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Numerical Simulation for Transient Diffusion Convection Reaction Problems of a Class of Anisotropic FGMs
Version 1
: Received: 12 April 2023 / Approved: 12 April 2023 / Online: 12 April 2023 (11:47:19 CEST)
A peer-reviewed article of this Preprint also exists.
Azis, M.I. A NumericalInvestigation for a Class of Transient-State Variable Coefficient DCR Equations. Mathematics 2023, 11, 2091. Azis, M.I. A NumericalInvestigation for a Class of Transient-State Variable Coefficient DCR Equations. Mathematics 2023, 11, 2091.
Abstract
In this paper a combined Laplace transform (LT) and boundary element method (BEM) is used to find numerical solutions to problems of anisotropic functionally graded media which are governed by the transient diffusion-convection-reaction equation. First, the variable coefficients governing equation is reduced to a constant coefficients equation. Then, the Laplace-transformed constant coefficients equation is transformed a boundary-only integral equation. Using a BEM, the numerical solutions in the frame of Laplace transform may then be obtained from this integral equation. Then the solutions are inversely transformed numerically using the Stehfest formula. Some problems considered are those of compressible or incompressible flow, and of media which are quadratically, exponentially and trigonometrically graded materials. The results obtained show that the analysis used to transform the variable coefficients equation into the constant coefficients equation is valid, and the mixed LT-BEM is easy to implement for obtaining the numerical solutions. The numerical solutions are verified by showing their accuracy and steady state. For symmetric problems, the symmetry of solutions is also justified. Moreover, the effect of the anisotropy and inhomogeneity of the material on the solutions are also shown, as to suggest that it is important to take the anisotropy and inhomogeneity into account when doing experimental studies.
Keywords
transient; diffusion convection reaction; anisotropic; functionally graded materials; simulation
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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