Numerical solutions to anisotropic FGM BVPs governed by the modified Helmholtz type equation

Syam, Rafiuddin; Fahruddin,; Azis, Moh. Ivan; Hayat, Amaury

doi:10.1088/1757-899x/619/1/012061

Cited by 3 publications

(1 citation statement)

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“…Rap et al [23], Ravnik and Škerget [25,26], Li et al [18] and Pettres and Lacerda [22] considered the case of isotropic diffusion and variable coefficients (inhomogeneous media). Recently Azis and co-workers had been working on steady state problems of anisotropic inhomogeneous media for several types of governing equations, for examples [5,32] for the modified Helmholtz equation, [4,14,24,30,27,11,17] for the diffusion convection reaction equation, [29,8,13,16] for the Laplace type equation, [10,2,20,21,15] for the Helmholtz equation.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation for Unsteady Anisotropic-Diffusion Convection Equation of Spatially Variable Coefficients and Incompressible Flow

Azis¹

2021

Tamkang J. Math.

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The anisotropic-diffusion convection equation of spatiallyvariable coefficients which is relevant for functionally graded mediais discussed in this paper to find numerical solutions by using acombined Laplace transform and boundary element method. The variablecoefficients equation is transformed to a constant coefficients equation.The constant coefficients equation is then Laplace-transformed sothat the time variable vanishes. The Laplace-transformed equationis consequently written in a pure boundary integral equation whichinvolves a time-free fundamental solution. The boundary integral equationis therefore employed to find numerical solutions using a standardboundary element method. Finally the results obtained are inverselytransformed numerically using the Stehfest formula to get solutionsin the time variable. The combined Laplace transform and boundaryelement method is easy to be implemented, efficient and accurate forsolving unsteady problems of anisotropic functionally graded mediagoverned by the diffusion convection equation.

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Section: Introductionmentioning

confidence: 99%

Numerical Simulation for Unsteady Anisotropic-Diffusion Convection Equation of Spatially Variable Coefficients and Incompressible Flow

Azis¹

2021

Tamkang J. Math.

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A boundary-only element method for 2D unsteady diffusion convection reaction problems of trigonometrically graded anisotropic materials

Azis

2021

International Journal for Computational Methods in Engineering

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Numerical solutions to Helmholtz equation of anisotropic functionally graded materials

Paharuddin

Sakka

Taba

et al. 2019

J. Phys.: Conf. Ser.

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In this paper, interior 2D-BVPs for anisotropic FGMs governed by the Helmholtz equation with Dirichlet and Neumann boundary conditions are considered. The governing equation involves diffusivity and wave number coefficients which are spatially varying. The anisotropy of the material is presented in the diffusivity coefficient. And the inhomogeneity is described by both diffusivity and wave number. Three types of the gradation function considered are quadratic, exponential and trigonometric functions. A technique of transforming the variable coefficient governing equation to a constant coefficient equation is utilized for deriving a boundary integral equation. And a standard BEM is constructed from the boundary integral equation to find numerical solutions. Some particular examples of BVPs are solved to illustrate the application of the BEM. The results show the accuracy of the BEM solutions, especially for large wave numbers. They also show coherence between the flow vectors and scattering solutions, and the effect of the anisotropy and inhomogeneity of the material on the BEM solutions.

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Numerical solutions to anisotropic FGM BVPs governed by the modified Helmholtz type equation

Cited by 3 publications

References 10 publications

Numerical Simulation for Unsteady Anisotropic-Diffusion Convection Equation of Spatially Variable Coefficients and Incompressible Flow

Numerical Simulation for Unsteady Anisotropic-Diffusion Convection Equation of Spatially Variable Coefficients and Incompressible Flow

A boundary-only element method for 2D unsteady diffusion convection reaction problems of trigonometrically graded anisotropic materials

Numerical solutions to Helmholtz equation of anisotropic functionally graded materials

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