@article{Azis_2023, title={Numerical simulation for unsteady anisotropic-diffusion convection equation of spatially variable coefficients and incompressible flow}, volume={54}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/4069}, DOI={10.5556/j.tkjm.54.2023.4069}, abstractNote={<p>The anisotropic-diffusion convection equation of spatially<br>variable coefficients which is relevant for functionally graded media<br>is discussed in this paper to find numerical solutions by using a<br>combined Laplace transform and boundary element method. The variable<br>coefficients equation is transformed to a constant coefficients equation.<br>The constant coefficients equation is then Laplace-transformed so<br>that the time variable vanishes. The Laplace-transformed equation<br>is consequently written in a pure boundary integral equation which<br>involves a time-free fundamental solution. The boundary integral equation<br>is therefore employed to find numerical solutions using a standard<br>boundary element method. Finally the results obtained are inversely<br>transformed numerically using the Stehfest formula to get solutions<br>in the time variable. The combined Laplace transform and boundary<br>element method is easy to be implemented, efficient and accurate for<br>solving unsteady problems of anisotropic functionally graded media<br>governed by the diffusion convection equation.</p>}, number={1}, journal={Tamkang Journal of Mathematics}, author={Azis, Moh.Ivan}, year={2023}, month={Feb.}, pages={1–20} }