We address a class of schemes for the Euler equations with the following features: the space discretization is staggered, possible upwinding is performed with respect to the material velocity only and the internal energy balance is solved, with a correction term designed on consistency arguments. These schemes have been shown in previous works to preserve the convex of admissible states and have been extensively tested numerically. The aim of the present paper is twofold: we derive a local total energy equation satisfied by the solutions, so that the schemes are in fact conservative, and we prove that they are consistent in the Lax-Wendroff sense.

中文翻译：

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欧拉方程一类交错有限体积法的保守性和弱一致性

我们解决了一类具有以下特征的欧拉方程方案：空间离散化是交错的，可能的逆风仅针对材料速度进行，并且解决了内部能量平衡，并根据一致性参数设计了一个校正项。这些方案在之前的工作中已经被证明可以保留可容许状态的凸性，并且已经进行了广泛的数值测试。本文的目的有两个：我们推导出一个由解满足的局部总能量方程，因此这些方案实际上是保守的，并且我们证明它们在 Lax-Wendroff 意义上是一致的。