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A Boundary Integral Equation Formulation for an Unsteady Anisotropic-Diffusion Convection Equation of Exponentially Variable Coefficients and Compressible Flow

Mohammad Ivan Azis
경북대학교 자연과학대학 수학과|2022.09|Kyungpook Mathematical Journal|제62권 제3호|pp. 557-581|DOI https://doi.org/10.5666/KMJ.2022.62.3.557

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키워드

Laplace transformvariable coefficientsanisotropic functionally graded materialsunsteady diffusion convection equationKebu dayaanRisetdan Teknologi Indonesia
주제분류수학

초록

The anisotropic-diffusion convection equation with exponentially variable co efficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coeffi cients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace transformed equation is consequently written as a boundary integral equation which in volves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation.

Abstract

The anisotropic-diffusion convection equation with exponentially variable co efficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coeffi cients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace transformed equation is consequently written as a boundary integral equation which in volves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation.

참고문헌 (40)

  1. M. Abramowitz, "Handbook of Mathematical Functions: With For-mulas, Graphs and Mathematical Tables" (1972), Dover Publications
  2. M. A. H. Assagaf, "Numerical simulation for steady anisotropic-diffusion convection problems of compressible flow in exponentially graded media", J. Phys. Conf. Ser, 1341(8), pp.082016~ (2019)
  3. M. I. Azis, "Fundamental solutions to two types of 2D boundary value problems of anisotropic materials", Far East J. Math. Sci, 101(11), pp.2405~2420 (2017)
  4. M. I. Azis, "BEM solutions to exponentially variable coefficient Helmholtz equation of anisotropic media", J. Phys. Conf. Ser, 1277(1), pp.012036~ (2019)
  5. M. I. Azis, "Numerical solutions for the Helmholtz boundary value problems of anisotropic homogeneous media", J. Comput. Phys, 381, pp.42~51 (2019)
  6. M. I. Azis, "Standard-BEM solutions to two types of anisotropic-diffusion convection reaction equations with variable coefficients", Eng. Anal. Bound. Elem, 105, pp.87~93 (2019)
  7. M. I. Azis, "Numerical simulation of two-dimensional modified Helmholtz problems for anisotropic functionally graded materials", J. King Saud Univ. Sci, 32(3), pp.2096~2102 (2020)
  8. S. Baja, "Boundary element method solutions for steady anisotropic-diffusion convection problems of incompressible flow in quadratically graded media", J. Phys. Conf. Ser, 1341(6), pp.062019~ (2019)
  9. Fendoğlu H, "DBEM and DRBEM solutions to 2D transient convection-diffusion-reaction type equations", Eng. Anal. Bound. Elem, 93, pp.124~134 (2018)
  10. A. Haddade, "Numerical solutions to a class of scalar elliptic BVPs for anisotropic", IOP Conf. Ser.: Earth Environ. Sci, 279(1), pp.012007~ (2019)
  11. A. Haddade, "Nu-merical solutions for anisotropic-diffusion convection problems of incompressible flow in exponentially graded media", J. Phys. Conf. Ser, 1341(8), pp.082015~ (2019)
  12. S. Hamzah, "Numerical solutions to anisotropic BVPs for quadratically graded media governed by a Helmholtz equation", IOP Conf. Ser.: Mater. Sci. Eng, 619(1), pp.012060~ (2019)
  13. S. Hamzah, "Numerical solution to diffusion convection-reaction equation with trigonometrically variable coefficients of incompressible flow", J. Phys. Conf. Ser, 1341(8), pp.082005~ (2019)
  14. H. Hassanzadeh, "Comparison of different numerical Laplace inversion methods for engineering applications", Appl. Math. Comput, 189, pp.1966~1981 (2007)
  15. E. Hernandez-Martinez, "Non-standard finite difference schemes based on Green’s function formulations for reac-tionadiffusionaconvection systems", Chemical Engineering Science, 94, pp.245~255 (2013)
  16. St. N. Jabir, "BEM solutions to a class of elliptic BVPs for anisotropic trigonometrically graded media", IOP Conference Series: Materials Science and Engineering, 619(1), pp.012059~ (2019)
  17. A. R. Jalil, "Numerical simulation for anisotropic-diffusion convection reaction problems of inhomogeneous media", J. Phys. Conf. Ser, 1341(8), pp.082013~ (2019)
  18. N. Khaeruddin, "Boundary value problems governed by Helmholtz equation for anisotropic trigonometrically graded ma-terials: A boundary element method solution", J. Phys. Conf. Ser, 1341(6), pp.062007~ (2019)
  19. N. Lanafie, "A class of variable coefficient elliptic equations solved using BEM", IOP Conference Series: Materials Science and Engineering, 619(1), pp.012025~ (2019)
  20. N. Lanafie, "On the derivation of a boundary element method for diffusion convection-reaction problems of compressible flow in exponentially inhomogeneous media", J. Phys. Conf. Ser, 1341(6), pp.062013~ (2019)
  21. Q. Li, "Lattice Boltzmann model for a class of convection- diffusion equations with variable coefficients", Comput. Math. Appl, 70, pp.548~561 (2015)
  22. M. Meenal, "Two-dimensional contaminant transport modeling using mesh free point collocation method (PCM)", Eng. Anal. Bound. Elem, 36, pp.551~561 (2012)
  23. B. Nurwahyu, "Numerical solutions for BVPs governed by a Helmholtz equation of anisotropic FGM", IOP Conference Series: Earth and Environmental Science, 279(1), pp.012008~ (2019)
  24. Paharuddin, "Numerical solutions to Helmholtz equation of anisotropic functionally graded materials", J. Phys. Conf. Ser, 1341(8), pp.082012~ (2019)
  25. R. Pettres, "Numerical analysis of an advective diffusion domain coupled with a diffusive heat source", Eng. Anal. Bound. Elem, 84, pp.129~140 (2017)
  26. A. Rap, "DRBEM for Cauchy convection-diffusion problems with variable coefficients", Eng. Anal. Bound. Elem, 28, pp.1321~1333 (2004)
  27. N. Rauf, "A numer-ical study on the effect of the material’s anisotropy in diffusion convection reaction problems", J. Phys. Conf. Ser, 1341(8), pp.082014~ (2019)
  28. J. Ravnik, "A gradient free integral equation for diffusion–convection equation with variable coefficient and velocity", Eng. Anal. Bound. Elem, 37, pp.683~690 (2013)
  29. J. Ravnik, "Integral equation formulation of an unsteady diffusion - convection equation with variable coefficient and velocity", Comput. Math. Appl, 66, pp.2477~2488 (2014)
  30. I. Raya, "Diffusion convection-reaction equation in exponentially graded media of incompressible flow: Boundary element method solutions", J. Phys. Conf. Ser, 1341(8), pp.082004~ (2019)
  31. Sakka, "On the derivation of a boundary element method for steady anisotropic-diffusion convection problems of incompressible flow in trigonometrically graded media", J. Phys. Conf. Ser, 1341(6), pp.062020~ (2019)
  32. N. Salam, "A boundary element method for a class of elliptic boundary value problems of functionally graded media", Eng. Anal. Bound. Elem, 84, pp.186~190 (2017)
  33. N. Salam, "A boundary element method for anisotropic-diffusion convection-reaction equation in quadratically graded media of incompressible flow", J. Phys. Conf. Ser, 1341(8), pp.082003~ (2019)
  34. "Com-munications of the ACM", 1970, 47~49
  35. S. Suryani, "A boundary element method solution to spatially variable coefficients diffusion convection equation of anisotropic media", J. Phys. Conf. Ser, 1341(6), pp.062018~ (2019)
  36. R. Syam, "Numerical solutions to anisotropic FGM BVPs governed by the modified Helmholtz type equation", IOP Conference Series: Materials Science and Engineering, 619(1), pp.012061~ (2019)
  37. F. Wang, "Singular boundary method for transient convection- diffusion problems with time-dependent fundamental solution", Int. J. Heat Mass Transf, 114, pp.1126~1134 (2017)
  38. X-H. Wu, "An analysis of the convection–diffusion problems using meshless and mesh based methods", Eng. Anal. Bound. Elem, 36, pp.1040~1048 (2012)
  39. H. Yoshida, "Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation", J. Comput. Phys, 229, pp.7774~7795 (2010)
  40. C. Zoppou, "Analytical solution of a spatially variable coefficient advection-diffusion equation in up to three dimensions", Appl. Math. Model, 23, pp.667~685 (1999)

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