论文标题
线性力矩模型近似Knudsen层
Linear Moment Models to Approximate Knudsen Layers
论文作者
论文摘要
我们为线性矩系统的半空间提出了一个良好的麦克斯韦型边界条件。作为鲍尔茨曼方程的降低，矩方程可用于模型在固体壁附近的knudsen层，在该壁上应处方适当的边界条件。利用正交分解，我们用阻尼项与系统分开零件，然后在其上施加一类新的麦克斯韦型边界条件。由于新的边界条件，我们表明半空间边界值问题接受了具有明确表达式的独特解决方案。立即，实现了线性力矩系统的良好性。我们将程序应用于Shakhov碰撞项的经典流问题，例如速度滑移和温度跳跃问题。该模型只能使用少量时间以很高的精度捕获Knudsen层。
We propose a well-posed Maxwell-type boundary condition for the linear moment system in half-space. As a reduction of the Boltzmann equation, the moment equations are available to model Knudsen layers near a solid wall, where proper boundary conditions should be prescribed. Utilizing an orthogonal decomposition, we separate the part with a damping term from the system and then impose a new class of Maxwell-type boundary conditions on it. Due to the new boundary condition, we show that the half-space boundary value problem admits a unique solution with explicit expressions. Instantly, the well-posedness of the linear moment system is achieved. We apply the procedure to classical flow problems with the Shakhov collision term, such as the velocity slip and temperature jump problems. The model can capture Knudsen layers with very high accuracy using only a few moments.
