论文标题
具有正确prandtl编号的ES-BGK模型的固定流量
Stationary Flows of the ES-BGK model with the correct Prandtl number
论文作者
论文摘要
椭圆形BGK模型（ES-BGK）是BGK模型的一般版本，其中BGK模型的放松操作员的本地Maxwellian扩展到具有Prandtl参数$ν$的椭圆形高斯，因此可以在Navier-Stokes limip中计算出正确的传输系数。在这项工作中，我们考虑了具有混合边界条件的平板中ES-BGK模型的固定溶液的存在和独特性。从下方对温度张量的均匀控制中出现了关键困难之一。在非关键的情况下，$（-1/2 <ν<1）$，我们利用温度张量等效于该范围的温度的属性。在关键情况下，$（ν= -1/2）$，在这种等价关系破裂的情况下，我们观察到，可以通过$ x $方向以$ x $方向的散装速度大小来控制边界通量的差异，这使得可以从下方绑定温度张量。
Ellipsoidal BGK model (ES-BGK) is a generalized version of the BGK model where the local Maxwellian in the relaxation operator of the BGK model is extended to an ellipsoidal Gaussian with a Prandtl parameter $ν$, so that the correct transport coefficients can be computed in the Navier-Stokes limit. In this work, we consider the existence and uniqueness of stationary solutions for the ES-BGK model in a slab imposed with the mixed boundary conditions. One of the key difficulties arise in the uniform control of the temperature tensor from below. In the non-critical case $(-1/2<ν<1)$, we utilize the property that the temperature tensor is equivalent to the temperature in this range. In the critical case, $(ν=-1/2)$, where such equivalence relation breaks down, we observe that the size of bulk velocity in $x$ direction can be controlled by the discrepancy of boundary flux, which enables one to bound the temperature tensor from below.
