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首页> 外文期刊>Journal of Computational Physics >A unified gas kinetic scheme with moving mesh and velocity space adaptation
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A unified gas kinetic scheme with moving mesh and velocity space adaptation

机译：具有运动网格和速度空间自适应的统一气体动力学方案

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There is great difficulty for direct Boltzmann solvers to simulate high Knudsen number flow due to the severe steep slope and high concentration of the gas distribution function in a local particle velocity space. Local mesh adaptation becomes necessary in order to make the Boltzmann solver to be a practical tool in aerospace applications. The present research improves the unified gas-kinetic scheme (UGKS) in the following two aspects. First, the UGKS is extended in a physical space with moving mesh. This technique is important to study a freely flying object in a rarefied environment. Second, the adaptive quadtree method in the particle velocity space is implemented in the UGKS. Due to the new improvements in the discretization of a gas distribution function in the six dimensional phase space, the adaptive unified gas kinetic scheme (AUGKS) is able to deal with a wide range of flow problems under extreme flying conditions, such as the whole unsteady flying process of an object from a highly rarefied to a continuum flow regime. After validating the scheme, the capability of AUGKS is demonstrated in the following two challenge test cases. The first case is about the free movement of an ellipse flying at initial Mach number 5 in a rarefied flow at different Knudsen numbers. The force on the ellipse and the unsteady trajectory of the ellipse movement are fully captured. The gas distribution function around the ellipse is analyzed. The second case is about the study of unsteady flight of a nozzle under a bursting process of the compressed gas expanding into a rarefied environment. Due to the strong expansion wave and the huge density difference between interior and exterior regions around the nozzle, the particle distribution function changes dramatically in the particle velocity space. The use of an adaptive velocity space in the AUGKS becomes necessary to simulate such a flow and to control the computational cost to a tolerable level. The second test is a challenge problem for any existing rarefied flow solver.
机译：直接Boltzmann求解器很难模拟高Knudsen数流，这是因为局部粒子速度空间中的陡峭陡坡和气体分布函数的高度集中。为了使Boltzmann求解器成为航空航天应用中的实用工具，必须进行局部网格自适应。本研究从以下两个方面改进了统一气体动力学方案（UGKS）。首先，UGKS在具有移动网格的物理空间中扩展。该技术对于在稀疏环境中研究自由飞行的物体非常重要。其次，在UGKS中实现了粒子速度空间中的自适应四叉树方法。由于对六维相空间中的气体分布函数离散化的新改进，自适应统一气体动力学方案（AUGKS）能够处理极端飞行条件下的各种流动问题，例如整个不稳定物体从高度稀疏到连续流动状态的飞行过程。验证方案后，在以下两个挑战测试案例中展示了AUGKS的功能。第一种情况是在初始马赫数为5的椭圆中，在稀有流中以不同的努德森数自由飞行的自由运动。椭圆上的力和椭圆运动的不稳定轨迹被完全捕获。分析了椭圆周围的气体分布函数。第二种情况是关于在压缩气体膨胀成稀疏环境的破裂过程中喷嘴的不稳定飞行的研究。由于强大的膨胀波和喷嘴周围内部和外部区域之间的巨大密度差，粒子分布函数在粒子速度空间中发生了巨大变化。在AUGKS中使用自适应速度空间对于模拟这样的流并将控制成本控制在可容忍的水平变得很有必要。对于任何现有的稀疏流求解器，第二项测试都是一个挑战性问题。

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