Search results for: finite difference

Authors: Yasser El-Henawy, M. Abd El-Kader, Gamal H. Moustafa

Abstract:

A theoretical study of a humidification dehumidification solar desalination unit has been carried out to increase understanding the effect of weather conditions on the unit productivity. A humidification-dehumidification (HD) solar desalination unit has been designed to provide fresh water for population in remote arid areas. It consists of solar water collector and air collector; to provide the hot water and air to the desalination chamber. The desalination chamber is divided into humidification and dehumidification towers. The circulation of air between the two towers is maintained by the forced convection. A mathematical model has been formulated, in which the thermodynamic relations were used to study the flow, heat and mass transfer inside the humidifier and dehumidifier. The present technique is performed in order to increase the unit performance. Heat and mass balance has been done and a set of governing equations has been solved using the finite difference technique. The unit productivity has been calculated along the working day during the summer and winter sessions and has compared with the available experimental results. The average accumulative productivity of the system in winter has been ranged between 2.5 to 4 kg/m2.day, while the average summer productivity has been found between 8 to 12 kg/m2 day.

Keywords: solar desalination, solar collector, humidification and dehumidification, simulation, finite difference, water productivity

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Authors: Momoh Omeiza Sheidu

Abstract:

Finite element method as a method of providing solutions to problems in computational bio mechanics provides a framework for modeling the function of tissues that integrates structurally from cell to organ system and functionally across the physiological processes that affect tissue mechanics or are regulated by mechanical forces. In this paper, we present an integrative finite element strategy for solution to problems in tissue bio mechanics as a case study.

Keywords: finite element, biomechanics, modeling, computational biomechanics

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Authors: Najibullah M, Soumendra Nath Kuiry

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Dams and reservoirs are perceived for their estimable alms to irrigation, water supply, flood control, electricity generation, etc. which civilize the prosperity and wealth of society across the world. Meantime the dam breach could cause devastating flood that can threat to the human lives and properties. Failures of large dams remain fortunately very seldom events. Nevertheless, a number of occurrences have been recorded in the world, corresponding in an average to one to two failures worldwide every year. Some of those accidents have caused catastrophic consequences. So it is decisive to predict the dam break flow for emergency planning and preparedness, as it poses high risk to life and property. To mitigate the adverse impact of dam break, modeling is necessary to gain a good understanding of the temporal and spatial evolution of the dam-break floods. This study will mainly deal with one-dimensional (1D) dam break modeling. Less commonly used in the hydraulic research community, another possible option for modeling the rapidly varied dam-break flows is the extended Boussinesq equations (BEs), which can describe the dynamics of short waves with a reasonable accuracy. Unlike the Shallow Water Equations (SWEs), the BEs taken into account the wave dispersion and non-hydrostatic pressure distribution. To capture the dam-break oscillations accurately it is very much needed of at least fourth-order accurate numerical scheme to discretize the third-order dispersion terms present in the extended BEs. The scope of this work is therefore to develop an 1D fourth-order accurate in both space and time Boussinesq model for dam-break flow analysis by using finite-volume / finite difference scheme. The spatial discretization of the flux and dispersion terms achieved through a combination of finite-volume and finite difference approximations. The flux term, was solved using a finite-volume discretization whereas the bed source and dispersion term, were discretized using centered finite-difference scheme. Time integration achieved in two stages, namely the third-order Adams Basforth predictor stage and the fourth-order Adams Moulton corrector stage. Implementation of the 1D Boussinesq model done using PYTHON 2.7.5. Evaluation of the performance of the developed model predicted as compared with the volume of fluid (VOF) based commercial model ANSYS-CFX. The developed model is used to analyze the risk of cascading dam failures similar to the Panshet dam failure in 1961 that took place in Pune, India. Nevertheless, this model can be used to predict wave overtopping accurately compared to shallow water models for designing coastal protection structures.

Keywords: Boussinesq equation, Coastal protection, Dam-break flow, One-dimensional model

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Authors: H. Bensouilah, H. Boucherit, M. Lahmar

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A theoretical investigation on the effects of both steady-state and dynamic deformations of the foils on the dynamic performance characteristics of a self-acting air foil journal bearing operating under small harmonic vibrations is proposed. To take into account the dynamic deformations of foils, the perturbation method is used for determining the gas-film stiffness and damping coefficients for given values of excitation frequency, compressibility number, and compliance factor of the bump foil. The nonlinear stationary Reynolds’ equation is solved by means of the Galerkins’ finite element formulation while the finite differences method are used to solve the first order complex dynamic equations resulting from the perturbation of the nonlinear transient compressible Reynolds’ equation. The stiffness of a bump is uniformly distributed throughout the bearing surface (generation I bearing). It was found that the dynamic properties of the compliant finite length journal bearing are significantly affected by the compliance of foils especially when the dynamic deformation of foils is considered in addition to the static one by applying the principle of superposition.

Keywords: elasto-aerodynamic lubrication, air foil bearing, steady-state deformation, dynamic deformation, stiffness and damping coefficients, perturbation method, fluid-structure interaction, Galerk infinite element method, finite difference method

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Authors: Bang-Fuh Chen, Chih-Chun Chu

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The flow induced cylinder vibration or earthquake-induced cylinder motion are moving in an arbitrary direction with time. The phenomenon of flow across cylinder is highly nonlinear and a linear-superposition of flow pattern across separated oscillating direction of cylinder motion is not valid to obtain the flow pattern across a cylinder oscillating in multiple directions. A novel finite difference scheme is developed to simulate the viscous flow across an arbitrary moving circular cylinder and we call this a complete 2D (two-dimensional) flow-cylinder interaction. That is, the cylinder is simultaneously oscillating in x- and y- directions. The time-dependent domain and meshes associated with the moving cylinder are mapped to a fixed computational domain and meshes, which are time independent. The numerical results are validated by several bench mark studies. Several examples are introduced including flow across steam-wise, transverse oscillating cylinder and flow across rotating cylinder and flow across arbitrary moving cylinder. The Morison’s formula can not describe the complex interaction phenomenon between cross flow and oscillating circular cylinder. And the completed 2D computational fluid dynamic analysis should be made to obtain the correct hydrodynamic force acting on the cylinder.

Keywords: 2D cylinder, finite-difference method, flow-cylinder interaction, flow induced vibration

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Authors: Chih-Hsien Chen, Yi-Hung Ho, Chih-Wei Wang, Chih-Wei Chang, Yen-Nien Chen, Chih-Han Chang, Chun-Ting Li

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Laminotomy is a spinal decompression surgery compatible with a minimally invasive approach. However, the unilateral laminotomy for bilateral side decompression leads to more perioperative complications than the bilateral laminotomy. Although the unilateral laminotomy removes the least bone tissue among the spinal decompression surgeries, the difference of spinal stability between unilateral and bilateral laminotomy and laminectomy is rarely investigated. This study aims to compare the biomechanical effects of unilateral and bilateral laminotomy and laminectomy on the lumbar spine by finite element (FE) simulation. A three-dimensional FE model of the lumbar spine (L1–L5) was constructed with the vertebral body, discs, and ligaments, as well as the sacrum was constructed. Three different surgical methods, namely unilateral laminotomy, bilateral laminotomy and laminectomy, at L3–L4 and L4–L5 were considered. Partial pedicle and entire ligamentum flavum were removed to simulate bilateral decompression in laminotomy. The entire lamina and spinal processes from the lower L3 to upper L5 were detached in the laminectomy model. Then, four kinds of loadings, namely flexion, extension, lateral bending and rotation, were applied on the lumbar with various decompression conditions. The results indicated that the bilateral and unilateral laminotomy both increased the range of motion (ROM) compared with intact lumbar, while the laminectomy increased more ROM than both laminotomy did. The difference of ROM between the bilateral and unilateral laminotomy was very minor. Furthermore, bilateral laminotomy demonstrated similar poster element stress with unilateral laminotomy. Unilateral and bilateral laminotomy are equally suggested to bilateral decompression of lumbar spine with minimally invasive technique because limited effect was aroused due to more bone remove in the bilateral laminotomy on the lumbar stability. Furthermore, laminectomy is the last option for lumbar decompression.

Keywords: minimally invasive technique, lumbar decompression, laminotomy, laminectomy, finite element method

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Authors: Swati Sharma, R. P. Sharma

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We intend to study the nonlinear evolution of the parallel propagating finite frequency Alfvén wave (also called Dispersive Alfvén wave/Hall MHD wave) propagating in the solar wind regime of the solar region when a perpendicularly propagating magnetosonic wave is present in the background. The finite frequency Alfvén wave behaves differently from the usual non-dispersive behavior of the Alfvén wave. To study the nonlinear processes (such as filamentation) taking place in the solar regions such as solar wind, the dynamical equation of both the waves are derived. Numerical simulation involving finite difference method for the time domain and pseudo spectral method for the spatial domain is then performed to analyze the transient evolution of these waves. The power spectra of the Dispersive Alfvén wave is also investigated. The power spectra shows the distribution of the magnetic field intensity of the Dispersive Alfvén wave over different wave numbers. For DAW the spectra shows a steepening for scales larger than the proton inertial length. This means that the wave energy gets transferred to the solar wind particles as the wave reaches higher wave numbers. This steepening of the power spectra can be explained on account of the finite frequency of the Alfvén wave. The obtained results are consistent with the observations made by CLUSTER spacecraft.

Keywords: solar wind, turbulence, dispersive alfven wave

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Authors: Dua K. S. Y. Klaas, Monzur A. Imteaz, Ika Sudiayem, Elkan M. E. Klaas, Eldav C. M. Klaas

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Due to its porous nature, karst terrains – geomorphologically developed from dissolved formations, is vulnerable to water shortage and deteriorated water quality. Therefore, a solid comprehension on sub-surface flow of karst landscape is essential to assess the long-term availability of groundwater resources. In this paper, a single-continuum model using a finite difference model, MODLFOW, was constructed to represent an unconfined carbonate aquifer in a tropical karst island of Rote in Indonesia. The model, spatially discretized in 20 x 20 m grid cells, was calibrated and validated using available groundwater level and atmospheric variables. In the calibration and validation steps, Parameter Estimation (PEST) and geostatistical pilot point methods were employed to estimate hydraulic conductivity and specific yield values. The results show that the model is able to represent the sub-surface flow indicated by good model performances both in calibration and validation steps. The final model can be used as a robust representation of the system for future study on climate and land use scenarios.

Keywords: carbonate aquifer, karst, sub-surface flow, groundwater model

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Authors: Abdulmajid Mukhtar Afat

Abstract:

This paper aims at introducing nondeterministic finite automata with ε value which is used to perform some operations on languages. a program is created to implement the algorithm that converts nondeterministic finite automata with ε value (ε-NFA) to deterministic finite automata (DFA).The program is written in c++ programming language. The program inputs are FA 5-tuples from text file and then classifies it into either DFA/NFA or ε -NFA. For DFA, the program will get the string w and decide whether it is accepted or rejected. The tracking path for an accepted string is saved by the program. In case of NFA or ε-NFA automation, the program changes the automation to DFA to enable tracking and to decide if the string w exists in the regular language or not.

Keywords: DFA, NFA, ε-NFA, eclose, finite automata, operations on languages

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Authors: M. Ömer Timurağaoğlu, Adem Doğangün, Ramazan Livaoğlu

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The evaluation of performance of infilled reinforced concrete (RC) frames has been a significant challenge for engineers. The strengthening of infill walls has been an important concern to enhance the behavior of RC infilled frames. The aim of this study is to investigate the behaviour of retrofitted infill walls of RC frames using finite element analysis. For this purpose, a one storey, one bay infilled and strengthened infilled RC frame which have the same geometry and material properties with the frames tested in laboratory are modelled using different analytical approaches. A fibrous material is used to strengthen infill walls and frame. As a consequence, the results of the finite element analysis were evaluated of whether these analytical approaches estimate the behavior or not. To model the infilled and strengthened infilled RC frames, a finite element program ABAQUS is used. Finally, data obtained from the nonlinear finite element analysis is compared with the experimental results.

Keywords: finite element analysis, infilled RC frames, infill wall, strengthening

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Authors: K. S. Chai, S. H. Chan

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In this paper, the earth retaining wall anchored by discrete deadman anchor to support excavations in sand is modelled and analysed by finite element analysis. A study is conducted to examine how deadman anchorage system helps in reducing the deflection of earth retaining wall. A simplified numerical model is suggested in order to reduce the simulation duration. A comparison between 3-D and 2-D finite element analyses is illustrated.

Keywords: finite element, earth retaining wall, deadman anchor, sand

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Authors: Gubhinder Kundhi, Paul Rilstone

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It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. Finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap.

Keywords: bootstrap, Instrumental Variable, Edgeworth expansions, Saddlepoint expansions

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Authors: Ž. Nikolić, H. Smoljanović, N. Živaljić

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This paper presents numerical model based on finite-discrete element method for analysis of the structural response of dry stone masonry structures under static and dynamic loads. More precisely, each discrete stone block is discretized by finite elements. Material non-linearity including fracture and fragmentation of discrete elements as well as cyclic behavior during dynamic load are considered through contact elements which are implemented within a finite element mesh. The application of the model was conducted on several examples of these structures. The performed analysis shows high accuracy of the numerical results in comparison with the experimental ones and demonstrates the potential of the finite-discrete element method for modelling of the response of dry stone masonry structures.

Keywords: dry stone masonry structures, dynamic load, finite-discrete element method, static load

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Authors: K. Noah, F.-S. Lien

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In Computational Fluid Dynamics (CFD), there are a variety of numerical methods, of which some depend on macroscopic model representatives. These models can be solved by finite-volume, finite-element or finite-difference methods on a microscopic description. However, the lattice Boltzmann method (LBM) is considered to be a mesoscopic particle method, with its scale lying between the macroscopic and microscopic scales. The LBM works well for solving incompressible flow problems, but certain limitations arise from solving compressible flows, particularly at high Mach numbers. An improved lattice Boltzmann model for compressible flow problems is presented in this research study. A higher-order Taylor series expansion of the Maxwell equilibrium distribution function is used to overcome limitations in LBM when solving high-Mach-number flows. Large eddy simulation (LES) is implemented in LBM to simulate turbulent jet flows. The results have been validated with available experimental data for turbulent compressible free jet flow at subsonic speeds.

Keywords: compressible lattice Boltzmann method, multiple relaxation times, large eddy simulation, turbulent jet flows

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Authors: Mehrnaz Alibeikloo, Hadi Khabbaz, Behzad Fatahi

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Probabilistic analysis has become one of the most popular methods to quantify and manage geotechnical risks due to the spatial variability of soil input parameters. The correlation length is one of the key factors of quantifying spatial variability of soil parameters which is defined as a distance within which the random variables are correlated strongly. This paper aims to assess the impact of correlation length on the long-term settlement of soft soils improved with preloading. The concept of 'worst-case' spatial correlation length was evaluated by determining the probability of failure of a real case study of Vasby test fill. For this purpose, a finite difference code was developed based on axisymmetric consolidation equations incorporating the non-linear elastic visco-plastic model and the Karhunen-Loeve expansion method. The results show that correlation length has a significant impact on the post-construction settlement of soft soils in a way that by increasing correlation length, probability of failure increases and the approach to asymptote.

Keywords: Karhunen-Loeve expansion, probability of failure, soft soil settlement, 'worst case' spatial correlation length

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Authors: Wu Di, Yeo Khoon Seng, Lim Tee Tai

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The typical insects employ a flapping-wing mode of flight. The numerical simulations on free flight of a model fruit fly (Re=143) including hovering and are presented in this paper. Unsteady aerodynamics around a flapping insect is studied by solving the three-dimensional Newtonian dynamics of the flyer coupled with Navier-Stokes equations. A hybrid-grid scheme (Generalized Finite Difference Method) that combines great geometry flexibility and accuracy of moving boundary definition is employed for obtaining flow dynamics. The results show good points of agreement and consistency with the outcomes and analyses of other researchers, which validate the computational model and demonstrate the feasibility of this computational approach on analyzing fluid phenomena in insect flight. The present modeling approach also offers a promising route of investigation that could complement as well as overcome some of the limitations of physical experiments in the study of free flight aerodynamics of insects. The results are potentially useful for the design of biomimetic flapping-wing flyers.

Keywords: free hovering flight, flapping wings, fruit fly, insect aerodynamics, leading edge vortex (LEV), computational fluid dynamics (CFD), Navier-Stokes equations (N-S), fluid structure interaction (FSI), generalized finite-difference method (GFD)

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Authors: A. Ja, J. Belabid, A. Cheddadi

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This paper reports the numerical simulation of double diffusive natural convection flows within a horizontal annular filled with a saturated porous medium. The analysis concerns the influence of the different parameters governing the problem, namely, the Rayleigh number Ra, the Lewis number Le and the buoyancy ratio N, on the heat and mass transfer and on the flow structure, in the case of a fixed radius ratio R = 2. The numerical model used for the discretization of the dimensionless equations governing the problem is based on the finite difference method, using the ADI scheme. The study is focused on steady-state solutions in the cooperation situation.

Keywords: natural convection, double-diffusion, porous medium, annular geometry, finite differences

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Authors: Toshanlal Meenpal, Ankita Meenpal

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A very important technique in reversible data hiding field is Difference expansion. Secret message as well as the cover image may be completely recovered without any distortion after data extraction process due to reversibility feature. In general, in any difference expansion scheme embedding is performed by integer transform in the difference image acquired by grouping two neighboring pixel values. This paper proposes an improved reversible difference expansion embedding scheme. We mainly consider edge direction for embedding by modifying the difference of two neighboring pixels values. In general, the larger difference tends to bring a degraded stego image quality than the smaller difference. Image quality in the range of 0.5 to 3.7 dB in average is achieved by the proposed scheme, which is shown through the experimental results. However payload wise it achieves almost similar capacity in comparisons with previous method.

Keywords: information hiding, wedge direction, difference expansion, integer transform

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Authors: Oswaldo Otero, Eduardo A. Orozco, Ana M. Herrera

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In this work, we present results from analytical and numerical studies of the electron acceleration by a TE₀₁₁ cylindrical microwave mode in a static homogeneous magnetic field under electron cyclotron resonance (ECR) condition. The stability of the orbits is analyzed using the particle orbit theory. In order to get a better understanding of the interaction wave-particle, we decompose the azimuthally electric field component as the superposition of right and left-hand circular polarization standing waves. The trajectory, energy and phase-shift of the electron are found through a numerical solution of the relativistic Newton-Lorentz equation in a finite difference method by the Boris method. It is shown that an electron longitudinally injected with an energy of 7 keV in a radial position r=Rc/2, being Rc the cavity radius, is accelerated up to energy of 90 keV by an electric field strength of 14 kV/cm and frequency of 2.45 GHz. This energy can be used to produce X-ray for medical imaging. These results can be used as a starting point for study the acceleration of electrons in a magnetic field changing slowly in time (GYRAC), which has some important applications as the electron cyclotron resonance ion proton accelerator (ECR-IPAC) for cancer therapy and to control plasma bunches with relativistic electrons.

Keywords: Boris method, electron cyclotron resonance, finite difference method, particle orbit theory, X-ray

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Authors: L. Srikanth, D. Neelima Satyam

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The transmission line towers are one of the important life line structures in the distribution of power from the source to the various places for several purposes. The predominant external loads which act on these towers are wind and earthquake loads. In this present study tower is analyzed using Indian Standards IS: 875:1987 (Wind Load), IS: 802:1995 (Structural Steel), IS:1893:2002 (Earthquake) and dynamic analysis of tower has been performed considering ground motion of 2001 Bhuj Earthquake (India). The dynamic analysis was performed considering a tower system consisting two towers spaced 800m apart and 35m height each. This analysis has been performed using numerical time stepping finite difference method which is central difference method were employed by a developed MATLAB program to get the normalized ground motion parameters includes acceleration, frequency, velocity which are important in designing the tower. The tower is analyzed using response spectrum analysis.

Keywords: response spectra, dynamic analysis, central difference method, transmission tower

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Authors: D. B. Gohil

Abstract:

Closed die forging is a very complex process, and measurement of actual forces for real material is difficult and time consuming. Hence, the modelling technique has taken the advantage of carrying out the experimentation with the proper model material which needs lesser forces and relatively low temperature. The results of experiments on the model material then may be correlated with the actual material by using the theory of similarity. There are several methods available to resolve the complexity involved in the closed die forging process. Finite Element Method (FEM) and Finite Difference Method (FDM) are relatively difficult as compared to the slab method. The slab method is very popular and very widely used by the people working on shop floor because it is relatively easy to apply and reasonably accurate for most of the common forging load requirement computations.

Keywords: experimentation, forging, process modeling, strain distribution

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Authors: Komeil Valipourian

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Urban advances and the growing need for developing infrastructures has increased the importance of deep excavations. In this study, after the introducing probability analysis as an important issue, an attempt has been made to apply it for the deep excavation project of Bangkok’s Metro as a case study. For this, the numerical probability model has been developed based on the Finite Difference Method and Monte Carlo sampling approach. The results indicate that disregarding the issue of probability in this project will result in an inappropriate design of the retaining structure. Therefore, probabilistic redesign of the support is proposed and carried out as one of the applications of probability analysis. A 50% reduction in the flexural strength of the structure increases the failure probability just by 8% in the allowable range and helps improve economic conditions, while maintaining mechanical efficiency. With regard to the lack of efficient design in most deep excavations, by considering geometrical and geotechnical variability, an attempt was made to develop an optimum practical design standard for deep excavations based on failure probability. On this basis, a practical relationship is presented for estimating the maximum allowable horizontal displacement, which can help improve design conditions without developing the probability analysis.

Keywords: numerical probability modeling, deep excavation, allowable maximum displacement, finite difference method (FDM)

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

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In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration-free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results are in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes. Semi-Lagrangian method, iteration-free method, nonlinear advection-diffusion equation, second-order backward difference formula

Keywords: Semi-Lagrangian method, iteration free method, nonlinear advection-diffusion equation, second-order backward difference formula

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Authors: Ali Ateş, Ansar B. Mwimbo, Ali H. Abdulkarim

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General transport equation has a wide range of application in Fluid Mechanics and Heat Transfer problems. In this equation, generally when φ variable which represents a flow property is used to represent fluid velocity component, general transport equation turns into momentum equations or with its well known name Navier-Stokes equations. In these non-linear differential equations instead of seeking for analytic solutions, preferring numerical solutions is a more frequently used procedure. Finite difference method is a commonly used numerical solution method. In these equations using velocity and pressure gradients instead of stress tensors decreases the number of unknowns. Also, continuity equation, by integrating the system, number of equations is obtained as number of unknowns. In this situation, velocity and pressure components emerge as two important parameters. In the solution of differential equation system, velocities and pressures must be solved together. However, in the considered grid system, when pressure and velocity values are jointly solved for the same nodal points some problems confront us. To overcome this problem, using staggered grid system is a referred solution method. For the computerized solutions of the staggered grid system various algorithms were developed. From these, two most commonly used are SIMPLE and SIMPLER algorithms. In this study Navier-Stokes equations were numerically solved for Newtonian flow, whose mass or gravitational forces were neglected, for incompressible and laminar fluid, as a hydro dynamically fully developed region and in two dimensional cartesian coordinate system. Finite difference method was chosen as the solution method. This is a parametric study in which varying values of velocity components, pressure and Reynolds numbers were used. Differential equations were discritized using central difference and hybrid scheme. The discritized equation system was solved by Gauss-Siedel iteration method. SIMPLE and SIMPLER were used as solution algorithms. The obtained results, were compared for central difference and hybrid as discritization methods. Also, as solution algorithm, SIMPLE algorithm and SIMPLER algorithm were compared to each other. As a result, it was observed that hybrid discritization method gave better results over a larger area. Furthermore, as computer solution algorithm, besides some disadvantages, it can be said that SIMPLER algorithm is more practical and gave result in short time. For this study, a code was developed in DELPHI programming language. The values obtained in a computer program were converted into graphs and discussed. During sketching, the quality of the graph was increased by adding intermediate values to the obtained result values using Lagrange interpolation formula. For the solution of the system, number of grid and node was found as an estimated. At the same time, to indicate that the obtained results are satisfactory enough, by doing independent analysis from the grid (GCI analysis) for coarse, medium and fine grid system solution domain was obtained. It was observed that when graphs and program outputs were compared with similar studies highly satisfactory results were achieved.

Keywords: finite difference method, GCI analysis, numerical solution of the Navier-Stokes equations, SIMPLE and SIMPLER algoritms

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Authors: T. Kritsana, P. Sawitri, P. Teeratas

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This article aims to study the effect of pressure on rocket motor case by Finite Element Method simulation to select optimal material in rocket motor manufacturing process. In this study, cylindrical tubes with outside diameter of 122 mm and thickness of 3 mm are used for simulation. Defined rocket motor case materials are AISI4130, AISI1026, AISI1045, AL2024 and AL7075. Internal pressure used for the simulation is 22 MPa. The result from Finite Element Method shows that at a pressure of 22 MPa rocket motor case produced by AISI4130, AISI1045 and AL7075 can be used. A comparison of the result between AISI4130, AISI1045 and AL7075 shows that AISI4130 has minimum principal stress and confirm the results of Finite Element Method by the used of calculation method found that, the results from Finite Element Method has good reliability.

Keywords: rocket motor case, finite element method, principal stress, simulation

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Authors: Subhajit Das, Nirjhar Dhang

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Structural damage detection is a challenging work in the field of structural health monitoring (SHM). The damage detection methods mainly focused on the determination of the location and severity of the damage. Model updating is a well known method to locate and quantify the damage. In this method, an error function is defined in terms of difference between the signal measured from ‘experiment’ and signal obtained from undamaged finite element model. This error function is minimised with a proper algorithm, and the finite element model is updated accordingly to match the measured response. Thus, the damage location and severity can be identified from the updated model. In this paper, an error function is defined in terms of modal data viz. frequencies and modal assurance criteria (MAC). MAC is derived from Eigen vectors. This error function is minimized by teaching-learning-based optimization (TLBO) algorithm, and the finite element model is updated accordingly to locate and quantify the damage. Damage is introduced in the model by reduction of stiffness of the structural member. The ‘experimental’ data is simulated by the finite element modelling. The error due to experimental measurement is introduced in the synthetic ‘experimental’ data by adding random noise, which follows Gaussian distribution. The efficiency and robustness of this method are explained through three examples e.g., one truss, one beam and one frame problem. The result shows that TLBO algorithm is efficient to detect the damage location as well as the severity of damage using modal data.

Keywords: damage detection, finite element model updating, modal assurance criteria, structural health monitoring, teaching learning based optimization

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Authors: Maria Neagu

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This paper presents the heat and mass driven natural convection succession in a Darcy thermally stratified porous medium that embeds a vertical semi-infinite impermeable wall of constant heat flux and concentration. The scale analysis of the system determines the two possible maps of the heat and mass driven natural convection sequence along the wall as a function of the process parameters. These results are verified using the finite differences method applied to the conservation equations.

Keywords: finite difference method, natural convection, porous medium, scale analysis, thermal stratification

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Authors: B. Chetti, W. A. Crosby

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This paper presents a numerical analysis for the dynamic performance of a finite journal bearing lubricated with couple stress fluid taking into account the effect of the deformation of the bearing liner. The modified Reynolds equation has been solved by using finite difference technique. The dynamic characteristics in terms of stiffness coefficients, damping coefficients, critical mass and whirl ratio are evaluated for different values of eccentricity ratio and elastic coefficient for a journal bearing lubricated with a couple stress fluids and a Newtonian fluid. The results show that the dynamic characteristics of journal bearings lubricated with couple stress fluids are improved compared to journal bearings lubricated with Newtonian fluids.

Keywords: journal bearing, elastohydrodynamic, stability, couple stress

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Authors: Nana Adjoah Mbroh, Suares Clovis Oukouomi Noutchie

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Singularly perturbed problems are parameter dependent problems, and they play major roles in the modelling of real-life situational problems in applied sciences. Thus, designing efficient numerical schemes to solve these problems is of much interest since the exact solutions of such problems may not even exist. Generally, singularly perturbed problems are identified by a small parameter multiplying at least the highest derivative in the equation. The presence of this parameter causes the solution of these problems to be characterized by rapid oscillations. This unique feature renders classical numerical schemes inefficient since they are unable to capture the behaviour of the exact solution in the part of the domain where the rapid oscillations are present. In this paper, a numerical scheme is proposed to solve a singularly perturbed Volterra Integro-differential equation. The scheme is based on the midpoint rule and employs the non-standard finite difference scheme to solve the differential part whilst the composite trapezoidal rule is used for the integral part. A fully fledged error estimate is performed, and Richardson extrapolation is applied to accelerate the convergence of the scheme. Numerical simulations are conducted to confirm the theoretical findings before and after extrapolation.

Keywords: midpoint rule, non-standard finite difference schemes, Richardson extrapolation, singularly perturbed problems, trapezoidal rule, uniform convergence

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Authors: Hossain Samani, Mohammad Ehteram

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In this paper, we consider finite volume method (FVM) in water hammer. We will simulate these techniques on a looped network with complex boundary conditions. After comparing methods, we see the FVM method as the best method. We compare the results of FVM with experimental data. Finite volume using staggered grid is applied for solving water hammer equations.

Keywords: hydraulic transient, water hammer, interpolation, non-liner interpolation

Procedia PDF Downloads 315