Pub Date : 2012-08-31DOI: 10.5923/J.AM.20110101.02
C. Provatidis
This paper investigates higher-order approximations in order to extract Sturm-Liouville eigenvalues in one-dimensional vibration problems in continuum mechanics. Several alternative global approximations of polynomial form such as Lagrange, Bernstein, Legendre as well as Chebyshev of first and second kind are discussed. In an instructive way, closed form analytical formulas are derived for the stiffness and mass matrices up to the quartic degree. A rigorous proof for the transformation of the matrices, when the basis changes, is given. Also, a theoretical explanation is provided for the fact that all the aforementioned alternative pairs of matrices lead to identical eigenvalues. The theory is sustained by one numerical example under three types of boundary conditions.
{"title":"Equivalent Finite Element Formulations for the Calculation of Eigenvalues Using Higher-Order Polynomials","authors":"C. Provatidis","doi":"10.5923/J.AM.20110101.02","DOIUrl":"https://doi.org/10.5923/J.AM.20110101.02","url":null,"abstract":"This paper investigates higher-order approximations in order to extract Sturm-Liouville eigenvalues in one-dimensional vibration problems in continuum mechanics. Several alternative global approximations of polynomial form such as Lagrange, Bernstein, Legendre as well as Chebyshev of first and second kind are discussed. In an instructive way, closed form analytical formulas are derived for the stiffness and mass matrices up to the quartic degree. A rigorous proof for the transformation of the matrices, when the basis changes, is given. Also, a theoretical explanation is provided for the fact that all the aforementioned alternative pairs of matrices lead to identical eigenvalues. The theory is sustained by one numerical example under three types of boundary conditions.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20120203.02
G. Moatimid, M. Moussa, R. El-Shiekh, A. A. El-Satar
By using symbolic computation, we apply Auxiliary equation method to construct exact solutions of Non-Linear Klein-Gordon equation. We show that Auxiliary equation method provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
{"title":"Exact Elliptic Solution for Non-Linear Klein-Gordon Equation Via Auxiliary Equation Method","authors":"G. Moatimid, M. Moussa, R. El-Shiekh, A. A. El-Satar","doi":"10.5923/J.AM.20120203.02","DOIUrl":"https://doi.org/10.5923/J.AM.20120203.02","url":null,"abstract":"By using symbolic computation, we apply Auxiliary equation method to construct exact solutions of Non-Linear Klein-Gordon equation. We show that Auxiliary equation method provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20110102.17
Pratiksha Saxena
Linear programming techniques have been extensively used for animal diet formulation for more than last fifty years. To overcome the drawback of linear approximation of objective function for diet formulation, a mathematical model based on nonlinear programming technique is proposed to measure animal performance in terms of milk yield and weight gain. At the second step, it compares the result of proposed program with that of linear programming model. Result of proposed model gives better results using nonlinear programming. Thus the study is an attempt to develop a nonlinear programming model for optimal planning and best use of nutrient ingredients. Research on nutrition is under process for more than hundred years. Diet formulation is a process by which different ingredients are combined to provide necessary nutrition to animals at different stages of production. A diet should supply all essential nutrients and energy to maintain vital physiological functions of growth, reproduction and health of animals. Diet should be highly digestible and should have very less adverse environmental effect. A number of methods have been defined for the formulation of animal diet; square method, two by two matrix methods, simultaneous equation method, trial and error method and linear programming method to formulate least cost diet. Linear programming is widely used for this purpose. Diet formulated by linear programming is based on assumption of linearity between animal yield and nutrient ingredients included in the diet. To overcome the assumption of linearity and to include complexity of different nutrient ingredients, a nonlinear model is proposed in this paper to maximize milk yield. This concept of non-linear programming may be used to maximize the weight gain of the animal or animal yields approximately. A combination spreadsheet is represented for ration formulation using linear programming (VandeHaar M. J., Black J. R., 1991). Chance-constrained programming is used to formulate commercial feeds for animals (William B. Roush, Robert H. Stock, Terri L. Cravener and Thomas H. D'Alfonso, 1994). Genetic algorithms are applied for the cost
近50多年来，线性规划技术在动物饲料配方中得到了广泛应用。为克服日粮配方中目标函数线性逼近的缺点，提出了一种基于非线性规划技术的动物产奶量和增重数学模型。第二步，将所提方案的结果与线性规划模型的结果进行比较。该模型采用非线性规划方法得到了较好的结果。因此，本研究试图建立一种非线性规划模型，以实现营养成分的最优规划和最佳利用。对营养学的研究已经进行了一百多年。饲料配方是将不同的成分混合在一起，在不同的生产阶段为动物提供必要的营养的过程。饲粮应提供所有必需的营养和能量，以维持动物生长、繁殖和健康的重要生理功能。饮食应该是高度可消化的，应该对环境的不利影响很小。已经确定了许多动物饲料配方的方法;采用平方法、二乘二矩阵法、联立方程法、试错法和线性规划法制定最小成本饮食。线性规划被广泛用于此目的。通过线性规划制定的日粮是基于动物产量与日粮中营养成分之间的线性关系的假设。为了克服线性假设和考虑不同营养成分的复杂性，本文提出了一个非线性模型，以最大限度地提高产奶量。这种非线性规划的概念可以用来最大化动物的增重或动物产量的近似。使用线性规划表示定量公式的组合电子表格(VandeHaar M. J.， Black J. R.， 1991)。机会约束规划用于制定动物的商业饲料(William B. Roush, Robert H. Stock, Terri L. craver和Thomas H. D'Alfonso, 1994)。采用遗传算法求解成本
{"title":"Comparison of Linear and Nonlinear Programming Techniques for Animal Diet","authors":"Pratiksha Saxena","doi":"10.5923/J.AM.20110102.17","DOIUrl":"https://doi.org/10.5923/J.AM.20110102.17","url":null,"abstract":"Linear programming techniques have been extensively used for animal diet formulation for more than last fifty years. To overcome the drawback of linear approximation of objective function for diet formulation, a mathematical model based on nonlinear programming technique is proposed to measure animal performance in terms of milk yield and weight gain. At the second step, it compares the result of proposed program with that of linear programming model. Result of proposed model gives better results using nonlinear programming. Thus the study is an attempt to develop a nonlinear programming model for optimal planning and best use of nutrient ingredients. Research on nutrition is under process for more than hundred years. Diet formulation is a process by which different ingredients are combined to provide necessary nutrition to animals at different stages of production. A diet should supply all essential nutrients and energy to maintain vital physiological functions of growth, reproduction and health of animals. Diet should be highly digestible and should have very less adverse environmental effect. A number of methods have been defined for the formulation of animal diet; square method, two by two matrix methods, simultaneous equation method, trial and error method and linear programming method to formulate least cost diet. Linear programming is widely used for this purpose. Diet formulated by linear programming is based on assumption of linearity between animal yield and nutrient ingredients included in the diet. To overcome the assumption of linearity and to include complexity of different nutrient ingredients, a nonlinear model is proposed in this paper to maximize milk yield. This concept of non-linear programming may be used to maximize the weight gain of the animal or animal yields approximately. A combination spreadsheet is represented for ration formulation using linear programming (VandeHaar M. J., Black J. R., 1991). Chance-constrained programming is used to formulate commercial feeds for animals (William B. Roush, Robert H. Stock, Terri L. Cravener and Thomas H. D'Alfonso, 1994). Genetic algorithms are applied for the cost","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20120204.04
R. Shah, Dilip B. Patel
This paper theoretically studied the effects of various porous structure on the action of the squeeze film formed when a curved upper plate with porous facing approached an impermeable and flat lower plate using ferrofluid as lubricant. Two porous structures given by Kozeny - Carman( a globular sphere model ) and Irmay ( a capillary fissures model ) are considered for the study. Expressions are obtained for pressure and load capacity under an external magnetic field oblique the lower plate. It is found that the load capacity is increased in both the cases with the increase of magnetization. It is also found that the load capacity increased substantially in the case of concave plates and in the case of porous structure given by Kozeny - Carman. The load capacity is more for the porous structure given by Kozeny – Carman.
{"title":"Squeeze Film Based on Ferrofluid in Curved Porous Circular Plates with Various Porous Structure","authors":"R. Shah, Dilip B. Patel","doi":"10.5923/J.AM.20120204.04","DOIUrl":"https://doi.org/10.5923/J.AM.20120204.04","url":null,"abstract":"This paper theoretically studied the effects of various porous structure on the action of the squeeze film formed when a curved upper plate with porous facing approached an impermeable and flat lower plate using ferrofluid as lubricant. Two porous structures given by Kozeny - Carman( a globular sphere model ) and Irmay ( a capillary fissures model ) are considered for the study. Expressions are obtained for pressure and load capacity under an external magnetic field oblique the lower plate. It is found that the load capacity is increased in both the cases with the increase of magnetization. It is also found that the load capacity increased substantially in the case of concave plates and in the case of porous structure given by Kozeny - Carman. The load capacity is more for the porous structure given by Kozeny – Carman.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20120202.08
D. Fisseha, V. K. Katiyar
Sickle cell disease (SCD) is a disease of abnormal rheology. The rheological properties of normal erythrocytes appear to be largely determined by those of the red cell membrane. In SCD, the intracellular polymerization of sickle he- moglobin upon deoxygnation leads to marked increase in intracellular viscosity and elastic stiffness and also having indirect effects on cell membrane .To examine mathematically, the abnormal cell rheology behavior due to polymerization process and that due membrane abnormalities , we mechanically modeled the whole cell deformability as viscoelastic solid and proposed a Voigt-model of nonlinear viscoelastic solid constitutive relation as " mixture''of an elastic and viscous dissipative parts, with parameters of elastic and viscous moduli. The elastic part used to express stress-strain relations via strain energy function of the material and the viscous part derivation depends on strain - rate of deformation. The combination of both constitutive expressions is used to predict the viscoelastic properties of normal and sickle erythrocyte. Furthermore, sickle hemoglobin polymerization also leads to alter the osmotic behavior of the cell and to investigate such osmotic effect; we employ the van't Hoff law of osmotic pressure versus volume relation. The analysis of both formulations presented well the abnormal rheological /mechanical characterization of sickle erythrocyte membrane as we understood and concluded from our results.
{"title":"Analysis of Mechanical Behavior of Red Cell Membrane in Sickle Cell Disease","authors":"D. Fisseha, V. K. Katiyar","doi":"10.5923/J.AM.20120202.08","DOIUrl":"https://doi.org/10.5923/J.AM.20120202.08","url":null,"abstract":"Sickle cell disease (SCD) is a disease of abnormal rheology. The rheological properties of normal erythrocytes appear to be largely determined by those of the red cell membrane. In SCD, the intracellular polymerization of sickle he- moglobin upon deoxygnation leads to marked increase in intracellular viscosity and elastic stiffness and also having indirect effects on cell membrane .To examine mathematically, the abnormal cell rheology behavior due to polymerization process and that due membrane abnormalities , we mechanically modeled the whole cell deformability as viscoelastic solid and proposed a Voigt-model of nonlinear viscoelastic solid constitutive relation as \" mixture''of an elastic and viscous dissipative parts, with parameters of elastic and viscous moduli. The elastic part used to express stress-strain relations via strain energy function of the material and the viscous part derivation depends on strain - rate of deformation. The combination of both constitutive expressions is used to predict the viscoelastic properties of normal and sickle erythrocyte. Furthermore, sickle hemoglobin polymerization also leads to alter the osmotic behavior of the cell and to investigate such osmotic effect; we employ the van't Hoff law of osmotic pressure versus volume relation. The analysis of both formulations presented well the abnormal rheological /mechanical characterization of sickle erythrocyte membrane as we understood and concluded from our results.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20120203.05
N. Jain, D. Chaudhary, D. K. Vijay
We analyse an unsteady three dimensional free convection flow with combined heat and mass transfer over a vertical plate embedded in a porous medium with time dependent suction velocity and transverse sinusoidal permeability. The unsteadiness is due to the time dependent suction velocity. The governing equations with the boundary conditions are first converted into dimensionless form by non-similar transformations and then resulting system of coupled non-linear partial differential equations are solved by series expansion method. The effects of different parameters are shown on velocity (u), cross flow velocity (w), temperature (θ), Concentration (C), Skin friction (τx) and Nusselt number (Nu) graphically. We observe that skin friction is higher in air (Pr=0.71) than in water (Pr=7) but result differs for Nusselt number.
{"title":"Unsteady Three Dimensional Free Convection Heat and Mass Transfer Flow Embedded in a Porous Medium with Periodic Permeability and Constant Heat and Mass Flux","authors":"N. Jain, D. Chaudhary, D. K. Vijay","doi":"10.5923/J.AM.20120203.05","DOIUrl":"https://doi.org/10.5923/J.AM.20120203.05","url":null,"abstract":"We analyse an unsteady three dimensional free convection flow with combined heat and mass transfer over a vertical plate embedded in a porous medium with time dependent suction velocity and transverse sinusoidal permeability. The unsteadiness is due to the time dependent suction velocity. The governing equations with the boundary conditions are first converted into dimensionless form by non-similar transformations and then resulting system of coupled non-linear partial differential equations are solved by series expansion method. The effects of different parameters are shown on velocity (u), cross flow velocity (w), temperature (θ), Concentration (C), Skin friction (τx) and Nusselt number (Nu) graphically. We observe that skin friction is higher in air (Pr=0.71) than in water (Pr=7) but result differs for Nusselt number.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20120204.06
D. Demir, N. Bildik
This paper discusses solving one of the important equations in Physics; which is the one-dimensional heat equation. For that purpose, we use cubic B-spline fin ite elements within a Collocation method. The scheme of the method is presented and the stability analysis is investigated by considering Fourier stability method. On the other hand, a comparative study between the numerical and the analytic solution is illustrated by the figure and the tables. The results demonstrate the reliability and the efficiency of the method.
{"title":"The Numerical Solution of Heat Problem Using Cubic B-Splines","authors":"D. Demir, N. Bildik","doi":"10.5923/J.AM.20120204.06","DOIUrl":"https://doi.org/10.5923/J.AM.20120204.06","url":null,"abstract":"This paper discusses solving one of the important equations in Physics; which is the one-dimensional heat equation. For that purpose, we use cubic B-spline fin ite elements within a Collocation method. The scheme of the method is presented and the stability analysis is investigated by considering Fourier stability method. On the other hand, a comparative study between the numerical and the analytic solution is illustrated by the figure and the tables. The results demonstrate the reliability and the efficiency of the method.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20120204.08
N. Phu, L. T. Quang, L. Dung
The set-valued differential equations (SDEs) are important parts of the set-valued analysis theory. It was investigeted by professor Lakshmikantham V., and many other authors (see(1)-(6),(8)-(10)). Beside that, we have to studied the problems of existence, co mparison and stability of set solutions to the set-valued control differential equations (SCDEs) (see(7),(11)-(16)). In this paper, we present the problems of boundedness for set solutions to the Set Control Differential Equations (SCDEs) by the Lyapunov-like functions and by admisib le control- feedback.
{"title":"On the Boundedness Properties of Solutions to Set Control Differential Equations","authors":"N. Phu, L. T. Quang, L. Dung","doi":"10.5923/J.AM.20120204.08","DOIUrl":"https://doi.org/10.5923/J.AM.20120204.08","url":null,"abstract":"The set-valued differential equations (SDEs) are important parts of the set-valued analysis theory. It was investigeted by professor Lakshmikantham V., and many other authors (see(1)-(6),(8)-(10)). Beside that, we have to studied the problems of existence, co mparison and stability of set solutions to the set-valued control differential equations (SCDEs) (see(7),(11)-(16)). In this paper, we present the problems of boundedness for set solutions to the Set Control Differential Equations (SCDEs) by the Lyapunov-like functions and by admisib le control- feedback.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20110102.11
Habib Jafari, R. Hashemi
The locally D-optimal design was derived for simple linear regression with the error term of Skew-Normal distribution. In this paper, to obtain a D-optimal design, the locally D-optimal criterion was considered, because of depending the information matrix on unknown parameters.
{"title":"Optimal Designs in a Simple Linear Regression with Skew-Normal Distribution for Error Term","authors":"Habib Jafari, R. Hashemi","doi":"10.5923/J.AM.20110102.11","DOIUrl":"https://doi.org/10.5923/J.AM.20110102.11","url":null,"abstract":"The locally D-optimal design was derived for simple linear regression with the error term of Skew-Normal distribution. In this paper, to obtain a D-optimal design, the locally D-optimal criterion was considered, because of depending the information matrix on unknown parameters.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Convection-Diffusion Problems occur very frequently in applied sciences and engineering. In this paper, the cru x of research articles published by numerous researchers during 2007-2011 in referred journals has been presented and this leads to conclusions and recommendations about what methods to use on Convection-Diffusion Problems. It is found that engineers and scientists are using finite element method, finite volu me method, finite volu me element method etc. in flu id mechanics. Here we discuss real life problems of fluid engineering solved by various numerical methods .which is very useful for finding solution of those type of governing equation, whose analytical solution are not easily found. Co mputational fluid dynamics is a branch of Engineering and science that,(1) with the help of d igital co mputers, produces quantitative prediction of fluid-flow phenomenon based on those conservation laws governing fluid mot ion. These predictions normally occur under those conditions defined in terms of flow geo metry. Convection- Diffusion Problems arises where fluid flow p lays a significant role .We must account for the effects of convection. Diffusion occurs always alongside convection in nature. The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flo w, in the modeling of semiconductors, and so forth(3). This paper describes several fin ite difference schemes for solving the convection-diffusion equation. Therefore; we examine computation methods to predict comb ined convection- diffusion equation. The convection-diffusion equation is a parabolic partial differential equation combin ing the diffusion equation and the advection equation, which describes physical phenomena where part icles or energy (or other physical quantities) are transferred inside a physical system due to two processes: diffusion and convection. In its simplest form (when the diffusion coefficient and the convection velocity are constant and there are no sources or sinks) the equation takes the form as following: 2 c D c v c t
对流扩散问题在应用科学和工程中经常出现。在本文中，介绍了2007-2011年期间众多研究人员在参考期刊上发表的研究文章的要点，并由此得出结论，并建议使用什么方法来解决对流扩散问题。在流感力学中，工程师和科学家们正在使用有限元法、有限体积法、有限体积元法等。本文讨论了用各种数值方法求解的流体工程实际问题，这对于求解那些不易找到解析解的控制方程是非常有用的。计算流体动力学是工程和科学的一个分支，它:(1)在数字计算机的帮助下，根据控制流体运动的守恒定律对流体流动现象进行定量预测。这些预测通常发生在根据流动几何定义的条件下。对流-扩散问题出现在流体流动p起重要作用的地方，我们必须考虑对流的影响。在自然界中，扩散总是与对流同时发生。对流扩散输运问题的数值解在科学和工程中有许多重要的应用。这些问题出现在许多应用中，如空气和地下水污染物的输送、油藏流动、半导体建模等等(3)。本文介绍了求解对流扩散方程的几种有限差分格式。因此;我们研究了预测梳状对流-扩散方程的计算方法。对流扩散方程是扩散方程和平流方程结合的抛物型偏微分方程，它描述了部分粒子或能量(或其他物理量)在物理系统内通过扩散和对流两个过程传递的物理现象。在最简单的形式下(当扩散系数和对流速度恒定且没有源和汇时)，方程的形式如下:2c D c v ct
{"title":"A Recent Development of Numerical Methods for Solving Convection-Diffusion Problems","authors":"Anand Shukla, Akhilesh Kumar Singh, Pushpinder Singh","doi":"10.5923/J.AM.20110101.01","DOIUrl":"https://doi.org/10.5923/J.AM.20110101.01","url":null,"abstract":"Convection-Diffusion Problems occur very frequently in applied sciences and engineering. In this paper, the cru x of research articles published by numerous researchers during 2007-2011 in referred journals has been presented and this leads to conclusions and recommendations about what methods to use on Convection-Diffusion Problems. It is found that engineers and scientists are using finite element method, finite volu me method, finite volu me element method etc. in flu id mechanics. Here we discuss real life problems of fluid engineering solved by various numerical methods .which is very useful for finding solution of those type of governing equation, whose analytical solution are not easily found. Co mputational fluid dynamics is a branch of Engineering and science that,(1) with the help of d igital co mputers, produces quantitative prediction of fluid-flow phenomenon based on those conservation laws governing fluid mot ion. These predictions normally occur under those conditions defined in terms of flow geo metry. Convection- Diffusion Problems arises where fluid flow p lays a significant role .We must account for the effects of convection. Diffusion occurs always alongside convection in nature. The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flo w, in the modeling of semiconductors, and so forth(3). This paper describes several fin ite difference schemes for solving the convection-diffusion equation. Therefore; we examine computation methods to predict comb ined convection- diffusion equation. The convection-diffusion equation is a parabolic partial differential equation combin ing the diffusion equation and the advection equation, which describes physical phenomena where part icles or energy (or other physical quantities) are transferred inside a physical system due to two processes: diffusion and convection. In its simplest form (when the diffusion coefficient and the convection velocity are constant and there are no sources or sinks) the equation takes the form as following: 2 c D c v c t","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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