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首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >New unconditionally stable scheme for solving the convection-diffusion equation based on the Associated Hermite orthogonal functions
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New unconditionally stable scheme for solving the convection-diffusion equation based on the Associated Hermite orthogonal functions

机译：基于相关Hermite正交功能解决对流扩散方程的新无条件稳定方案

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摘要

In this article, a new unconditionally stable scheme, based on the Associated Hermite orthogonal functions combined with first-order upwind scheme (AH-FUS), is proposed for solving the convection-diffusion equation. To eliminate the time variable from the computations, the time derivatives are expanded by Hermite functions, and a Galerkin's temporal testing procedure is introduced to the expanded equation. A set of implicit difference equations are derived in AH domain under no convergent conditions, and the numerical results can be obtained by solving the expanded coefficients recursively. Two numerical examples were considered to verify the accuracy and the efficiency of the proposed scheme.
机译：在本文中，提出了一种基于相关的Hermite正交函数与一阶Upwind方案（AH-FU）组合的新的无条件稳定方案，用于解决对流扩散方程。 为了消除从计算中的时间变量，时间衍生物由Hermite函数扩展，并将Galerkin的时间测试程序引入扩展方程。 在没有收敛条件下，一组隐式差分方程在AH域中导出，并且可以通过递归求解扩展系数来获得数值结果。 认为两个数值例子验证了所提出的方案的准确性和效率。

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