Low-rank compression of resolvent operators for high-Re flows
Abstract
Theoretical analysis of turbulent flows has been a challenge due to its complex nonlinear dynamics that span across a wide range of spatial and temporal scales. With ever increasing computational resources being readily available to fluid mechanicians, access to high-fidelity flow field data has become possible. However, extracting physical insights from data beyond the traditional statistical analysis for their uses in applications including flow control or system designs has been limited. This is due to the fact that analysis can be burdened by the extremely large degrees of freedom of turbulent flows that require significant computational power and memory allocations. In recent years, resolvent analysis has gained interest from the fluid mechanics community for its ability to reveal the input-output relationship with respect to a base state, including timeaveraged turbulent flow. Resolvent analysis is based on the concept of a particular solution under forcing. For this reason, resolvent analysis provides insights on how the flow responds to harmonic input to the system as well as the transient dynamics. As such, the resolvent analysis becomes a very attractive tool for characterizing, modeling, and controlling high-dimensional turbulent flows. Noteworthy here is that resolvent analysis can be performed about time-averaged turbulent base flows if fluctuations about the base states are statistically stationary. Resolvent analysis stands out as essentially the only operator-based modal analysis techniques that can handle practical engineering flows at high Reynolds numbers. However, the applications of resolvent analysis are generally restricted to simple laminar flows or flows of moderate Reynolds numbers. The time is now ripe to address the curse of dimensionality and extend the applicability of resolvent analysis. With the so-called Òbig dataÓ and Òbig operatorsÓ being the focus of analysis by applied mathematicians and data scientists in recent years, ground breaking concepts have emerged in the development of computationally tractable techniques that can help expand the horizon of resolvent analysis for high-dimensional flows. Included in these recent advances are randomized numerical linear algebra, compression of low-rank operators, and discrete adjoint analysis. In this proposed work, we combine the latest concepts from data science to revisit the original resolvent analysis and reformulate its algorithm for computational speedup and reduction in memory requirement. The proposed eÀort will focus not only on the computational issues but also on lowering the hurdle for implementing resolvent analysis into preexisting DNS/LES codes. The current work will develop theoretical formulations for performing resolvent analysis with the ability to separate time-scales from multi-physics flow problems. Moreover, the results from resolvent analysis at high-Reynolds number require some level of interpretability. As flows become more complex, one often encounters increased levels of incoherence in the state variables. In these situations, open questions arise about how resolvent analysis techniques should be utilized to examine the flow physics. The latter part of the project will focus on disseminating the developed low-rank compression techniques appropriate for complex high-dimensional fluid flows by seeking advice from our industrial partners. Robustness of developed techniques for data quality will also be examined for novel data structures.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jun 25, 2021
- Source ID
- W911NF2110060
Entities
People
- Kunihiko Taira
Organizations
- Army Contracting Command
- United States Army
- University of California, Los Angeles