多原子分子椭球BGK模型半拉格朗日格式的收敛性估计
Convergence estimates of a semi-Lagrangian scheme for the ellipsoidal BGK model for polyatomic molecules
摘要：
本文对多原子椭球BGK模型提出了一种新的半拉格朗日格式。为了避免对流项和小Knudsen数带来的时间步长限制，我们将对流项的半拉格朗日方法与松弛项的隐式处理相结合。我们展示了如何显式地解决隐式步骤，从而获得一个有效的和稳定的计划，任何努森数。我们还得到了一个明确的误差估计的收敛性所提出的计划的每一个固定值的Knudsen数。
英文摘要：
In this paper, we propose a new semi-Lagrangian scheme for the polyatomic ellipsoidal BGK model. In order to avoid time step restrictions coming from convection term and small Knudsen number, we combine a semi-Lagrangian approach for the convection term with an implicit treatment for the relaxation term. We show how to explicitly solve the implicit step, thus obtaining an efficient and stable scheme for any Knudsen number. We also derive an explicit error estimate on the convergence of the proposed scheme for every fixed value of the Knudsen number.
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