A flexible gradient method for unstructured‐grid solvers,International Journal for Numerical Methods in Fluids

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A flexible gradient method for unstructured‐grid solvers
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-01-10 , DOI: 10.1002/fld.4955
Hiroaki Nishikawa ₁

Affiliation

In this short note, we introduce a flexible explicit gradient method for efficient and robust unstructured‐grid computations. As shown, the method serves as a memory‐efficient alternative to the multiple least‐squares gradients needed by conflicting requirements for inviscid, viscous, and turbulence‐model source terms (e.g., vorticity), in practical computational‐fluid‐dynamics solvers. The flexible method computes the gradient of a numerical solution in a cell by averaging the face gradients defined by the alpha‐damped formula with a parameter

α_{g}

based on a single set of least‐squares gradients. We show that a small

α_{g}

gives less‐accurate gradients similar to unweighted least‐squares gradients, and a large

α_{g}

produces accurate gradients similar to weighted least‐squares gradients. Therefore, it allows us to obtain two types of gradients by changing the value of

α_{g}

without storing more than one set of least‐squares coefficients. Moreover, the method yields fourth‐order accurate gradients with

α_{g} = 10 / 3

on a regular grid. The method is demonstrated for two‐dimensional inviscid and viscous flows on unstructured grids.

中文翻译：

非结构化网格求解器的灵活梯度方法

在本简短说明中，我们介绍了一种灵活的显式梯度方法，用于有效且健壮的非结构化网格计算。如图所示，在实际的计算流体动力学求解器中，该方法可以有效地替代无粘性，粘性和湍流模型源项（例如涡度）的需求冲突所需要的多个最小二乘梯度。灵活的方法通过将由alpha阻尼公式定义的面部梯度与参数求平均值来计算单元格中数值解的梯度