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首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >Design of high-order difference scheme and analysis of solution characteristics - Part I: General formulation of high-order difference schemes and analysis of convective stability
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Design of high-order difference scheme and analysis of solution characteristics - Part I: General formulation of high-order difference schemes and analysis of convective stability

机译：高阶差分格式的设计与解特征分析-第一部分：高阶差分格式的一般表示与对流稳定性分析。

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摘要

In this article, a general design method of second-order difference schemes is presented. By this method, we can easily design any second-order or higher-order difference scheme instead of using complex Lagrange interpolation methods or spline functions. Moreover, it is proved that all existing second-order difference schemes in numerical heat transfer fit this general design style. In addition, based on this general style of second-order scheme, the general style of a second-order absolutely stable scheme is deduced, and the stability definitions are shown in a normalized variable diagram. Finally, through studying the solution characteristics of 14 second-order difference schemes, it is found that, to second order precise, absolutely stable schemes obtained from the general method can achieve good convergence even when the grid Pelect number reaches 100,000. However, at the same time, the false diffusion of the scheme tends to increase along with the increasing value of ai (coefficient in the interface variable definition).
机译：本文提出了一种通用的二阶差分格式设计方法。通过这种方法，我们可以轻松设计任何二阶或更高阶差分方案，而不用使用复杂的Lagrange插值方法或样条函数。此外，事实证明，所有现有的数值传热中的二阶差分方案都符合这种通用设计风格。另外，基于这种二阶方案的一般风格，推导了二阶绝对稳定方案的一般风格，并在归一化变量图中显示了稳定性定义。最后，通过研究14种二阶差分方案的求解特性，发现，即使当网格Pelect数达到100,000时，用通用方法获得的绝对稳定方案也能达到良好的收敛性。但是，与此同时，该方案的错误扩散往往会随着ai值（接口变量定义中的系数）的增加而增加。

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