空间变系数和不可压缩流非定常各向异性扩散对流方程的数值模拟

IF 0.7 Q2 MATHEMATICS Tamkang Journal of Mathematics Pub Date : 2021-11-10 DOI:10.5556/j.tkjm.54.2023.4069
M. Azis
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引用次数: 0

摘要

本文讨论了与功能梯度介质有关的空间变系数各向异性扩散对流方程,并采用拉普拉斯变换与边界元法相结合的方法求出数值解。变系数方程转化为常系数方程。然后对常系数方程进行拉普拉斯变换,使时间变量消失。因此,拉普拉斯变换方程可以写成一个涉及无时基本解的纯边界积分方程。因此,采用标准边界元法,利用边界积分方程求数值解。最后利用Stehfest公式对所得结果进行数值反变换,得到时间变量下的解。对于扩散对流方程控制的各向异性功能梯度介质的非定常问题,拉普拉斯变换与边界元相结合的方法易于实现、高效、准确。
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Numerical Simulation for Unsteady Anisotropic-Diffusion Convection Equation of Spatially Variable Coefficients and Incompressible Flow
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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期刊介绍: To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
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