An LT-BEM for an unsteady diffusion-convection problem of another class of anisotropic FGMs

References

• S.A. Al-Bayati and L.C. Wrobel, A novel dual reciprocity boundary element formulation for two-dimensional transient convection–diffusion–reaction problems with variable velocity, Eng. Anal. Bound. Elem. 94 (2018), pp. 60–68.
   Web of Science ®Google Scholar
• S.A. Al-Bayati and L.C. Wrobel, The dual reciprocity boundary element formulation for convection-diffusion-reaction problems with variable velocity field using different radial basis functions, Int. J. Mech. Sci. 145 (2018), pp. 367–377.
   Web of Science ®Google Scholar
• C.N. Angstmann, B.I. Henry, B.A. Jacobs, and A.V. McGann, Numeric solution of advection–diffusion equations by a discrete time random walk scheme, Numer. Methods Partial Differ. Equ. 36 (2020), pp. 680–704.
   Web of Science ®Google Scholar
• M.I. Azis, A boundary integral investigation for unsteady modified Helmholtz problems of some other classes of anisotropic functionally graded materials, Int. J. Comput. Mater. Sci. Eng. 10(1) (2021), pp. 2150005.doi:https://doi.org/10.1142/S2047684121500056
   Web of Science ®Google Scholar
• M.I. Azis, Standard-BEM solutions to two types of anisotropic-diffusion convection reaction equations with variable coefficients, Eng. Anal. Bound. Elem. 105 (2019), pp. 87–93.
   Web of Science ®Google Scholar
• M.I. Azis, I. Solekhudin, M.H. Aswad, and A.R. Jalil, Numerical simulation of two-dimensional modified Helmholtz problems for anisotropic functionally graded materials, J. King Saud Univ. – Sci.32(3) (2020), pp. 2096–2102.
   Web of Science ®Google Scholar
• M.I. Azis, M. Abbaszadeh, M. Dehghan, and I. Solekhudin, A boundary-only integral equation method for parabolic problems of another class of anisotropic functionally graded materials, Mater. Today Commun. 26 (2021), pp. 101956.
   Web of Science ®Google Scholar
• S. Bouhiri, A. Lamnii, and M. Lamnii, Cubic quasi-interpolation spline collocation method for solving convection–diffusion equations, Math. Comput. Simul. 164 (2019), pp. 33–45.
   Web of Science ®Google Scholar
• F. Bounouara, K.H. Benrahou, I. Belkorissat, and A. Tounsi, A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation, Steel Compos. Struct. 20 (2016), pp. 227–249.
   Web of Science ®Google Scholar
• C.L.N. Cunha, J.A.M. Carrer, M.F. Oliveira, and V.L. Costa, A study concerning the solution of advection–diffusion problems by the Boundary Element Method, Eng. Anal. Bound. Elem. 65 (2016), pp. 79–94.
   Web of Science ®Google Scholar
• S.M. Daghash, P. Servio, and A.D. Rey, Elastic properties and anisotropic behavior of structure-H (sH) gas hydrate from first principles, Chem. Eng. Sci. 227 (2020), pp. 115948.
   Web of Science ®Google Scholar
• A. Haddade, M.I. Azis, Z. Djafar, S.N. Jabir, and B. Nurwahyu, Numerical solutions to a class of scalar elliptic BVPs for anisotropic quadratically graded media, IOP Conf. Ser.: Earth Environ. Sci.279(1) (2019), pp. 012007.
   Google Scholar
• S. Hamzah, M.I. Azis, and A.K. Amir, Numerical solutions to anisotropic BVPs for quadratically graded media governed by a Helmholtz equation, IOP Conf. Ser.: Mater. Sci. Eng. 619(1) (2019), pp. 012060.
   Google Scholar
• B. Karami, D. Shahsavari, M. Janghorban, and A. Tounsi, Resonance behavior of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets, Int. J. Mech. Sci. 156 (2019), pp. 94–105.
   Web of Science ®Google Scholar
• C. Limberkar, A. Patel, K. Patel, S. Nair, J. Joy, K.D. Patel, G.K. Solanki, and V.M. Pathak, Anisotropic study of photo-bolometric effect in Sb0.15Ge0.85Se ternary alloy at low temperature, J. Alloys Compd. 846 (2020), pp. 156391.
   Web of Science ®Google Scholar
• Y. Ma, C-P. Sun, D.A. Haake, B.M. Churchill, and C-M. Ho, A high-order alternating direction implicit method for the unsteady convection-dominated diffusion problem, Int. J. Numer. Methods Fluids 70 (2012), pp. 703–712.
   Web of Science ®Google Scholar
• M. Meenal and T.I. Eldho, Two-dimensional contaminant transport modeling using mesh free point collocation method (PCM), Eng. Anal. Bound. Elem. 36 (2012), pp. 551–561.
   Web of Science ®Google Scholar
• R. Pettres and L.A de Lacerda, Numerical analysis of an advective diffusion domain coupled with a diffusive heat source, Eng. Anal. Bound. Elem. 84 (2017), pp. 129–140.
   Web of Science ®Google Scholar
• V. Popov and T.T. Bui, A meshless solution to two-dimensional convection–diffusion problems, Eng. Anal. Bound. Elem. 34 (2010), pp. 680–689.
   Web of Science ®Google Scholar
• A. Rap, L. Elliott, D.B. Ingham, D. Lesnic, and X. Wen, DRBEM for Cauchy convection-diffusion problems with variable coefficients, Eng. Anal. Bound. Elem. 28 (2004), pp. 1321–1333.
   Web of Science ®Google Scholar
• J. Ravnik and L. Škerget, A gradient free integral equation for diffusion–convection equation with variable coefficient and velocity, Eng. Anal. Bound. Elem. 37 (2013), pp. 683–690.
   Web of Science ®Google Scholar
• J. Ravnik and L. Škerget, Integral equation formulation of an unsteady diffusion–convection equation with variable coefficient and velocity, Comput. Math. Appl. 66 (2014), pp. 2477–2488.
   Web of Science ®Google Scholar
• J. Ravnik and J. Tibuat, Fast boundary-domain integral method for unsteady convection-diffusion equation with variable diffusivity using the modified Helmholtz fundamental solution, Numer. Algorithms 82 (2019), pp. 1441–1466.
   Web of Science ®Google Scholar
• N. Salam, A. Haddade, D.L. Clements, and M.I. Azis, A boundary element method for a class of elliptic boundary value problems of functionally graded media, Eng. Anal. Bound. Elem. 84 (2017), pp. 186–190.
   Web of Science ®Google Scholar
• N. Samec and L. Škerget, Integral formulation of a diffusive–convective transport equation for reacting flows, Eng. Anal. Bound. Elem. 28 (2004), pp. 1055–1060.
   Web of Science ®Google Scholar
• Y. Shih, J-Y. Cheng, and K.-T. Chen, An exponential-fitting finite element method for convection–diffusion problems, Appl. Math. Comput. 217 (2011), pp. 5798–5809.
   Web of Science ®Google Scholar
• F. Wang, W. Chen, A. Tadeu, and C.G. Correia, Singular boundary method for transient convection–diffusion problems with time-dependent fundamental solution, Int. J. Heat. Mass. Transf. 114 (2017), pp. 1126–1134.
   Web of Science ®Google Scholar
• T. Wei and M. Xu, An integral equation approach to the unsteady convection–diffusion equations, Appl. Math. Comput. 274 (2016), pp. 55–64.
   Web of Science ®Google Scholar
• X.-H. Wu, Z.-J. Chang, Y.-L. Lu, W.-Q. Tao, and S.-P. Shen, An analysis of the convection–diffusion problems using meshless and mesh based methods, Eng. Anal. Bound. Elem. 36 (2012), pp. 1040–1048.
   Web of Science ®Google Scholar
• H. Yoshida and M. Nagaoka, Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation, J. Comput. Phys. 229 (2010), pp. 7774–7795.
   Web of Science ®Google Scholar
• Z.U. Yusuf, Scattering of electromagnetic waves by an impedance sheet junction in anisotropic plasma, Optik 224 (2020), pp. 165513.
   Web of Science ®Google Scholar