Niyazi Şahin - Academia.edu (original) (raw)
Papers by Niyazi Şahin
International Journal of Nonlinear Sciences and Numerical Simulation, Jan 13, 2022
Large eddy simulation (LES) seeks to predict the dynamics of the organized structures in the flow... more Large eddy simulation (LES) seeks to predict the dynamics of the organized structures in the flow, that is, local spatial averages u ̄ baru\bar{u}baru of the velocity u of the fluid. Although LES has been extensively used to model turbulent flows, very often, the model has difficulty predicting turbulence generated by interactions of a flow with a boundary. A critical problem in LES is to find appropriate boundary conditions for the flow averages, which depend on the behavior of the unknown flow near the wall. In the light of the works of Navier and Maxwell, we use boundary conditions on the wall. We compute the appropriate friction coefficient β for channel flows and investigate its asymptotic behavior as the averaging radius δ → 0 and as the Reynolds number Re → ∞. No-slip conditions are recovered in the first limit, and free-slip conditions are recovered in the second limit. This study is not intended to develop new theories of the turbulent boundary layer; we use available boundary layer theories to improve numerical boundary conditions for flow averages.
Numerical Methods for Partial Differential Equations, Jul 21, 2010
Akgönüllü, N., Şahin, N. and Sezer, M.(2011), A Hermite collocation method for the approximate so... more Akgönüllü, N., Şahin, N. and Sezer, M.(2011), A Hermite collocation method for the approximate solutions of high-order linear Fredholm integro-differential equations. Numerical Methods for Partial Differential Equations, 27: 17071721. doi: 10.1002/num. ...
Computers & mathematics with applications, Aug 1, 2011
International Journal of Computer Mathematics, Sep 1, 2011
... View all references 1313. Razzaghi, M. and Yousefi, S. 2005. ... [CrossRef], [Web of Science ... more ... View all references 1313. Razzaghi, M. and Yousefi, S. 2005. ... [CrossRef], [Web of Science ®] View all references and the direct method based on Fourier and block-pulse functions by Asady et al. 11. Asady, B., Tavassoli Kajani, M., Hadi Vencheh, A. and Heydari, A. 2005. ...
Applied Mathematics and Computation, Sep 1, 2013
In this paper, we present a numerical scheme for the approximate solutions of the onedimensional ... more In this paper, we present a numerical scheme for the approximate solutions of the onedimensional parabolic convection-diffusion model problems. This method is based on the Bessel collocation method used for some problems of ordinary differential equations. In fact, the approximate solution of the problem in the truncated Bessel series form is obtained by this method. By substituting truncated Bessel series solution into the problem and by using the matrix operations and the collocation points, the suggested scheme reduces the problem to a linear algebraic equation system. By solving this equation system, the unknown Bessel coefficients can be computed. An error estimation technique is given for the considered problem and the method. To show the accuracy and the efficiency of the method, numerical examples are implemented and the comparisons are given by the other methods.
Mathematical and Computer Modelling, Feb 1, 2012
Journal of Numerical Mathematics, 2011
Journal of Numerical Mathematics, 2012
Computers & mathematics with applications, Oct 1, 2004
The problem of predicting features of turbulent flows occurs in many applications such as geophys... more The problem of predicting features of turbulent flows occurs in many applications such as geophysical flows, turbulent mixing, pollution dispersal, and even in the design of artificial hearts. One promising approach is large eddy simulation (LES), which seeks to predict local spatial averages fi of the fluid's velocity u. In some applications, the LES equations are solved over moderate time intervals and the core difficulty is associated with modeling near wall turbulence in complex geometries. Thus, one important problem in LES is to find appropriate boundary conditions for the flow averages which depend on the behavior of the unknown flow near the wall. Inspired by early works of Navier and Maxwell, we develop such boundary conditions of the form O.n=0 and t3(6, Re, IQ. r[) ft. r + 2Re-1 n. D (fi) • r = O on the wall. We derive effective friction coefficients ~3 appropriate for both channel flows and recirculating flows and study their asymptotic behavior as the averaging radius 5 --* 0 and as the Reynolds number Re --~ oe. In the first limit, no-slip conditions are recovered. In the second, free-slip conditions are recovered. Our goal herein is not to develop new theories of turbulent boundary layers but rather to use existing boundary layer theories to improve numerical boundary conditions for flow averages. ~) 2004 Elsevier Ltd. All rights reserved.
arXiv (Cornell University), Apr 13, 2017
International Journal of Nonlinear Sciences and Numerical Simulation, 2022
Large eddy simulation (LES) seeks to predict the dynamics of the organized structures in the flow... more Large eddy simulation (LES) seeks to predict the dynamics of the organized structures in the flow, that is, local spatial averages u ̄ baru\bar{u}baru of the velocity u of the fluid. Although LES has been extensively used to model turbulent flows, very often, the model has difficulty predicting turbulence generated by interactions of a flow with a boundary. A critical problem in LES is to find appropriate boundary conditions for the flow averages, which depend on the behavior of the unknown flow near the wall. In the light of the works of Navier and Maxwell, we use boundary conditions on the wall. We compute the appropriate friction coefficient β for channel flows and investigate its asymptotic behavior as the averaging radius δ → 0 and as the Reynolds number Re → ∞. No-slip conditions are recovered in the first limit, and free-slip conditions are recovered in the second limit. This study is not intended to develop new theories of the turbulent boundary layer; we use available boundary la...
In this paper, a matrix method for approximately solving certain linear differential equations is... more In this paper, a matrix method for approximately solving certain linear differential equations is presented. This method is called Morgan-Voyce matrix method and converts a linear differential equation into a matrix equation. Then, the equation reduces to a matrix equation corresponding to a system of linear algebraic equations with unknown Morgan-Voyce coefficients. The examples are included to demonstrate the applicability of the technique.
Mathematical and Computer Modelling, 2012
Pollution has become a very serious threat to our environment. Monitoring pollution is the first ... more Pollution has become a very serious threat to our environment. Monitoring pollution is the first step toward planning to save the environment. In this paper, the pollution problem of three lakes with interconnecting channels has been studied. A collocation method is presented to solve modeling the pollution of a system of lakes by a system of differential equations. By using Bessel polynomials and collocation points, this method transforms modeling the pollution of a system of lakes into the matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. A numerical example is included to demonstrate the validity and applicability of the technique. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on computer using a program written in MATLAB.
Zeitschrift für Naturforschung A, 2011
In this paper, a numerical matrix method, which is based on collocation points, is presented for ... more In this paper, a numerical matrix method, which is based on collocation points, is presented for the approximate solution of a system of high-order linear differential-difference equations with variable coefficients under the mixed conditions in terms of Bessel polynomials. Numerical examples are included to demonstrate the validity and applicability of the technique and comparisons are made with existing results. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on computer using a program written in MATLAB v7.6.0 (R2008a).
The problem of predicting features of turbulent flows occurs in many applications such as geophys... more The problem of predicting features of turbulent flows occurs in many applications such as geophysical flows, turbulent mixing, pollution dispersal and even in the design of artificial hearts. One promising approach is large eddy simulation (LES), which seeks to predict local spatial averages u of the fluid's velocity u. In some applications, often the LES equations are solved over moderate time intervals and the core difficulty is associated with modeling near wall turbulence in complex geometries. Thus, one important problem in LES is to find appropriate boundary conditions for the flow averages which depend on the behavior of the unknown flow near the wall. Inspired by early works of Navier and Maxwell, we develop such boundary conditions of the form u˙n =0and bd,Re, u˙t u˙t+2Re -1n˙D u˙ t=0 on the wall. We derive effective friction coefficients B appropriate for both channel flows and recirculating flows and study their asymptotic behavior as the averagin...
Numerical Methods for Partial Differential Equations, 2011
This article is concerned with a generalization of a functional differential equation known as th... more This article is concerned with a generalization of a functional differential equation known as the pantograph equation which contains a linear functional argument. In this article, we introduce a collocation method based on the Bessel polynomials for the approximate solution of the pantograph equations. The method is illustrated by studying the initial value problems. The results obtained are compared by the known results. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011
Numerical Methods for Partial Differential Equations, 2010
Akgönüllü, N., Şahin, N. and Sezer, M.(2011), A Hermite collocation method for the approximate so... more Akgönüllü, N., Şahin, N. and Sezer, M.(2011), A Hermite collocation method for the approximate solutions of high-order linear Fredholm integro-differential equations. Numerical Methods for Partial Differential Equations, 27: 17071721. doi: 10.1002/num. ...
Mathematical Methods in the Applied Sciences, 2012
In this paper, a collocation method is presented to find the approximate solution of high‐order l... more In this paper, a collocation method is presented to find the approximate solution of high‐order linear complex differential equations in rectangular domain. By using collocation points defined in a rectangular domain and the Bessel polynomials, this method transforms the linear complex differential equations into a matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. The proposed method gives the analytic solution when the exact solutions are polynomials. Numerical examples are included to demonstrate the validity and applicability of the technique and the comparisons are made with existing results. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on a computer using a program written in MATLAB v7.6.0 (R2008a). Copyright © 2012 John Wiley & Sons, Ltd.
Journal of Numerical Mathematics, 2012
International Journal of Nonlinear Sciences and Numerical Simulation, Jan 13, 2022
Large eddy simulation (LES) seeks to predict the dynamics of the organized structures in the flow... more Large eddy simulation (LES) seeks to predict the dynamics of the organized structures in the flow, that is, local spatial averages u ̄ baru\bar{u}baru of the velocity u of the fluid. Although LES has been extensively used to model turbulent flows, very often, the model has difficulty predicting turbulence generated by interactions of a flow with a boundary. A critical problem in LES is to find appropriate boundary conditions for the flow averages, which depend on the behavior of the unknown flow near the wall. In the light of the works of Navier and Maxwell, we use boundary conditions on the wall. We compute the appropriate friction coefficient β for channel flows and investigate its asymptotic behavior as the averaging radius δ → 0 and as the Reynolds number Re → ∞. No-slip conditions are recovered in the first limit, and free-slip conditions are recovered in the second limit. This study is not intended to develop new theories of the turbulent boundary layer; we use available boundary layer theories to improve numerical boundary conditions for flow averages.
Numerical Methods for Partial Differential Equations, Jul 21, 2010
Akgönüllü, N., Şahin, N. and Sezer, M.(2011), A Hermite collocation method for the approximate so... more Akgönüllü, N., Şahin, N. and Sezer, M.(2011), A Hermite collocation method for the approximate solutions of high-order linear Fredholm integro-differential equations. Numerical Methods for Partial Differential Equations, 27: 17071721. doi: 10.1002/num. ...
Computers & mathematics with applications, Aug 1, 2011
International Journal of Computer Mathematics, Sep 1, 2011
... View all references 1313. Razzaghi, M. and Yousefi, S. 2005. ... [CrossRef], [Web of Science ... more ... View all references 1313. Razzaghi, M. and Yousefi, S. 2005. ... [CrossRef], [Web of Science ®] View all references and the direct method based on Fourier and block-pulse functions by Asady et al. 11. Asady, B., Tavassoli Kajani, M., Hadi Vencheh, A. and Heydari, A. 2005. ...
Applied Mathematics and Computation, Sep 1, 2013
In this paper, we present a numerical scheme for the approximate solutions of the onedimensional ... more In this paper, we present a numerical scheme for the approximate solutions of the onedimensional parabolic convection-diffusion model problems. This method is based on the Bessel collocation method used for some problems of ordinary differential equations. In fact, the approximate solution of the problem in the truncated Bessel series form is obtained by this method. By substituting truncated Bessel series solution into the problem and by using the matrix operations and the collocation points, the suggested scheme reduces the problem to a linear algebraic equation system. By solving this equation system, the unknown Bessel coefficients can be computed. An error estimation technique is given for the considered problem and the method. To show the accuracy and the efficiency of the method, numerical examples are implemented and the comparisons are given by the other methods.
Mathematical and Computer Modelling, Feb 1, 2012
Journal of Numerical Mathematics, 2011
Journal of Numerical Mathematics, 2012
Computers & mathematics with applications, Oct 1, 2004
The problem of predicting features of turbulent flows occurs in many applications such as geophys... more The problem of predicting features of turbulent flows occurs in many applications such as geophysical flows, turbulent mixing, pollution dispersal, and even in the design of artificial hearts. One promising approach is large eddy simulation (LES), which seeks to predict local spatial averages fi of the fluid's velocity u. In some applications, the LES equations are solved over moderate time intervals and the core difficulty is associated with modeling near wall turbulence in complex geometries. Thus, one important problem in LES is to find appropriate boundary conditions for the flow averages which depend on the behavior of the unknown flow near the wall. Inspired by early works of Navier and Maxwell, we develop such boundary conditions of the form O.n=0 and t3(6, Re, IQ. r[) ft. r + 2Re-1 n. D (fi) • r = O on the wall. We derive effective friction coefficients ~3 appropriate for both channel flows and recirculating flows and study their asymptotic behavior as the averaging radius 5 --* 0 and as the Reynolds number Re --~ oe. In the first limit, no-slip conditions are recovered. In the second, free-slip conditions are recovered. Our goal herein is not to develop new theories of turbulent boundary layers but rather to use existing boundary layer theories to improve numerical boundary conditions for flow averages. ~) 2004 Elsevier Ltd. All rights reserved.
arXiv (Cornell University), Apr 13, 2017
International Journal of Nonlinear Sciences and Numerical Simulation, 2022
Large eddy simulation (LES) seeks to predict the dynamics of the organized structures in the flow... more Large eddy simulation (LES) seeks to predict the dynamics of the organized structures in the flow, that is, local spatial averages u ̄ baru\bar{u}baru of the velocity u of the fluid. Although LES has been extensively used to model turbulent flows, very often, the model has difficulty predicting turbulence generated by interactions of a flow with a boundary. A critical problem in LES is to find appropriate boundary conditions for the flow averages, which depend on the behavior of the unknown flow near the wall. In the light of the works of Navier and Maxwell, we use boundary conditions on the wall. We compute the appropriate friction coefficient β for channel flows and investigate its asymptotic behavior as the averaging radius δ → 0 and as the Reynolds number Re → ∞. No-slip conditions are recovered in the first limit, and free-slip conditions are recovered in the second limit. This study is not intended to develop new theories of the turbulent boundary layer; we use available boundary la...
In this paper, a matrix method for approximately solving certain linear differential equations is... more In this paper, a matrix method for approximately solving certain linear differential equations is presented. This method is called Morgan-Voyce matrix method and converts a linear differential equation into a matrix equation. Then, the equation reduces to a matrix equation corresponding to a system of linear algebraic equations with unknown Morgan-Voyce coefficients. The examples are included to demonstrate the applicability of the technique.
Mathematical and Computer Modelling, 2012
Pollution has become a very serious threat to our environment. Monitoring pollution is the first ... more Pollution has become a very serious threat to our environment. Monitoring pollution is the first step toward planning to save the environment. In this paper, the pollution problem of three lakes with interconnecting channels has been studied. A collocation method is presented to solve modeling the pollution of a system of lakes by a system of differential equations. By using Bessel polynomials and collocation points, this method transforms modeling the pollution of a system of lakes into the matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. A numerical example is included to demonstrate the validity and applicability of the technique. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on computer using a program written in MATLAB.
Zeitschrift für Naturforschung A, 2011
In this paper, a numerical matrix method, which is based on collocation points, is presented for ... more In this paper, a numerical matrix method, which is based on collocation points, is presented for the approximate solution of a system of high-order linear differential-difference equations with variable coefficients under the mixed conditions in terms of Bessel polynomials. Numerical examples are included to demonstrate the validity and applicability of the technique and comparisons are made with existing results. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on computer using a program written in MATLAB v7.6.0 (R2008a).
The problem of predicting features of turbulent flows occurs in many applications such as geophys... more The problem of predicting features of turbulent flows occurs in many applications such as geophysical flows, turbulent mixing, pollution dispersal and even in the design of artificial hearts. One promising approach is large eddy simulation (LES), which seeks to predict local spatial averages u of the fluid's velocity u. In some applications, often the LES equations are solved over moderate time intervals and the core difficulty is associated with modeling near wall turbulence in complex geometries. Thus, one important problem in LES is to find appropriate boundary conditions for the flow averages which depend on the behavior of the unknown flow near the wall. Inspired by early works of Navier and Maxwell, we develop such boundary conditions of the form u˙n =0and bd,Re, u˙t u˙t+2Re -1n˙D u˙ t=0 on the wall. We derive effective friction coefficients B appropriate for both channel flows and recirculating flows and study their asymptotic behavior as the averagin...
Numerical Methods for Partial Differential Equations, 2011
This article is concerned with a generalization of a functional differential equation known as th... more This article is concerned with a generalization of a functional differential equation known as the pantograph equation which contains a linear functional argument. In this article, we introduce a collocation method based on the Bessel polynomials for the approximate solution of the pantograph equations. The method is illustrated by studying the initial value problems. The results obtained are compared by the known results. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011
Numerical Methods for Partial Differential Equations, 2010
Akgönüllü, N., Şahin, N. and Sezer, M.(2011), A Hermite collocation method for the approximate so... more Akgönüllü, N., Şahin, N. and Sezer, M.(2011), A Hermite collocation method for the approximate solutions of high-order linear Fredholm integro-differential equations. Numerical Methods for Partial Differential Equations, 27: 17071721. doi: 10.1002/num. ...
Mathematical Methods in the Applied Sciences, 2012
In this paper, a collocation method is presented to find the approximate solution of high‐order l... more In this paper, a collocation method is presented to find the approximate solution of high‐order linear complex differential equations in rectangular domain. By using collocation points defined in a rectangular domain and the Bessel polynomials, this method transforms the linear complex differential equations into a matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. The proposed method gives the analytic solution when the exact solutions are polynomials. Numerical examples are included to demonstrate the validity and applicability of the technique and the comparisons are made with existing results. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on a computer using a program written in MATLAB v7.6.0 (R2008a). Copyright © 2012 John Wiley & Sons, Ltd.
Journal of Numerical Mathematics, 2012