Search results for: Euler equations
1257 A Numerical Method for Diffusion and Cahn-Hilliard Equations on Evolving Spherical Surfaces
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 14961256 Spline Collocation for Solving System of Fredholm and Volterra Integral Equations
Authors: N. Ebrahimi, J. Rashidinia
Abstract:
In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.
Keywords: Convergence analysis, Cubic B-spline, Newton- Cotes formula, System of Fredholm and Volterra integral equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21881255 A Numerical Model Simulation for an Updraft Gasifier Using High Temperature Steam
Authors: T. M. Ismail, M. Abd El-Salam
Abstract:
A mathematical model study was carried out to investigate gasification of biomass fuels using high temperature air and steam as a gasifying agent using high-temperature air up to 1000°C. In this study, a 2D computational fluid dynamics model was developed to study the gasification process in an updraft gasifier, considering drying, pyrolysis, combustion, and gasification reactions. The gas and solid phases were resolved using a Euler−Euler multiphase approach, with exchange terms for the momentum, mass, and energy. The standard k−ε turbulence model was used in the gas phase, and the particle phase was modeled using the kinetic theory of granular flow. The results show that the present model giving a promise way in its capability and sensitivity for the parameter affects that influence the gasification process.
Keywords: Computational fluid dynamics, gasification, biomass fuel, fixed bed gasifier
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 28131254 Refitting Equations for Peak Ground Acceleration in Light of the PF-L Database
Authors: M. Breška, I. Peruš, V. Stankovski
Abstract:
The number of Ground Motion Prediction Equations (GMPEs) used for predicting peak ground acceleration (PGA) and the number of earthquake recordings that have been used for fitting these equations has increased in the past decades. The current PF-L database contains 3550 recordings. Since the GMPEs frequently model the peak ground acceleration the goal of the present study was to refit a selection of 44 of the existing equation models for PGA in light of the latest data. The algorithm Levenberg-Marquardt was used for fitting the coefficients of the equations and the results are evaluated both quantitatively by presenting the root mean squared error (RMSE) and qualitatively by drawing graphs of the five best fitted equations. The RMSE was found to be as low as 0.08 for the best equation models. The newly estimated coefficients vary from the values published in the original works.
Keywords: Ground Motion Prediction Equations, Levenberg-Marquardt algorithm, refitting PF-L database.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14861253 On Symmetries and Exact Solutions of Einstein Vacuum Equations for Axially Symmetric Gravitational Fields
Authors: Nisha Goyal, R.K. Gupta
Abstract:
Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained.Keywords: Gravitational fields, Lie Classical method, Exact solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19251252 On the System of Nonlinear Rational Difference Equations
Authors: Qianhong Zhang, Wenzhuan Zhang
Abstract:
This paper is concerned with the global asymptotic behavior of positive solution for a system of two nonlinear rational difference equations. Moreover, some numerical examples are given to illustrate results obtained.
Keywords: Difference equations, stability, unstable, global asymptotic behavior.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24501251 ψ-exponential Stability for Non-linear Impulsive Differential Equations
Authors: Bhanu Gupta, Sanjay K. Srivastava
Abstract:
In this paper, we shall present sufficient conditions for the ψ-exponential stability of a class of nonlinear impulsive differential equations. We use the Lyapunov method with functions that are not necessarily differentiable. In the last section, we give some examples to support our theoretical results.Keywords: Exponential stability, globally exponential stability, impulsive differential equations, Lyapunov function, ψ-stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 39231250 An Iterative Method for Quaternionic Linear Equations
Authors: Bin Yu, Minghui Wang, Juntao Zhang
Abstract:
By the real representation of the quaternionic matrix, an iterative method for quaternionic linear equations Ax = b is proposed. Then the convergence conditions are obtained. At last, a numerical example is given to illustrate the efficiency of this method.
Keywords: Quaternionic linear equations, Real representation, Iterative algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17551249 Simulation of the Temperature and Heat Gain by Solar Parabolic Trough Collector in Algeria
Authors: M. Ouagued, A. Khellaf
Abstract:
The objectif of the present work is to determinate the potential of the solar parabolic trough collector (PTC) for use in the design of a solar thermal power plant in Algeria. The study is based on a mathematical modeling of the PTC. Heat balance has been established respectively on the heat transfer fluid (HTF), the absorber tube and the glass envelop using the principle of energy conservation at each surface of the HCE cross-sectionn. The modified Euler method is used to solve the obtained differential equations. At first the results for typical days of two seasons the thermal behavior of the HTF, the absorber and the envelope are obtained. Then to determine the thermal performances of the heat transfer fluid, different oils are considered and their temperature and heat gain evolutions compared.Keywords: Direct solar irradiance, solar radiation in Algeria, solar parabolic trough collector, heat balance, thermal oil performance
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 36441248 A New Splitting H1-Galerkin Mixed Method for Pseudo-hyperbolic Equations
Authors: Yang Liu, Jinfeng Wang, Hong Li, Wei Gao, Siriguleng He
Abstract:
A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.
Keywords: Pseudo-hyperbolic equations, splitting system, H1-Galerkin mixed method, error estimates.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14931247 Numerical Investigation of Two-dimensional Boundary Layer Flow Over a Moving Surface
Authors: Mahmoud Zarrini, R.N. Pralhad
Abstract:
In this chapter, we have studied Variation of velocity in incompressible fluid over a moving surface. The boundary layer equations are on a fixed or continuously moving flat plate in the same or opposite direction to the free stream with suction and injection. The boundary layer equations are transferred from partial differential equations to ordinary differential equations. Numerical solutions are obtained by using Runge-Kutta and Shooting methods. We have found numerical solution to velocity and skin friction coefficient.
Keywords: Boundary layer, continuously moving surface, shooting method, skin friction coefficient.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15681246 Constructing Approximate and Exact Solutions for Boussinesq Equations using Homotopy Perturbation Padé Technique
Authors: Mohamed M. Mousa, Aidarkhan Kaltayev
Abstract:
Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM analytical solution. The results reveal that the HPM with the enhancement of PA is a very effective, convenient and quite accurate to such types of partial differential equations.Keywords: Homotopy perturbation method, Padé approximants, cubic Boussinesq equation, modified Boussinesq equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 45591245 Complexity Reduction Approach with Jacobi Iterative Method for Solving Composite Trapezoidal Algebraic Equations
Authors: Mohana Sundaram Muthuvalu, Jumat Sulaiman
Abstract:
In this paper, application of the complexity reduction approach based on half- and quarter-sweep iteration concepts with Jacobi iterative method for solving composite trapezoidal (CT) algebraic equations is discussed. The performances of the methods for CT algebraic equations are comparatively studied by their application in solving linear Fredholm integral equations of the second kind. Furthermore, computational complexity analysis and numerical results for three test problems are also included in order to verify performance of the methods.
Keywords: Complexity reduction approach, Composite trapezoidal scheme, Jacobi method, Linear Fredholm integral equations
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15851244 A Hybrid Overset Algorithm for Aerodynamic Problems with Moving Objects
Authors: S. M. H. Karimian, F. S. Salehi, H. Alisadeghi
Abstract:
A two-dimensional moving mesh algorithm is developed to simulate the general motion of two rotating bodies with relative translational motion. The grid includes a background grid and two sets of grids around the moving bodies. With this grid arrangement rotational and translational motions of two bodies are handled separately, with no complications. Inter-grid boundaries are determined based on their distances from two bodies. In this method, the overset concept is applied to hybrid grid, and flow variables are interpolated using a simple stencil. To evaluate this moving mesh algorithm unsteady Euler flow is solved for different cases using dual-time method of Jameson. Numerical results show excellent agreement with experimental data and other numerical results. To demonstrate the capability of present algorithm for accurate solution of flow fields around moving bodies, some benchmark problems have been defined in this paper.
Keywords: Moving mesh, Overset grid, Unsteady Euler, Relative motion.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16861243 Free Vibration Analysis of Functionally Graded Beams
Authors: Gholam Reza Koochaki
Abstract:
This work presents the highly accurate numerical calculation of the natural frequencies for functionally graded beams with simply supported boundary conditions. The Timoshenko first order shear deformation beam theory and the higher order shear deformation beam theory of Reddy have been applied to the functionally graded beams analysis. The material property gradient is assumed to be in the thickness direction. The Hamilton-s principle is utilized to obtain the dynamic equations of functionally graded beams. The influences of the volume fraction index and thickness-to-length ratio on the fundamental frequencies are discussed. Comparison of the numerical results for the homogeneous beam with Euler-Bernoulli beam theory results show that the derived model is satisfactory.Keywords: Functionally graded beam, Free vibration, Hamilton's principle.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21171242 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (III)
Authors: Li Ge
Abstract:
In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using Leray-Schauder theory:Keywords: impulsive differential equations, impulsive integraldifferential equation, boundary value problems
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11571241 Hybrid Function Method for Solving Nonlinear Fredholm Integral Equations of the Second Kind
Authors: jianhua Hou, Changqing Yang, and Beibo Qin
Abstract:
A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.
Keywords: Hybrid functions, Fredholm integral equation, Blockpulse, Chebyshev polynomials, product operational matrix.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13841240 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (I)
Authors: Li Ge
Abstract:
In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:Keywords: impulsive differential equations, impulsive integraldifferentialequation, boundary value problems
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11871239 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (II)
Authors: Li Ge
Abstract:
In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:Keywords: impulsive differential equations, impulsive integraldifferentialequation, boundary value problems
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10911238 On a Class of Inverse Problems for Degenerate Differential Equations
Authors: Fadi Awawdeh, H.M. Jaradat
Abstract:
In this paper, we establish existence and uniqueness of solutions for a class of inverse problems of degenerate differential equations. The main tool is the perturbation theory for linear operators.Keywords: Inverse Problem, Degenerate Differential Equations, Perturbation Theory for Linear Operators
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16241237 On the Approximate Solution of Continuous Coefficients for Solving Third Order Ordinary Differential Equations
Authors: A. M. Sagir
Abstract:
This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y0, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.
Keywords: Block Method, Hybrid, Linear Multistep, Self starting, Third Order Ordinary Differential Equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17571236 Symmetries, Conservation Laws and Reduction of Wave and Gordon-type Equations on Riemannian Manifolds
Authors: Sameerah Jamal, Abdul Hamid Kara, Ashfaque H. Bokhari
Abstract:
Equations on curved manifolds display interesting properties in a number of ways. In particular, the symmetries and, therefore, the conservation laws reduce depending on how curved the manifold is. Of particular interest are the wave and Gordon-type equations; we study the symmetry properties and conservation laws of these equations on the Milne and Bianchi type III metrics. Properties of reduction procedures via symmetries, variational structures and conservation laws are more involved than on the well known flat (Minkowski) manifold.
Keywords: Bianchi metric, conservation laws, Milne metric, symmetries.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17661235 Investigation of Stability of Functionally Graded Material when Encountering Periodic Loading
Authors: M. Amiri
Abstract:
In this work, functionally graded materials (FGMs), subjected to loading, which varies with time has been studied. The material properties of FGM are changing through the thickness of material as power law distribution. The conical shells have been chosen for this study so in the first step capability equations for FGM have been obtained. With Galerkin method, these equations have been replaced with time dependant differential equations with variable coefficient. These equations have solved for different initial conditions with variation methods. Important parameters in loading conditions are semi-vertex angle, external pressure and material properties. Results validation has been done by comparison between with those in previous studies of other researchers.
Keywords: Impulsive semi-vertex angle, loading, functionally graded materials, composite material.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11911234 Some Static Isotropic Perfect Fluid Spheres in General Relativity
Authors: Sachin Kumar, Y. K. Gupta, J. R. Sharma
Abstract:
In the present article, a new class of solutions of Einstein field equations is investigated for a spherically symmetric space-time when the source of gravitation is a perfect fluid. All the solutions have been derived by making some suitable arrangements in the field equations. The solutions so obtained have been seen to describe Schwarzschild interior solutions. Most of the solutions are subjected to the reality conditions. As far as the authors are aware the solutions are new.Keywords: Einstein's equations, General Relativity, PerfectFluid, Spherical symmetric.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13221233 Numerical Simulation of a Conventional Heat Pipe
Authors: Shoeib Mahjoub, Ali Mahtabroshan
Abstract:
The steady incompressible flow has been solved in cylindrical coordinates in both vapour region and wick structure. The governing equations in vapour region are continuity, Navier-Stokes and energy equations. These equations have been solved using SIMPLE algorithm. For study of parameters variation on heat pipe operation, a benchmark has been chosen and the effect of changing one parameter has been analyzed when the others have been fixed.
Keywords: Vapour region, conventional heat pipe, numerical simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 41761232 Dynamic Time Warping in Gait Classificationof Motion Capture Data
Authors: Adam Świtoński, Agnieszka Michalczuk, Henryk Josiński, Andrzej Polański, KonradWojciechowski
Abstract:
The method of gait identification based on the nearest neighbor classification technique with motion similarity assessment by the dynamic time warping is proposed. The model based kinematic motion data, represented by the joints rotations coded by Euler angles and unit quaternions is used. The different pose distance functions in Euler angles and quaternion spaces are considered. To evaluate individual features of the subsequent joints movements during gait cycle, joint selection is carried out. To examine proposed approach database containing 353 gaits of 25 humans collected in motion capture laboratory is used. The obtained results are promising. The classifications, which takes into consideration all joints has accuracy over 91%. Only analysis of movements of hip joints allows to correctly identify gaits with almost 80% precision.
Keywords: Biometrics, dynamic time warping, gait identification, motion capture, time series classification, quaternion distance functions, attribute ranking.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25991231 Single Image Defogging Method Using Variational Approach for Edge-Preserving Regularization
Authors: Wan-Hyun Cho, In-Seop Na, Seong-ChaeSeo, Sang-Kyoon Kim, Soon-Young Park
Abstract:
In this paper, we propose the variational approach to solve single image defogging problem. In the inference process of the atmospheric veil, we defined new functional for atmospheric veil that satisfy edge-preserving regularization property. By using the fundamental lemma of calculus of variations, we derive the Euler-Lagrange equation foratmospheric veil that can find the maxima of a given functional. This equation can be solved by using a gradient decent method and time parameter. Then, we can have obtained the estimated atmospheric veil, and then have conducted the image restoration by using inferred atmospheric veil. Finally we have improved the contrast of restoration image by various histogram equalization methods. The experimental results show that the proposed method achieves rather good defogging results.
Keywords: Image defogging, Image restoration, Atmospheric veil, Transmission, Variational approach, Euler-Lagrange equation, Image enhancement.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 29331230 Vibration Control of a Functionally Graded Carbon Nanotube-Reinforced Composites Beam Resting on Elastic Foundation
Authors: Gholamhosein Khosravi, Mohammad Azadi, Hamidreza Ghezavati
Abstract:
In this paper, vibration of a nonlinear composite beam is analyzed and then an active controller is used to control the vibrations of the system. The beam is resting on a Winkler-Pasternak elastic foundation. The composite beam is reinforced by single walled carbon nanotubes. Using the rule of mixture, the material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are determined. The beam is cantilever and the free end of the beam is under follower force. Piezoelectric layers are attached to the both sides of the beam to control vibrations as sensors and actuators. The governing equations of the FG-CNTRC beam are derived based on Euler-Bernoulli beam theory Lagrange- Rayleigh-Ritz method. The simulation results are presented and the effects of some parameters on stability of the beam are analyzed.Keywords: Carbon nanotubes, vibration control, piezoelectric layers, elastic foundation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12441229 A High Order Theory for Functionally Graded Shell
Authors: V. V. Zozulya
Abstract:
New theory for functionally graded (FG) shell based on expansion of the equations of elasticity for functionally graded materials (GFMs) into Legendre polynomials series has been developed. Stress and strain tensors, vectors of displacements, traction and body forces have been expanded into Legendre polynomials series in a thickness coordinate. In the same way functions that describe functionally graded relations has been also expanded. Thereby all equations of elasticity including Hook-s law have been transformed to corresponding equations for Fourier coefficients. Then system of differential equations in term of displacements and boundary conditions for Fourier coefficients has been obtained. Cases of the first and second approximations have been considered in more details. For obtained boundary-value problems solution finite element (FE) has been used of Numerical calculations have been done with Comsol Multiphysics and Matlab.
Keywords: Shell, FEM, FGM, legendre polynomial.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15801228 Dynamic Modeling of Tow Flexible Link Manipulators
Authors: E. Abedi, A. Ahmadi Nadooshan, S. Salehi
Abstract:
Modeling and vibration of a flexible link manipulator with tow flexible links and rigid joints are investigated which can include an arbitrary number of flexible links. Hamilton principle and finite element approach is proposed to model the dynamics of flexible manipulators. The links are assumed to be deflection due to bending. The association between elastic displacements of links is investigated, took into account the coupling effects of elastic motion and rigid motion. Flexible links are treated as Euler-Bernoulli beams and the shear deformation is thus abandoned. The dynamic behavior due to flexibility of links is well demonstrated through numerical simulation. The rigid-body motion and elastic deformations are separated by linearizing the equations of motion around the rigid body reference path. Simulation results are shown on for both position and force trajectory tracking tasks in the presence of varying parameters and unknown dynamics remarkably well. The proposed method can be used in both dynamic simulation and controller design.Keywords: Flexible manipulator, flexible link, dynamicmodeling, end point.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2468