Computation of High Reynolds Number Flows Using Vorticity Confinement: I. Formulation
Computation of High Reynolds Number Flows Using Vorticity Confinement: I. Formulation
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使用涡度约束计算高雷诺数流：I. 公式
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发表时间：
2005
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影响因子：
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通讯作者：
Lesong Wang
中科院分区：
文献类型：
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作者：
J. Steinhoff;Nicholas F. Lynn;Lesong Wang
本文描述了一种计算方法，它是为捕捉高雷诺数不可压缩流中的薄涡区而设计的。涡度约束（VC）方法的主要目的是捕捉这些小尺度涡结构的基本特征，并直接在欧拉计算网格上用一种非常有效的差分方法模拟它们。从本质上讲，小尺度被建模为非线性孤立波，“生活”在格子上无限期。该方法允许对流结构在少至2个网格单元上建模，由于它们在长距离上不确定地对流，因此没有数值扩散，并且不需要合并或重新连接的特殊逻辑。它也可以作为一个非常有效的替代RANS模型的附着和分离的边界层和涡面和细丝。此外，该方法很容易允许无滑移条件下的边界被视为“浸入”表面在均匀的，不一致的网格，没有复杂的逻辑要求涉及“切”单元。本文介绍了VC的基本方法。这比以前提供的更为全面。VC与众所周知的冲击和接触不连续性捕获方法之间有密切的相似之处。这些讨论是为了解释VC背后的B概念，因为它比传统的CFD方法更先进。探讨了VC在LES近似中对湍流流动的高效计算提供的一些可能性。这是因为VC在网格单元上方的尺度上具有负耗散的能力，但它会饱和，不会导致发散。此功能允许1。近似消除了数值扩散，从而可以避免更复杂的高阶低耗散的方案。然后可以捕获网格单元级的小尺度涡结构，从而非常有效地利用网格上的可用自由度。2.后向散射的近似处理。这涉及以自然的方式将（建模的）亚网格动能添加到流中，而不需要随机强迫，并且恢复由（隐式）滤波去除的一些不稳定性。虽然它用于复杂的、附加的和分离的流动以及尾涡已有多年，但它作为大涡模拟方法的使用是相对较新的。在文献[0]中，给出了一些LES的初步结果。
A computational method is described that has been d esigned to capture thin vortical regions in high Re ynolds number incompressible flows. The principal objecti ve of the method—Vorticity Confinement (VC)—is to capture the essential features of these small-scale vortical structures and model them with a very efficient difference met hod directly on an Eulerian computational grid. Essentially, th e small scales are modeled as nonlinear solitary waves that “live” on the lattice indefinitely. The method allo ws convecting structures to be modeled over as few as 2 grid cells with no numerical spreading as they convect indefin itely over long distances, with no special logic re quired for merging or reconnection. It also serves as a very efficient substitute for RANS models of attached a nd separating boundary layers and vortex sheets and filaments. Fu rther, the method easily allows boundaries with no- slip conditions to be treated as “immersed” surfaces in uniform, non-conforming grids, with no requirements for complex logic involving “cut” cells. In this paper a description of the basic VC method is given. This is more comprehensive than has been previously available. There are close analogies between VC and well-known shock and contact discontinuity capturi ng methodologies. These are discussed to explain the b asic ideas behind VC, since it is somewhat differen t than conventional CFD methods. Some of the possibilitie s that VC offers towards very efficient computation of turbulent flows in the LES approximations are explored. Thes e stem from the ability of VC to act as a negative dissipation at scales just above a grid cell, but that saturates a nd does not lead to divergence. This feature allows 1. approximate cancellation of numerical diffusion, so that more complex, high order-low dissipation s chemes can be avoided. Small-scale vortical structures at the grid cell level can then be captured, resulting in very efficient use of the available degrees of freedom o n the grid. 2. approximate treatment of backscatter. This invol ves the addition of (modeled) subgrid kinetic energ y to the flow in a natural way, without requiring stochastic forcing, and which restores some of the instabilit ies that are removed by the (implicit) filtering. Although used for a number of years for complex, at tached and separating flows, and trailing vortices, its use as an LES method is relatively recent. In Ref. [0], some initial LES results are presented.