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首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >Discussion on numerical stability and boundedness of convective discretized scheme
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Discussion on numerical stability and boundedness of convective discretized scheme

机译：对流离散方案的数值稳定性和有界性的讨论

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摘要

Existing methods for analyzing the stability of a discretized scheme for convection-diffusion terms are usually based on five assumptions, i.e., one-dimensional, linear, first kind of boundary condition, source term free, and uniform grid system. In this article we examine numerically whether deviation from one of the assumptions may enhance the stability of the discretized scheme. The second part of the article is devoted to the criterion of convective boundedness. It is shown that the convective boundedness criterion (CBC) proposed by Gaskell and Lau is only a sufficient condition. Another region in the normalized variable diagram is proposed within which any scheme defined is convectively bounded. Three new bounded high-resolution schemes defined in this region, SBECBC1, 2, and 3, are proposed, and numerical experiments for two advection problems and one diffusion-convection problem demonstrate the high-resolution ability of the SBECBCs for a sharp change in scalar profile. [References: 27]
机译：用于分析对流扩散项离散化方案的稳定性的现有方法通常基于五个假设，即一维，线性，第一类边界条件，无源项和统一网格系统。在本文中，我们从数值上检查了偏离其中一个假设是否可以增强离散化方案的稳定性。本文的第二部分致力于对流有界性的判据。结果表明，Gaskell和Lau提出的对流有界准则只是一个充分条件。提出了归一化变量图中的另一个区域，在该区域内定义的任何方案都是对流约束的。提出了在该区域定义的三种新的有界高分辨率方案SBECBC1、2和3，并且通过对两个对流问题和一个扩散对流问题的数值实验证明了SBECBC的高分辨率能够处理标量的急剧变化。个人资料。 [参考：27]

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