Dynamic Mode Decomposition – the step beyond POD
Dynamic Mode Decomposition (DMD) is the long-awaited research tool for advanced flow stability analysis – the missing link between experiments and stability calculations. One can perform temporal or spatial flow stability calculations using only experimental data as input. The technique’s capabilities are demonstrated here on time-resolved PIV data obtained in the wake of a cylinder in cross-flow.
Physical systems, such as fluid flow or mechanical vibrations, behave in characteristic patterns, known as modes. In a recirculating flow, for example, one may think of a hierarchy of vortices, a big main vortex driving smaller secondary ones and so on. The bulk of the motion of such systems can be faithfully described using only a few of those patterns. In a mathematical setting, these modes can be extracted from the governing equations using eigenvalue decomposition. But in many cases the mathematical model is very complicated or not available at all. In an experiment, the mathematical description is not at hand, and one has to rely on measured data only.
The Dynamic Mode Decomposition is a mathematical method to extract the relevant modes from experimental data, without any reliance on governing equations. It can thus be applied to any dynamic phenomenon that is described by appropriate data.
With this new advanced post-processing tool you will be able to conduct:
- temporal stability analysis
- spatial stability analysis
- subdomain analysis (even unstructured)
- three-dimensional analysis from two-dimensional slices
- receptivity analysis
- transient nonmodal growth and pseudospectra
What is the difference between Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD)?
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Proper Orthogonal Decomposition
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Dynamic Mode Decomposition
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- coherent structures based on spatial (or temporal) decorrelation
- temporal dynamics and phase information need to be tediously reconstructed
- ranking by energy content
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- modal structures based on temporal (or spatial) linear evolution dynamics
- temporal dynamics and phase and growth/decay information are readily available
- ranking by growth rate (stability)
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Figure 1: Animation of the velocity field behind a cylinder (flow is from right to left, colour represents vector length)
Figure 2: Higher dynamic modes that show the creation of vortices and the upward and downward shedding (colour represents vector length)
Figure 3: Complex spectrum of the velocity field. Lambda{r} represents the growth rate of the modes (positive values represent dynamically unstable modes). Lambda{i} represents the frequency of the modes. Note that lambda{i} is always present in pairs.
More information
Please stay tuned to our website until the official product launch during the 61st Annual DFD Meeting, San Antonio, Texas, November 23rd–25th, 2008. There is more exciting news to come!
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