Direct modeling for computational fluid dynamics
Direct modeling for computational fluid dynamics
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DOI：
10.1007/s10409-015-0453-2
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发表时间：
2015-05
影响因子：
3.5
通讯作者：
K. Xu
中科院分区：
文献类型：
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作者：
K. Xu
所有的流体动力学方程在它们的模拟尺度下都是有效的，如Boltzmann方程的粒子平均自由程和平均碰撞时间尺度以及NS方程的流体动力学尺度。当前的计算流体动力学（CFD）主要研究偏微分方程（PDE）的数值求解，其目的是获得偏微分方程的精确解。在这样的CFD实践中，很难开发出一个统一的方案，连续地涵盖从动力学到流体动力学尺度的流动物理，因为没有这样的控制方程可以从Boltzmann模型平滑地过渡到NS模型。流体动力学的研究需要超越传统的数值偏微分方程。新兴的工程应用，如近空间飞行的飞行器设计和微型设备中的流动和传热，确实需要进一步扩展气体动力学的概念到更大的物理现实领域，而不是传统的可区分的控制方程。在目前阶段，由于缺乏适当的工具，非平衡流物理尚未得到很好的探索或清楚的理解。不幸的是，在目前的数值偏微分方程的方法，这是很难开发这样一个有意义的工具，由于缺乏有效的偏微分方程。为了构造类似于构造Boltzmann或NS控制方程的建模过程的多尺度和多物理场模拟方法，数值算法的开发应基于物理建模的第一原理。在本文中，而不是遵循传统的数值偏微分方程路径，我们介绍了直接建模的CFD算法开发的原则。由于所有的计算都是在有限单元分辨率的离散空间中进行的，因此要模拟的流动物理必须在网格尺寸和时间步长尺度上进行。在这里，CFD或多或少是离散数值演化方程的直接构造，其中网格尺寸和时间步长将在建模过程中发挥动态作用。通过改变网格尺寸与局部粒子平均自由程的比值，该格式将捕捉从粒子运动输运和碰撞到流体动力学波传播的流动物理过程。在直接模拟的基础上，在统一的气体动力学方案中将捕获流动运动的连续动力学。该方案可以忠实地用于研究未探索的非平衡流物理在transition region.Graphical摘要最成功的控制方程的气体动力学的Navier-Stokes（NS）方程在流体动力学的规模和Boltzmann方程在动力学的规模。在这两个极限尺度之间，没有公认的非平衡流描述方程。如图2所示，动力学方程确定粒子输运和碰撞，流体动力学方程捕获波传播。计算流体动力学的直接建模是在从动力学到流体动力学的所有尺度上构造一个连续谱的控制方程。
AbstractAll fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. The current computational fluid dynamics (CFD) focuses on the numerical solution of partial differential equations (PDEs), and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numerical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require further expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional distinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools. Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of constructing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm development. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be modeled has to be done in the mesh size and time step scales. Here, the CFD is more or less a direct construction of discrete numerical evolution equations, where the mesh size and time step will play dynamic roles in the modeling process. With the variation of the ratio between mesh size and local particle mean free path, the scheme will capture flow physics from the kinetic particle transport and collision to the hydrodynamic wave propagation. Based on the direct modeling, a continuous dynamics of flow motion will be captured in the unified gas-kinetic scheme. This scheme can be faithfully used to study the unexplored non-equilibrium flow physics in the transition regime.Graphical AbstractThe most successful governing equations for gas dynamics are the Navier-Stokes (NS) equations in the hydrodynamic scale and the Boltzmann equation in the kinetic scale. Between these two limiting scales, there is no well-accepted equations for non-equilibrium flow description. As shown in Fig.2, the kinetic equation identifies particle transport and collision, and the hydrodynamic ones capture wave propagation. The direct modeling for computational fluid dynamics is to construct a continuous spectrum of governing equation in all scales from kinetic to hydrodynamic scales.