Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier-Stokes equations
Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier-Stokes equations
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DOI：
10.1016/j.jcp.2016.05.037
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发表时间：
2015-04
期刊：
影响因子：
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通讯作者：
Maciej Balajewicz;I. Tezaur;E. Dowell
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文献类型：
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作者：
Maciej Balajewicz;I. Tezaur;E. Dowell
为了使基于投影的流体流动降阶模型（ROM）稳定和准确，必须考虑截断子空间的动态特性。本文提出了一种稳定和增强基于投影的流体ROM的方法，其中截断模式占forpriority通过投影子空间的最小旋转。注意力集中在完整的非线性可压缩Navier-Stokes方程在特定的体积形式作为一个更一般的制定与通用的非线性问题的一步。与传统方法不同，不需要经验湍流模型项，并且保持ROM与导出ROM的Navier-Stokes方程之间的一致性。在数学上，该方法被制定为一个跟踪最小化问题的Stiefel流形。再生以及预测能力的方法进行了评估，对几个可压缩流问题，包括一个问题，涉及层流翼型与高攻角，和通道驱动的空腔流问题。
For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted fora priorivia a minimal rotation of the projection subspace. Attention is focused on the full non-linear compressible Navier–Stokes equations in specific volume form as a step toward a more general formulation for problems with generic non-linearities. Unlike traditional approaches, no empirical turbulence modeling terms are required, and consistency between the ROM and the Navier–Stokes equation from which the ROM is derived is maintained. Mathematically, the approach is formulated as a trace minimization problem on the Stiefel manifold. The reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems, including a problem involving laminar flow over an airfoil with a high angle of attack, and a channel-driven cavity flow problem.