# Numerical Simulation for Unsteady Anisotropic-Diffusion Convection Equation of Spatially Variable Coefficients and Incompressible Flow
> Azis M.I.

URL kanonis: https://discover.unhas.ac.id/publications/pub_scopus_85122343858
Jurnal / Konferensi: Tamkang Journal of Mathematics
Tahun terbit: 2021
DOI: https://doi.org/10.5556/j.tkjm.54.2023.4069
ISSN: 00492930
Kuartil SJR: Q4
Citations: 0

## Authors
- Azis M.I.

## Abstract
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.

## Keywords
- Mathematics
- Laplace transform
- Laplace's equation
- Mathematical analysis
- Convection–diffusion equation
- Green's function for the three-variable Laplace equation
- Diffusion equation
- Variable (mathematics)
- Boundary element method
- Constant (computer programming)
- Method of fundamental solutions
- Integral equation
- Boundary value problem
- Inverse Laplace transform
- Finite element method
- Singular boundary method
- Physics
- Thermodynamics
- Computer science
- Service (business)
- Economics
- Economy
- Programming language

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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