In the classical literature high order semi-Lagrangian schemes proposed for solving the BGK model of Boltzmann equation suffer from the phenomenon of order reduction when the Knudsen number becomes zero, i.e. in the fluid regime. In this brief note we provide local estimates with respect to small Knudsen number, which enables us to understand the order reduction phenomenon.

中文翻译：

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玻尔兹曼方程BGK模型半拉格朗日方法的降阶

在经典文献中，为求解 Boltzmann 方程的 BGK 模型而提出的高阶半拉格朗日方案会遇到当 Knudsen 数变为零时，即在流体状态下的阶数减少现象。在这个简短的说明中，我们提供了关于小 Knudsen 数的局部估计，这使我们能够理解阶数减少现象。