Search results for: numerical solutions

Authors: Imran Siddique

Abstract:

This paper deals with the helical flow of a Newtonian fluid in an infinite circular cylinder, due to both longitudinal and rotational shear stress. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms and satisfy all imposed initial and boundary conditions. For large times, these solutions reduce to the well-known steady-state solutions.

Keywords: Newtonian fluids, Velocity field, Exact solutions, Shear stress, Cylindrical domains.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1409

Authors: Jin Sup Kim, Woo Young Jung, Minho Kwon

Abstract:

In general dynamic analyses, lower mode response is of interest, however the higher modes of spatially discretized equations generally do not represent the real behavior and not affects to global response much. Some implicit algorithms, therefore, are introduced to filter out the high-frequency modes using intended numerical error. The objective of this study is to introduce the P-method and PC α-method to compare that with dissipation method and Newmark method through the stability analysis and numerical example. PC α-method gives more accuracy than other methods because it based on the α-method inherits the superior properties of the implicit α-method. In finite element analysis, the PC α-method is more useful than other methods because it is the explicit scheme and it achieves the second order accuracy and numerical damping simultaneously.

Keywords: Dynamic, α-Method, P-Method, PC α-Method, Newmark method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3020

Authors: Young Hee Geum

Abstract:

We propose the numerical method defined by

xn+1 = xn − λ[f(xn − μh(xn))/]f'(xn) , n ∈ N,

and determine the control parameter λ and μ to converge cubically. In addition, we derive the asymptotic error constant. Applying this proposed scheme to various test functions, numerical results show a good agreement with the theory analyzed in this paper and are proven using Mathematica with its high-precision computability.

Keywords: Asymptotic error constant, iterative method , multiple root, root-finding.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1455

Authors: Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: Conservation laws, diffusion equations, Cahn-Hilliard Equations, evolving surfaces.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1459

Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, a nonlinear delay population model is investigated. Choosing the delay as a bifurcation parameter, we demonstrate that Hopf bifurcation will occur when the delay exceeds a critical value. Global existence of bifurcating periodic solutions is established. Numerical simulations supporting the theoretical findings are included.

Keywords: Population model, Stability, Hopf bifurcation, Delay, Global Hopf bifurcation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1708

Authors: Joe Imae, Kenjiro Shinagawa, Tomoaki Kobayashi, Guisheng Zhai

Abstract:

We propose a new approach on how to obtain the approximate solutions of Hamilton-Jacobi (HJ) equations. The process of the approximation consists of two steps. The first step is to transform the HJ equations into the virtual time based HJ equations (VT-HJ) by introducing a new idea of ‘virtual-time’. The second step is to construct the approximate solutions of the HJ equations through a computationally iterative procedure based on the VT-HJ equations. It should be noted that the approximate feedback solutions evolve by themselves as the virtual-time goes by. Finally, we demonstrate the effectiveness of our approximation approach by means of simulations with linear and nonlinear control problems.

Keywords: Nonlinear Control, Optimal Control, Hamilton-Jacobi Equation, Virtual-Time

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1468

Authors: Ming Guan

Abstract:

This paper proposes a simple model of economic geography within the Dixit-Stiglitz-Iceberg framework that may be used to analyze migration patterns among three cities. The cost–benefit tradeoffs affecting incentives for three types of migration, including echelon migration, are discussed. This paper develops a tractable, heterogeneous-agent, general equilibrium model, where agents share constant human capital, and explores the relationship between the benefits of echelon migration and gross human capital. Using Chinese numerical solutions, we study the manifestation of echelon migration and how it responds to changes in transportation cost and elasticity of substitution. Numerical results demonstrate that (i) there are positive relationships between a migration-s benefit-and-wage ratio, (ii) there are positive relationships between gross human capital ratios and wage ratios as to origin and destination, and (iii) we identify 13 varieties of human capital convergence among cities. In particular, this model predicts population shock resulting from the processes of migration choice and echelon migration.

Keywords: Dixit-Stiglitz-Iceberg framework, elasticity , echelonmigration, trade-off

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1429

Authors: A. El Amri, M. El Yakhloufi Haddou, A. Khamlichi

Abstract:

The numerical simulation based on the Finite Element Method (FEM) is widely used in academic institutes and in the industry. It is a useful tool to predict many phenomena present in the classical manufacturing forming processes such as fracture. But, the results of such numerical model depend strongly on the parameters of the constitutive behavior model. The influences of thermal and mechanical loads cause damage. The temperature and strain rate dependent materials’ properties and their modelling are discussed. A Johnson-Cook Model of damage has been selected for the numerical simulations. Virtual software called the ABAQUS 6.11 is used for finite element analysis. This model was introduced in order to give information concerning crack initiation during thermal and mechanical loads.

Keywords: Thermomechanical fatigue, failure, numerical simulation, fracture, damages.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1445

Authors: Nik Mohd Asri Nik Long, Koo Lee Feng, Zainidin K. Eshkuvatov, A. A. Khaldjigitov

Abstract:

This paper study the behavior of the solution at the crack edges for an elliptical crack with developing cusps, Ω in the plane elasticity subjected to shear loading. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over Ω and it is then transformed into a similar equation over a circular region, D, using conformal mapping. An appropriate collocation points are chosen on the region D to reduce the hypersingular integral equation into a system of linear equations with (2N+1)(N+1) unknown coefficients, which will later be used in the determination of shear stress intensity factors and maximum shear stress intensity. Numerical solution for the considered problem are compared with the existing asymptotic solution, and displayed graphically. Our results give a very good agreement to the existing asymptotic solutions.

Keywords: Elliptical crack, stress intensity factors, hyper singular integral equation, shear loading, conformal mapping.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1651

Authors: Durga C. Dalal, Swapan K. Pandit

Abstract:

In this paper, a numerical study has been made to analyze the transient 2-D flows of a viscous incompressible fluid through channels with forward or backward constriction. Problems addressed include flow through sudden contraction and sudden expansion channel geometries with rounded and increasingly sharp reentrant corner. In both the cases, numerical results are presented for the separation and reattachment points, streamlines, vorticity and flow patterns. A fourth order accurate compact scheme has been employed to efficiently capture steady state solutions of the governing equations. It appears from our study that sharpness of the throat in the channel is one of the important parameters to control the strength and size of the separation zone without modifying the general flow patterns. The comparison between the two cases shows that the upstream geometry plays a significant role on vortex growth dynamics.

Keywords: Forward and backward constriction, HOC scheme, Incompressible viscous flows, Separation and reattachment points.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1640

Authors: Jonathan Bohn, Jorge Rebaza, Kaitlin Speer

Abstract:

The dynamics of a predator-prey model with continuous threshold policy harvesting functions on the prey is studied. Theoretical and numerical methods are used to investigate boundedness of solutions, existence of bionomic equilibria, and the stability properties of coexistence equilibrium points and periodic orbits. Several bifurcations as well as some heteroclinic orbits are computed.

Keywords: Predator-prey models, threshold harvesting, dynamicalsystems

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2257

Authors: A. C. Amaro de Faria Jr, A. M. Canone

Abstract:

Considering a scenario where our universe is taken as a 3d domain wall embedded in a 5d dimensional Minkowski space-time, we explore the existence of a richer class of solitonic solutions and their consequences for accelerating universes driven by collisions of bulk particle excitations with the walls. In particular it is shown that some of these solutions should play a fundamental role at the beginning of the expansion process. We present some of these solutions in cosmological scenarios that can be applied to models that describe the inflationary period of the Universe.

Keywords: Solitons, topological defects, Branes, kinks, accelerating universes in Brane scenarios.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 722

Authors: Mokhtar Djeddou, Amine Mehel, Georges Fokoua, Anne Tanière, Patrick Chevrier

Abstract:

Commuters’ exposure to air pollution, particularly to particle matter inside vehicles, is a significant health issue. Assessing particle concentrations and characterizing their distribution is an important first step in understanding and proposing solutions to improve car cabin air quality. It is known that particle dynamics is intimately driven by particle-turbulence interactions. In order to analyze and model pollutants distribution inside car cabins, it is crucial to examine first the single-phase flow topology and its associated turbulence characteristics. Within this context, Computational Fluid Dynamics (CFD) simulations were conducted to model airflow inside a full-scale car cabin using Reynolds Averaged Navier-Stokes (RANS) approach combined with the first order Realizable k-ε model to close the RANS equations. To assess the numerical model, a campaign of velocity field measurements at different locations in the front and back of the car cabin has been carried out using hot-wire anemometry technique. Comparison between numerical and experimental results shows a good agreement of velocity profiles. Additionally, visualization of streamlines shows the formation of jet flow developing out of the dashboard air vents and the formation of large vortex structures, particularly between the front and back-seat compartments. These vortical structures could play a key role in the accumulation and clustering of particles in a turbulent flow.

Keywords: Car cabin, CFD, hot-wire anemometry, vortical flow.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 384

Authors: Myung Jin Kim, Hyun Bae Jin, Wui Jun Chung

Abstract:

In this study, to accurately predict cavitation of a centrifugal pump, numerical analysis was compared with experimental results modeled on a small industrial centrifugal pump. In this study, numerical analysis was compared with experimental results modeled on a small industrial centrifugal pump for reliable prediction on cavitation of a centrifugal pump. To improve validity of the numerical analysis, transient analysis was conducted on the calculated domain of full-type geometry, such as an experimental apparatus. The numerical analysis from the results was considered to be a reliable prediction of cavitaion.

Keywords: Centrifugal Pump, Cavitation, NPSH, CFD.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4160

Authors: Mustafa Hasan Omar

Abstract:

The destruction effect of hydrocarbon solutions on concrete besides its high permeability have led researchers to try to improve the performance of concrete exposed to these solutions, hence improving the durability and usability of oil concrete structures. Recently, polymer concrete is considered one of the most important types of concrete, and its behavior after exposure to oil products is still unknown. In the present work, an experimental study has been carried out, in which the prepared epoxy polymer concrete immersed in different types of hydrocarbon exposure solutions (gasoline, kerosene, and gas oil) for 120 days and compared with the reference concrete left in the air. The results for outdoor specimens indicate that the mechanical properties are increased after 120 days, but the specimens that were immersed in gasoline, kerosene, and gas oil for the same period show a reduction in compressive strength by -21%, -27% and -23%, whereas in splitting tensile strength by -19%, -24% and -20%, respectively. The reductions in ultrasonic pulse velocity for cubic specimens are -17%, -22% and -19% and in cylindrical specimens are -20%, -25% and -22%, respectively.

Keywords: Epoxy resin, hydrocarbon solutions, mechanical properties, polymer concrete, ultrasonic pulse velocity.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 592

Authors: A.O. Ladjedel, B.T.Yahiaoui, C.L.Adjlout, D.O.Imine

Abstract:

In the present paper; an experimental and numerical investigations of drag reduction on a grooved circular cylinder have been performed. The experiments were carried out in closed circuit subsonic wind tunnel (TE44); the pressure distribution on the cylinder was conducted using a TE44DPS differential pressure scanner and the drag forces were measured using the TE81 balance. The display unit is linked to a computer, loaded with DATASLIM software for data analysis and logging of result. The numerical study was performed using the code ANSYS FLUENT solving the Reynolds Averaged Navier-Stokes (RANS) equations. The k-ε and k- ω SST models were tested. The results obtained from the experimental and numerical investigations have showed a reduction in the drag when using longitudinal grooves namely 2 and 6 on the cylinder.

Keywords: Circular cylinder, Drag, grooves, pressure distribution

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2780

Authors: K. Djellabi, M. E. H. Latreche

Abstract:

Induction heating computer simulation is a powerful tool for process design and optimization, induction coil design, equipment selection, as well as education and business presentations. The authors share their vast experience in the practical use of computer simulation for different induction heating and heat treating processes. In this paper treated with mathematical modeling and numerical simulation of induction heating furnaces with axisymmetric geometries for the numerical solution, we propose finite element methods combined with boundary (FEM) for the electromagnetic model using COMSOL® Multiphysics Software. Some numerical results for an industrial furnace are shown with high frequency.

Keywords: Numerical methods, Induction furnaces, Induction Heating, Finite element method, Comsol Multiphysics software.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7967

Authors: D. Šedivý, S. Fialová

Abstract:

The main purpose of this study is to show differences between the numerical solution of the flow through the artificial heart valve using Newtonian or non-Newtonian fluid. The simulation was carried out by a commercial computational fluid dynamics (CFD) package based on finite-volume method. An aortic bileaflet heart valve (Sorin Bicarbon) was used as a pattern for model of real heart valve replacement. Computed tomography (CT) was used to gain the accurate parameters of the valve. Data from CT were transferred in the commercial 3D designer, where the model for CFD was made. Carreau rheology model was applied as non-Newtonian fluid. Physiological data of cardiac cycle were used as boundary conditions. Outputs were taken the leaflets excursion from opening to closure and the fluid dynamics through the valve. This study also includes experimental measurement of pressure fields in ambience of valve for verification numerical outputs. Results put in evidence a favorable comparison between the computational solutions of flow through the mechanical heart valve using Newtonian and non-Newtonian fluid.

Keywords: Computational modeling, dynamic mesh, mechanical heart valve, non-Newtonian fluid, SDOF.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1558

Authors: Hamed Djalal

Abstract:

The aim of this paper is to perform a thermal-hydraulic analysis of the IAEA 10 MW benchmark reactor solving analytically and numerically, by mean of the finite volume method, respectively the steady state and transient forced convection in rectangular narrow channel between two parallel MTR-type fuel plates, imposed under a cosine shape heat flux. A comparison between both solutions is presented to determine the minimal coolant velocity which can ensure a safe reactor core cooling, where the cladding temperature should not reach a specific safety limit 90 °C. For this purpose, a computer program is developed to determine the principal parameter related to the nuclear core safety, such as the temperature distribution in the fuel plate and in the coolant (light water) as a function of the inlet coolant velocity. Finally, a good agreement is noticed between the both analytical and numerical solutions, where the obtained results are displayed graphically.

Keywords: Forced convection, friction factor pressure drop thermal hydraulic analysis, vertical heated rectangular channel.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 806

Authors: Anupma Bansal

Abstract:

We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.

Keywords: Klein-Gordon-Schödinger Equation, Lie Classical Method, Exact Solutions

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4484

Authors: Anupma Bansal, Rajeev Budhiraja, Manoj Pandey

Abstract:

In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. With the application of this method, we have tried to reduce it to time-fractional ordinary differential equation (ODE) which has been further studied for exact solutions.

Keywords: Nonlinear time-fractional hyperbolic PDE, Lie Classical method, exact solutions.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1315

Authors: Venkatesh C., K. Shanti Swarup

Abstract:

This paper investigates the impact on operating time delay and relay maloperation when 1st,2nd and 3rd order analog antialiasing filters are used in numerical distance protection. RC filter with cut-off frequency 90 Hz is used. Simulations are carried out for different SIR (Source to line Impedance Ratio), load, fault type and fault conditions using SIMULINK, where the voltage and current signals are fed online to the developed numerical distance relay model. Matlab is used for plotting the impedance trajectory. Investigation results shows that, about 75 % of the simulated cases, numerical distance relay operating time is not increased even-though there is a time delay when higher order filters are used. Relay maloperation (selectivity) also reduces (increases) when higher order filters are used in numerical distance protection.

Keywords: Antialiasing, capacitive voltage transformers, delay estimation, discrete Fourier transform (DFT), distance measurement, low-pass filters, source to line impedance ratio (SIR), protective relaying.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2752

Authors: Anežka Jurčíková, Miroslav Rosmanit

Abstract:

The subject of this paper is to verify the behavior of the truss-type CHS joint which is beyond the scope of use of the EN 1993-1-8. This is performed by using the numerical modeling in program ANSYS and the analytical methods recommended in the CIDECT publication. The recommendations for numerical modeling of such types of joints as well as for evaluation of load-bearing capacity of the joint are given in this paper. The results from both analytical and numerical models are compared.

Keywords: ANSYS, CHS joints, FEM, Lattice structure

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1866

Authors: P. Acharjee, S. K. Goswami

Abstract:

Particle Swarm Optimization (PSO) with elite PSO parameters has been developed for power flow analysis under practical constrained situations. Multiple solutions of the power flow problem are useful in voltage stability assessment of power system. A method of determination of multiple power flow solutions is presented using a hybrid of Particle Swarm Optimization (PSO) and local search technique. The unique and innovative learning factors of the PSO algorithm are formulated depending upon the node power mismatch values to be highly adaptive with the power flow problems. The local search is applied on the pbest solution obtained by the PSO algorithm in each iteration. The proposed algorithm performs reliably and provides multiple solutions when applied on standard and illconditioned systems. The test results show that the performances of the proposed algorithm under critical conditions are better than the conventional methods.

Keywords: critical conditions, ill-conditioned systems, localsearch technique, multiple power flow solutions, particle swarmoptimization.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1769

Authors: He Chao, Zhang Lei, Liu Ran, Li Ang

Abstract:

Temperature regulating system by gaseous nitrogen is of importance to the space environment simulator, which keeps the shrouds in the temperature range from -150°C to +150°C. Liquid nitrogen spray equipment is one of the most critical parts in the temperature regulating system by gaseous nitrogen. Y type jet atomizer and internal mixing atomizer of the liquid nitrogen spray equipment are studied in this paper, 2D/3D atomizer model was established and grid division was conducted respectively by the software of Catia and ICEM. Based on the above preparation, numerical simulation on the spraying process of the atomizer by FLUENT is performed. Using air and water as the medium, comparison between the tests and numerical simulation was conducted and the results of two ways match well. Hence, it can be conclude that this atomizer model can be applied in the numerical simulation of liquid nitrogen spray equipment.

Keywords: Space environmental simulator, liquid nitrogen spray, Y type jet atomizer, internal mixing atomizer, numerical simulation, fluent.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1958

Authors: Marco Actis Grande, Somlak Wannarumon

Abstract:

This paper proposes the numerical simulation of the investment casting of gold jewelry. It aims to study the behavior of fluid flow during mould filling and solidification and to optimize the process parameters, which lead to predict and control casting defects such as gas porosity and shrinkage porosity. A finite difference method, computer simulation software FLOW-3D was used to simulate the jewelry casting process. The simplified model was designed for both numerical simulation and real casting production. A set of sensor acquisitions were allocated on the different positions of the wax tree of the model to detect filling times, while a set of thermocouples were allocated to detect the temperature during casting and cooling. Those detected data were applied to validate the results of the numerical simulation to the results of the real casting. The resulting comparisons signify that the numerical simulation can be used as an effective tool in investment-casting-process optimization and casting-defect prediction.

Keywords: Computer fluid dynamic, Investment casting, Jewelry, Mould filling, Simulation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2689

Authors: Benshi Zhu

Abstract:

In this paper, the existence of multiple positive solutions for a class of third-order three-point discrete boundary value problem is studied by applying algebraic topology method.

Keywords: Positive solutions, Discrete boundary value problem, Third-order, Three-point, Algebraic topology

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1202

Authors: M. Zarebnia, S. Khani

Abstract:

In this paper first, a numerical method based on quasiinterpolation for solving nonlinear Fredholm integral equations of the Hammerstein-type is presented. Then, we approximate the solution of Hammerstein integral equations by Nystrom’s method. Also, we compare the methods with some numerical examples.

Keywords: Hammerstein integral equations, quasi-interpolation, Nystrom’s method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4432

Authors: Mohamed K. El Daou

Abstract:

We construct an exponentially weighted Legendre- Gauss Tau method for solving differential equations with oscillatory solutions. The proposed method is applied to Sturm-Liouville problems. Numerical examples illustrating the efficiency and the high accuracy of our results are presented.

Keywords: Oscillatory functions, Sturm-Liouville problems, legendre polynomial, gauss points.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1355

Authors: Minghui Wang, Luping Xu, Juntao Zhang

Abstract:

Based on the conjugate gradient (CG) algorithm, the constrained matrix equation AXB=C and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.

Keywords: Iterative method, symmetric arrowhead matrix, conjugate gradient algorithm.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1366