Solution of a laminar boundary layer flow via a numerical method

Abstract In this paper, the numerical solution of the Blasius problem is obtained using the collocation method based on rational Chebyshev functions. The Blasius equation is a nonlinear ordinary differential equation which arises in the boundary layer flow. The method reduces solving the equation to solving a system of nonlinear algebraic equations. The results presented here demonstrate reliability and efficiency of the method.

[1]  Shijun Liao,et al.  An explicit, totally analytic solution of laminar viscous flow over a semi-infinite flat plate , 1998 .

[2]  Ben-Yu Guo,et al.  Jacobi Approximations in Certain Hilbert Spaces and Their Applications to Singular Differential Equations , 2000 .

[3]  Mehdi Dehghan,et al.  Numerical solution of the one‐dimensional wave equation with an integral condition , 2007 .

[4]  Jianguo Lin,et al.  A new approximate iteration solution of Blasius equation , 1999 .

[5]  Abdul-Majid Wazwaz,et al.  The variational iteration method for solving two forms of Blasius equation on a half-infinite domain , 2007, Appl. Math. Comput..

[6]  Saeid Abbasbandy,et al.  A numerical solution of Blasius equation by Adomian’s decomposition method and comparison with homotopy perturbation method , 2007 .

[7]  Jie Shen,et al.  A Rational Approximation and Its Applications to Differential Equations on the Half Line , 2000, J. Sci. Comput..

[8]  L. Howarth,et al.  On the solution of the laminar boundary layer equations. , 1938, Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences.

[9]  J. Boyd,et al.  Pseudospectral methods on a semi-infinite interval with application to the Hydrogen atom: a comparison of the mapped Fourier-sine method with Laguerre series and rational Chebyshev expansions , 2003 .

[10]  A. Alizadeh-Pahlavan,et al.  On the analytical solution of viscous fluid flow past a flat plate , 2008 .

[11]  J. Boyd The Optimization of Convergence for Chebyshev Polynomial Methods in an Unbounded Domain , 1982 .

[12]  Ishak Hashim Comments on "A new algorithm for solving classical Blasius equation" by L. Wang , 2006, Appl. Math. Comput..

[13]  J. Boyd Orthogonal rational functions on a semi-infinite interval , 1987 .

[14]  D. Summers,et al.  The use of generalized Laguerre polynomials in spectral methods for nonlinear differential equations , 1998 .

[15]  Jie Shen,et al.  Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval , 2000, Numerische Mathematik.

[16]  F. Allan,et al.  On the analytic solutions of the nonhomogeneous Blasius problem , 2005 .

[17]  Mehdi Dehghan,et al.  Numerical solution of a mathematical model for capillary formation in tumor angiogenesis via the tau method , 2007 .

[18]  Abdul-Majid Wazwaz,et al.  The modified decomposition method and Padé approximants for a boundary layer equation in unbounded domain , 2006, Appl. Math. Comput..

[19]  D. Funaro,et al.  Approximation of some diffusion evolution equations in unbounded domains by hermite functions , 1991 .

[20]  Daniele Funaro,et al.  Computational aspects of pseudospectral Laguerre approximations , 1990 .

[21]  Lei Wang A new algorithm for solving classical Blasius equation , 2004, Appl. Math. Comput..

[22]  Guo Ben-Yu,et al.  Gegenbauer Approximation and Its Applications to Differential Equations on the Whole Line , 1998 .

[23]  G. Ben-yu Error estimation of Hermite spectral method for nonlinear partial differential equations , 1999 .

[24]  S. Liao An explicit, totally analytic approximate solution for Blasius’ viscous flow problems , 1999 .

[25]  Chen Cha'o-Kuang,et al.  The solution of the blasius equation by the differential transformation method , 1998 .

[26]  Ji-Huan He,et al.  A simple perturbation approach to Blasius equation , 2003, Appl. Math. Comput..

[27]  Hani I. Siyyam,et al.  Laguerre Tau Methods for Solving Higher-Order Ordinary Differential Equations , 2001 .

[28]  J. Boyd Spectral methods using rational basis functions on an infinite interval , 1987 .

[29]  Mohsen Razzaghi,et al.  Rational Legendre Approximation for Solving some Physical Problems on Semi-Infinite Intervals , 2004 .

[30]  A. Raptis,et al.  Effect of thermal radiation on MHD flow , 2004, Appl. Math. Comput..

[31]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[32]  Mohsen Razzaghi,et al.  Rational Chebyshev tau method for solving higher-order ordinary differential equations , 2004 .

[33]  Mehdi Dehghan,et al.  A Tau Method for the One-Dimensional Parabolic Inverse Problem Subject to Temperature Overspecification , 2006, Comput. Math. Appl..

[34]  Ji-Huan He Approximate analytical solution of Blasius' equation , 1998 .

[35]  Mehdi Dehghan,et al.  Modified rational Legendre approach to laminar viscous flow over a semi-infinite flat plate , 2008 .

[36]  Asai Asaithambi,et al.  Solution of the Falkner-Skan equation by recursive evaluation of Taylor coefficients , 2005 .

[37]  Jie Shen,et al.  Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions , 2000, SIAM J. Numer. Anal..

[38]  C. Christov A Complete Orthonormal System of Functions in $L^2 ( - \infty ,\infty )$ Space , 1982 .

[39]  Faiz Ahmad,et al.  An approximate analytic solution of the Blasius problem , 2008 .

[40]  Mohsen Razzaghi,et al.  Rational Chebyshev tau method for solving Volterra's population model , 2004, Appl. Math. Comput..

[41]  C. Bender,et al.  A new perturbative approach to nonlinear problems , 1989 .

[42]  H. Blasius Grenzschichten in Flüssigkeiten mit kleiner Reibung , 1907 .

[43]  Zhongqing Wang,et al.  Chebyshev rational spectral and pseudospectral methods on a semi‐infinite interval , 2002 .