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An accurate numerical analysis of the laminar two-dimensional flow of an incompressible Eyring-Powell fluid over a linear stretching sheet

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Abstract.

In this study, coupling the quasilinearization method (QLM) and indirect radial basis functions (IRBFs) method is proposed for solving the boundary layer flow of an Eyring-Powell fluid over an stretching sheet in unbounded domain. The QLM is used as a tool for confronting the nonlinearity of the problem and then the IRBFs method leads to stable computations for this problem. The IRBFs-QLM meshless method offers several advantages over the more conventional radial basis function approximation, nevertheless it has never been applied to problems in computational fluid dynamics (CFD), at least to the very best of our knowledge. It should be noted that the IRBFs-QLM scheme leads to full system equations which their coefficient matrices are the same for every QLM step. Therefore, we use a powerful non-iterative algorithm named the LU factorization method with partial pivoting to get rid of this system. Numerical results involving comparisons made with other methods indicate the numerically convergence of the proposed new method in this work. Effects of the material fluid parameters on the velocity field function and its derivative are also noteworthy to verify the accuracy of the proposed new approach and to demonstrate the superior performance of the IRBFs-QLM compared with spectral techniques presented elsewhere.

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References

  1. J. Rahimi, D.D. Ganji, M. Khaki, K. Hosseinzadeh, Alex. Eng. J. (2016) https://doi.org/10.1016/j.aej.2016.11.006

  2. T. Hayat, Z. Iqbal, M. Qasim, S. Obaidat, Int. J. Heat Mass Transfer 55, 1817 (2012)

    Article  Google Scholar 

  3. A.Q.M. Khaliq, D.A. Voss, S.H.K. Kazmi, J. Comput. Appl. Math. 222, 17 (2008)

    Article  MathSciNet  Google Scholar 

  4. J. Zhao, M. Davison, R.M. Corless, J. Comput. Appl. Math. 206, 306 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  5. X. Wu, W. Kong, Comput. Math. Appl. 50, 1241 (2005)

    Article  MathSciNet  Google Scholar 

  6. A. Arciniega, E. Allen, Appl. Math. Comput. 153, 165 (2004)

    MathSciNet  Google Scholar 

  7. R. Zvan, P.A. Forsyth, K.R. Vetzal, A general finite element approach for PDE option pricing models, PhD thesis, University of Waterloo, Waterloo (1998)

  8. L.V. Ballestra, C. Sgarra, Comput. Math. Appl. 60, 1571 (2010)

    Article  MathSciNet  Google Scholar 

  9. L.V. Ballestra, L. Cecere, Int. J. Appl. Math. 26, 203 (2013)

    Article  MathSciNet  Google Scholar 

  10. K. Parand, M. Delkhosh, J. Comput. Appl. Math. 317, 624 (2017)

    Article  MathSciNet  Google Scholar 

  11. K. Parand, J.A. Rad, M. Ahmadi, Eur. Phys. J. Plus 131, 300 (2016)

    Article  Google Scholar 

  12. K. Parand, H. Yousefi, M. Delkhosh, A. Ghaderi, Eur. Phys. J. Plus 131, 228 (2016)

    Article  Google Scholar 

  13. K. Parand, S. Khaleqi, Eur. Phys. J. Plus 131, 24 (2016)

    Article  Google Scholar 

  14. K. Parand, P. Mazaheri, H. Yousefi, M. Delkhosh, Eur. Phys. J. Plus 132, 77 (2017)

    Article  Google Scholar 

  15. K. Parand, M. Dehghan, A.R. Rezaei, S.M. Ghaderi, Comput. Phys. Commun. 181, 1096 (2010)

    Article  ADS  Google Scholar 

  16. K. Parand, S.A. Hossayni, J.A. Rad, Appl. Math. Model. 40, 993 (2016)

    Article  MathSciNet  Google Scholar 

  17. S.A. Hossayni, J.A. Rad, K. Parand, S. Abbasbandy, Int. J. Indust. Math. 7, 351 (2015)

    Google Scholar 

  18. J. Rad, J. Hook, E. Larsson, L.V. Sydow, J. Comput. Sci. (2017) https://doi.org/10.1016/j.jocs.2017.05.016

  19. J. Rad, K. Parand, Appl. Numer. Math. 115, 252 (2017)

    Article  MathSciNet  Google Scholar 

  20. J. Rad, K. Parand, Int. J. Comput. Math. 94, 1694 (2017)

    Article  MathSciNet  Google Scholar 

  21. J.A. Rad, K. Parand, L.V. Ballestra, Appl. Math. Comput. 251, 363 (2015)

    MathSciNet  Google Scholar 

  22. J.A. Rad, K. Parand, S. Abbasbandy, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 85, 337 (2015)

    Article  Google Scholar 

  23. J.A. Rad, K. Parand, S. Abbasbandy, Nonlinear Sci. Numer. Simul. 22, 1178 (2015)

    Article  Google Scholar 

  24. K. Parand, S. Abbasbandy, S. Kazem, A. Rezaei, Commun. Nonlinear. Sci. Numer. Simul. 16, 1396 (2011)

    Article  ADS  Google Scholar 

  25. K. Parand, S. Abbasbandy, S. Kazem, A. Rezaei, Phys. Scr. 83, 015011 (2011)

    Article  ADS  Google Scholar 

  26. K. Parand, S. Abbasbandy, S. Kazem, J.A. Rad, Commun. Nonlinear. Sci. Numer. Simul. 16, 4250 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  27. S. Kazem, J.A. Rad, K. Parand, S. Abbasbandy, Z. Naturforsch. A 66a, 591 (2011)

    ADS  Google Scholar 

  28. B. Fornberg, N. Flyer, J.M. Russell, IMA. J. Numer. Anal. 30, 149 (2010)

    Article  MathSciNet  Google Scholar 

  29. B. Fornberg, T. Dirscol, G. Wright, R. Charles, Comput. Math. Appl. 43, 473 (2002)

    Article  MathSciNet  Google Scholar 

  30. G. Liu, Y. Gu, An Introduction to Meshfree Methods and Their Programming (Springer, Netherlands, 2005)

  31. E. Shivanian, H.R. Khodabandehlo, Eur. Phys. J. Plus 129, 241 (2014)

    Article  Google Scholar 

  32. V.R. Hosseini, E. Shivanian, W. Chen, Eur. Phys. J. Plus 130, 33 (2015)

    Article  Google Scholar 

  33. M. Dehghan, D. Mirzaei, Appl. Numer. Math. 59, 1043 (2009)

    Article  MathSciNet  Google Scholar 

  34. M. Dehghan, A. Shokri, J. Comput. Appl. Math. 230, 400 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  35. M. Tatari, M. Dehghan, Eng. Anal. Bound. Elem. 34, 206 (2010)

    Article  MathSciNet  Google Scholar 

  36. J.A. Rad, K. Rashedi, K. Parand, H. Adibi, Eng. Comput. 33, 547 (2017)

    Article  Google Scholar 

  37. P. Assari, M. Dehghan, Eur. Phys. J. Plus 132, 199 (2017)

    Article  Google Scholar 

  38. H. Lin, S.N. Atluri, Comput. Model. Eng. Sci. 1, 45 (2000)

    Google Scholar 

  39. M. Dehghan, A. Ghesmati, Eng. Anal. Bound. Elem. 34, 324 (2010)

    Article  MathSciNet  Google Scholar 

  40. M. Dehghan, D. Mirzaei, Comput. Phys. Commun. 180, 1458 (2009)

    Article  ADS  Google Scholar 

  41. A. Shirzadi, V. Sladek, J. Sladek, Eng. Anal. Bound. Elem. 37, 8 (2013)

    Article  MathSciNet  Google Scholar 

  42. L. Lucy, Astron. J. 88, 1013 (1977)

    Article  ADS  Google Scholar 

  43. B.N.G. Touzot, P. Villon, Comput. Mech. 10, 307 (1992)

    Article  Google Scholar 

  44. A. Heryudono, E. Larsson, A. Ramage, L.V. Sydow, J. Sci. Comput. 67, 1089 (2016)

    Article  MathSciNet  Google Scholar 

  45. A. Safdari-Vaighani, A. Heryudono, E. Larsson, J. Sci. Comput. 64, 341 (2015)

    Article  MathSciNet  Google Scholar 

  46. V. Shcherbakov, E. Larsson, Comput. Math. Appl. 71, 185 (2016)

    Article  MathSciNet  Google Scholar 

  47. M. Dehghan, M. Abbaszadeh, Comput. Math. Appl. 73, 1270 (2017)

    Article  MathSciNet  Google Scholar 

  48. M. Dehghan, M. Abbaszadeh, Appl. Numer. Math. 109, 208 (2016)

    Article  MathSciNet  Google Scholar 

  49. E.J. Kansa, Comput. Math. Appl. 19, 127 (1990)

    Article  MathSciNet  Google Scholar 

  50. K. Parand, J.A. Rad, Appl. Math. Comput. 218, 5292 (2012)

    MathSciNet  Google Scholar 

  51. J.A. Rad, S. Kazem, K. Parand, Comput. Math. Appl. 64, 2049 (2012)

    Article  MathSciNet  Google Scholar 

  52. S. Atluri, S. Shen, The meshless local Petrov-Galerkin (MLPG) method (Tech Science Press, 2002)

  53. M. Dehghan, D. Mirzaei, Eng. Anal. Bound. Elem. 32, 747 (2008)

    Article  Google Scholar 

  54. H. Wendland, Scattered data approximation (Cambridge University Press, New York, 2005)

  55. G.E. Fasshauer, Meshfree Approximation Methods with MATLAB (Word Scientific Publishing, 2007)

  56. N. Mai-Duy, Int. J. Numer. Methods Eng. 62, 824 (2005)

    Article  Google Scholar 

  57. N. Mai-Duy, T. Tran-Cong, Neural Netw. 14, 185 (2001)

    Article  Google Scholar 

  58. M.D. Buhmann, Radial Basis Functions: Theory and Implementations (Cambridge University Press, New York, 2004)

  59. S. Rippa, Adv. Comput. Math. 11, 193 (1999)

    Article  MathSciNet  Google Scholar 

  60. J.G. Wang, G.R. Liu, Comput. Methods Appl. Mech. Eng. 191, 2611 (2002)

    Article  ADS  Google Scholar 

  61. L.V. Ballestra, G. Pacelli, J. Econ. Dyn. Cont. 37, 1142 (2013)

    Article  Google Scholar 

  62. L.V. Ballestra, G. Pacelli, Eng. Anal. Bound. Elem. 36, 1546 (2012)

    Article  MathSciNet  Google Scholar 

  63. L.V. Ballestra, G. Pacelli, Eng. Anal. Bound. Elem. 35, 1075 (2011)

    Article  MathSciNet  Google Scholar 

  64. R.E. Carlson, T.A. Foley, Comput. Math. Appl. 21, 29 (1991)

    Article  MathSciNet  Google Scholar 

  65. A.H.D. Cheng, M.A. Golberg, E.J. Kansa, Q. Zammito, Numer. Methods Part. Differ. Equ. 19, 571 (2003)

    Article  Google Scholar 

  66. G. Fasshauer, J. Zhang, Numer. Algorithms 45, 346 (2007)

    Article  ADS  Google Scholar 

  67. R. Franke, Math. Comput. 38, 181 (1982)

    Google Scholar 

  68. C. Franke, R. Schaback, Appl. Math. Comput. 93, 73 (1998)

    MathSciNet  Google Scholar 

  69. C.S. Huang, C.F. Lee, A.H.D. Cheng, Eng. Anal. Bound. Elem. 34, 802 (2010)

    Article  MathSciNet  Google Scholar 

  70. C.S. Huang, H.D. Yen, A.H.D. Cheng, Eng. Anal. Bound. Elem. 31, 614 (2007)

    Article  Google Scholar 

  71. A.E. Tarwater, A parameter study of Hardy’s multiquadric method for scattered data interpolation, Report UCRL-53670, Lawrence Livermore National Laboratory (1985)

  72. V.B. Mandelzweig, F. Tabakin, Comput. Phys. Commun. 141, 268 (2001)

    Article  ADS  Google Scholar 

  73. K. Parand, M. Shahini, M. Dehghan, J. Comput. Phys. 228, 8830 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  74. J. Wang, G. Liu, Int. J. Numer. Methods Eng. 54, 1623 (2002)

    Article  Google Scholar 

  75. G. Liu, Meshfree Methods: Moving Beyond the Finite Element Method (Taylor and Francis/CRC Press, Boca Raton, 2009)

  76. A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics (Springer-Verlag, New York, 2000)

  77. B.P. Flannery, W.H. Press, S.A. Teukolsky, W.T. Vetterling, Numerical recipes in Fortran 90: The art of parallel scientific computing (Cambridge University Press, New York, 1996)

  78. R.L. Burden, J.D. Fairs, Numerical Analysis (Thamson Books/cole, Belmont, CA, 2005)

  79. G. Dahlquist, A. Bjorck, Numerical Methods (Dover Publications, Mineola, New York, 1974)

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Authors and Affiliations

  1. Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C. Tehran, Iran

    Kourosh Parand & Yasaman Lotfi

  2. Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, G.C. Tehran, Iran

    Kourosh Parand & Jamal Amani Rad

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  1. Kourosh Parand
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  2. Yasaman Lotfi
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  3. Jamal Amani Rad
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Correspondence to Jamal Amani Rad.

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Parand, K., Lotfi, Y. & Amani Rad, J. An accurate numerical analysis of the laminar two-dimensional flow of an incompressible Eyring-Powell fluid over a linear stretching sheet. Eur. Phys. J. Plus 132, 397 (2017). https://doi.org/10.1140/epjp/i2017-11693-3

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