Abstract

Various methods for the accurate approximation of the gradients entering the diffusion fluxes are considered. Linear combinations of the 2nd order difference schemes for a non-uniform mesh that transform into 4th order schemes in the uniform case are investigated. We also consider 3rd and 4th order schemes for approximating gradients on a non-uniform mesh in the normal and tangential directions to the cell face, respectively, based on Lagrange polynomials. The initial testing is carried out on one-dimensional functions: a smooth Gauss function and a piecewise linear function. Next, the schemes are applied in direct numerical simulation of the Taylor–Green vortex.

中文翻译：

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用于比例解析模拟的方案中的梯度近似方法的比较

摘要

考虑了用于精确近似进入扩散通量的梯度的各种方法。研究了非均匀网格的二阶差分方案的线性组合，该线性组合在均匀情况下转换为四阶方案。我们还基于拉格朗日多项式，分别考虑了三阶和四阶方案，这些方案分别用于近似非均匀网格上朝向单元格面的法线和切线方向上的梯度。初始测试是针对一维函数执行的：平滑高斯函数和分段线性函数。接下来，该方案被应用于泰勒-格林涡旋的直接数值模拟。