This paper analyzes three formulations of the tensor artificial viscosity in two-dimensional Cartesian geometry, namely, Campbell-Shashkov viscosity, Lipnikov-Shashkov viscosity and Wendroff viscosity. We first present a general derivation of these three ones. The discrepancy between Campbell-Shashkov viscosity and Lipnikov-Shashkov viscosity is then provided, followed by the non-triviality proof of both viscosities. Some numerical results are provided to verify the analysis at the end.

中文翻译：

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二维笛卡尔几何中张量人工粘度的三种公式分析

本文分析了二维笛卡尔几何中张量人工黏度的三种公式，即坎贝尔-沙什科夫黏度，利普尼科夫-沙什科夫黏度和温德洛夫黏度。我们首先给出这三个的一般推导。然后提供了坎贝尔-肖什科夫粘度和利普尼科夫-肖什科夫粘度之间的差异，随后给出了两种粘度的非平凡性证明。最后提供一些数值结果来验证分析。