复杂流体的混合连续介质-动力学模型
On a hybrid continuum-kinetic model for complex fluids
摘要：
在目前的工作中，我们首先介绍了一个通用的框架来模拟复杂的多尺度流体，然后专注于推导和分析一个新的混合连续动力学模型。特别是，我们结合等熵宏观模型的微观行为的动力学表示的质量和动量守恒。在引入一个小尺度后，利用Irving-Kirkwood公式计算了复应力张量。后者要求在平衡态附近的动力学分布的扩展和在时间上快而空间尺度上小的动力学上的连续均匀化。对于一个新的混合连续动力学模型的线性稳定性分析的结果表明，在相关的低速政权和不稳定的高速政权的高模式的条件稳定性。大量的数值实验证实，所提出的多尺度模型可以反映复杂流体的新现象，不存在于标准牛顿流体。因此，所提出的一般技术可以成功地用于导出新的有趣的系统相结合的宏观和微观结构的一个给定的物理问题。
英文摘要：
In the present work, we first introduce a general framework for modelling complex multiscale fluids and then focus on the derivation and analysis of a new hybrid continuum-kinetic model. In particular, we combine conservation of mass and momentum for an isentropic macroscopic model with a kinetic representation of the microscopic behaviour. After introducing a small scale of interest, we compute the complex stress tensor by means of Irving-Kirkwood formula. The latter requires an expansion of kinetic distribution around an equilibrium state and a successive homogenization over the fast in time and small in space scale dynamics. For a new hybrid continuum-kinetic model the results of linear stability analysis indicates a conditional stability in the relevant low-speed regimes and instability for high speed regimes for higher modes. Extensive numerical experiments confirm that the proposed multiscale model can reflect new phenomena of complex fluids not being present in standard Newtonian fluids. Consequently, the proposed general technique can be successfully used to derive new interesting systems combining the macro and micro structure of a given physical problem.
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