnetic performance criteria of the induction motor. Modeling of the induction motor is done by the finite element method (FEM), which is a very powerful tool. In FEM, the results generally focus on performance criteria such as torque, torque fluctuation, efficiency, and current.

Keywords: induction motor, finite element method, optimization, rotor bar

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Authors: David Rafetseder, Walter Bauer, Florian Poltschak, Wolfgang Amrhein

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A flat double-stator linear induction machine (DSLIM) with a short squirrel-cage mover is designed for high thrust force at moderate speed < 5m/s. The performance and motor parameters are determined on the basis of a 2D time-transient simulation with the finite element (FE) software Maxwell 2015. Design guidelines and transformation rules for space vector theory of the LIM are presented. Resulting thrust calculated by flux and current vectors is compared with the FE results showing good coherence and reduced noise. The parameters of the equivalent circuit model are obtained.

Keywords: equivalent circuit model, finite element model, linear induction motor, space vector theory

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Authors: S. Yunus, A. Suratman, N. Mohamad Nor, M. Othman

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This paper presents the measurement and simulation results by Finite Element Method (FEM) for earth resistance (R_DC) for interconnected vertical ground rod configurations. The soil resistivity was measured using the Wenner four-pin Method, and R_DC was measured using the Fall of Potential (FOP) method, as outlined in the standard. Genetic Algorithm (GA) is employed to interpret the soil resistivity to that of a 2-layer soil model. The same soil resistivity data that were obtained by Wenner four-pin method were used in FEM for simulation. This paper compares the results of R_DC obtained by FEM simulation with the real measurement at field site. A good agreement was seen for R_DC obtained by measurements and FEM. This shows that FEM is a reliable software to be used for design of earthing systems. It is also found that the parallel rod system has a better performance compared to a similar setup using a grid layout.

Keywords: earthing system, earth electrodes, finite element method, genetic algorithm, earth resistances

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Authors: V. T. Ngo, D. M. Xie

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Frequently, in the design of machines, some of parameters that directly affect the rotor dynamics of the machines are not accurately known. In particular, bearing stiffness support is one such parameter. One of the most basic principles to grasp in rotor dynamics is the influence of the bearing stiffness on the critical speeds and mode shapes associated with a rotor-bearing system. Taking a rig shafting as an example, this paper studies the lateral vibration of the rotor with multi-degree-of-freedom by using Finite Element Method (FEM). The FEM model is created and the eigenvalues and eigenvectors are calculated and analyzed to find natural frequencies, critical speeds, mode shapes. Then critical speeds and mode shapes are analyzed by set bearing stiffness changes. The model permitted to identify the critical speeds and bearings that have an important influence on the vibration behavior.

Keywords: lateral vibration, finite element method, rig shafting, critical speed

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Authors: Kyu Chul Lee, Sung Hyun Yoo, Choon Ki Ahn, Myo Taeg Lim

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Recent experimental evidences have shown that because of a fast convergence and a nice accuracy, neural networks training via extended Kalman filter (EKF) method is widely applied. However, as to an uncertainty of the system dynamics or modeling error, the performance of the method is unreliable. In order to overcome this problem in this paper, a new finite impulse response (FIR) filter based learning algorithm is proposed to train radial basis function neural networks (RBFN) for nonlinear function approximation. Compared to the EKF training method, the proposed FIR filter training method is more robust to those environmental conditions. Furthermore, the number of centers will be considered since it affects the performance of approximation.

Keywords: extended Kalman filter, classification problem, radial basis function networks (RBFN), finite impulse response (FIR) filter

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Authors: Sultan Al Shafian, Mozaher Ul Kabir, Khondoker Istiak Ahmad, Masnun Abrar, Mahfuza Khanum, Hossain M. Shahin

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For structural evaluation of shallow foundation, the modulus of subgrade reaction is one of the most widely used and accepted parameter for its ease of calculations. To determine this parameter, one of the most common field method is Plate Load test method. In this field test method, the subgrade modulus is considered for a specific location and according to its application, it is assumed that the displacement occurred in one place does not affect other adjacent locations. For this kind of assumptions, the modulus of subgrade reaction sometimes forced the engineers to overdesign the underground structure, which eventually results in increasing the cost of the construction and sometimes failure of the structure. In the present study, the settlement of a shallow foundation has been analyzed using both conventional and numerical analysis. Around 25 plate load tests were conducted on a sand fill site in Bangladesh to determine the Modulus of Subgrade reaction of ground which is later used to design a shallow foundation considering different depth. After the collection of the field data, the field condition was appropriately simulated in a finite element software. Finally results obtained from both the conventional and numerical approach has been compared. A significant difference has been observed in the case of settlement while comparing the results. A proper correlation has also been proposed at the end of this research work between the two methods of in order to provide the most efficient way to calculate the subgrade modulus of the ground for designing the shallow foundation.

Keywords: modulus of subgrade reaction, shallow foundation, finite element analysis, settlement, plate load test

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Authors: Shady Sayed, Samer Wagdy, Ahmed Badawy, Moutaz M. Hegaze

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A symmetrical single mass resonant gyroscope is discussed in this paper. The symmetrical design allows matched resonant frequencies for driving and sensing vibration modes, which leads to amplifying the sensitivity of the gyroscope by the mechanical quality factor of the sense mode. It also achieves decoupled vibration modes for getting a low zero-rate output shift and more stable operation environment. A new suspension beams design is developed to get a symmetrical gyroscope with matched and decoupled modes at the same time. Finite element simulations are performed using ANSYS software package to verify the theoretical calculations. The gyroscope is fabricated from aluminum alloy 2024 substrate, the measured drive and sense resonant frequencies of the fabricated model are matched and equal 81.4 Hz with 5.7% error from the simulation results.

Keywords: decoupled mode shapes, resonant sensor, symmetrical gyroscope, finite element simulation

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Authors: Ayesha Sohail, Khadija Maqbool, Anila Asif, Haroon Ahmad

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The field of tissue engineering is an active area of research. Bone tissue engineering helps to resolve the clinical problems of critical size and non-healing defects by the creation of man-made bone tissue. We will design and validate an efficient numerical model, which will simulate the effective diffusivity in bone tissue engineering. Our numerical model will be based on the finite element analysis of the diffusion-reaction equations. It will have the ability to optimize the diffusivity, even at multi-scale, with the variation of time. It will also have a special feature, with which we will not only be able to predict the oxygen, glucose and cell density dynamics, more accurately, but will also sort the issues arising due to anisotropy. We will fix these problems with the help of modifying the governing equations, by selecting appropriate spatio-temporal finite element schemes, by adaptive grid refinement strategy and by transient analysis.

Keywords: scaffolds, porosity, diffusion, transient analysis

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Authors: S. Kumar, Rajesh Kumar, S. Mandal

Abstract:

Fiber Reinforced Polymer (FRP) is gaining popularity in many branch of engineering and various applications due to their light weight, specific strength per unit weight and high stiffness in particular direction. As the strength of material is high it can be used in thin walled structure as industrial roof sheds satisfying the strength constraint with comparatively lesser thickness. Analysis of bending behavior of FRP panel has been done here with variation in oriented angle of stiffener panels, fiber orientation, aspect ratio and boundary conditions subjected to transverse loading by using Finite Element Method. The effect of fiber orientation and thickness of ply has also been studied to determine the minimum thickness of ply for optimized section of stiffened FRP panel.

Keywords: bending behavior, fiber reinforced polymer, finite element method, orientation of stiffeners

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Authors: Rabah Haoui

Abstract:

Hypersonic flows around spatial vehicles during their reentry phase in planetary atmospheres are characterized by intense aerothermodynamics phenomena. The aim of this work is to analyze high temperature flows around an axisymmetric blunt body taking into account chemical and vibrational non-equilibrium for air mixture species and the no slip condition at the wall. For this purpose, the Navier-Stokes equations system is resolved by the finite volume methodology to determine the flow parameters around the axisymmetric blunt body especially at the stagnation point and in the boundary layer along the wall of the blunt body. The code allows the capture of shock wave before a blunt body placed in hypersonic free stream. The numerical technique uses the Flux Vector Splitting method of Van Leer. CFL coefficient and mesh size level are selected to ensure the numerical convergence.

Keywords: hypersonic flow, viscous flow, chemical kinetic, dissociation, finite volumes, frozen and non-equilibrium flow

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Authors: Atousa Ataieyan, Salvador A. Gomez-Lopera, Gennaro Sepede

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Today, due to the growing urban population and consequently, the increasing water demand in cities, the amount of contaminants entering the water resources is increasing. This can impose harmful effects on the quality of the downstream water. Therefore, predicting the concentration of discharged pollutants at different times and distances of the interested area is of high importance in order to carry out preventative and controlling measures, as well as to avoid consuming the contaminated water. In this paper, the concentration distribution of an injected conservative pollutant in a square reservoir containing four symmetric blocks and three sources using Finite Volume Method (FVM) is simulated. For this purpose, after estimating the flow velocity, classical Advection-Diffusion Equation (ADE) has been discretized over the studying domain by Backward Time- Backward Space (BTBS) scheme. Then, the discretized equations for each node have been derived according to the initial condition, boundary conditions and point contaminant sources. Finally, taking into account the appropriate time step and space step, a computational code was set up in MATLAB. Contaminant concentration was then obtained at different times and distances. Simulation results show how using BTBS differentiating scheme and FVM as a numerical method for solving the partial differential equation of transport is an appropriate approach in the case of two-dimensional contaminant transfer in an advective-diffusive flow.

Keywords: BTBS differentiating scheme, contaminant concentration, finite volume, mass transfer, water pollution

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Authors: Saghar Heidari

Abstract:

In this paper, we study the valuation problem of European continuous-installment options under Markov-modulated models with a partial differential equation approach. Due to the opportunity for continuing or stopping to pay installments, the valuation problem under regime-switching models can be formulated as coupled partial differential equations (CPDE) with free boundary features. To value the installment options, we express the truncated CPDE as a linear complementarity problem (LCP), then a finite element method is proposed to solve the resulted variational inequality. Under some appropriate assumptions, we establish the stability of the method and illustrate some numerical results to examine the rate of convergence and accuracy of the proposed method for the pricing problem under the regime-switching model.

Keywords: continuous-installment option, European option, regime-switching model, finite element method

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Authors: Falek Kamel

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Free vibration analysis of beams, based on the assumptions of Bernoulli-Euler theory, has been extensively studied. Many research works have focused on the study of transverse vibrations under the application of different boundary conditions where different theories have been applied. The stiffness and mass matrices considered are those obtained by assembling those resulting from the use of the finite element method. The Jacobi method has been used to solve the eigenvalue problem. These well-known concepts have been applied to the study of beams with constant geometric and mechanical characteristics having one to two overhangs with variable lengths. Murphy studied, by an algebraic solution approach, a simply supported beam with two overhangs of arbitrary length, allowing for an experimental determination of the elastic modulus E. The advantage of our article is that it offers the possibility of extending this approach to many interesting problems formed by transversely vibrating beams with various end constraints.

Keywords: beam, finite element, transverse vibrations, end restreint, Bernoulli-Euler theory

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