Spectral Proper Orthogonal Decomposition (SPOD) decomposes the space-time dataset into mutually orthogonal modes. Each mode oscillates at a single frequency and is ranked by the energy level. This repository contains a Pythonic realization of SPOD and its applications to a range of fluid mechanics problems.
The SPOD toolkit in this repository was originally written for analyzing compressor tip leakage flows [1], which is included as one of the example cases. Other example cases include a backward-facing step flow [2] and a jet flow [3]. If this script appears useful for your research, an explicit mention of the work [1] would be highly appreciated. If you are using any data from the example cases, please refer to the corresponding publications mentioned above.
The SPOD workflow is illustrated in the following figure. For a detailed understanding of SPOD, the readers are redirected to: (1) SPOD theory [4]; (2) SPOD algorithm [5]; (3) SPOD applications [6].
git clone https://github.com/HexFluid/spod_python.git
Download from this link and then unzip it.
Launch a terminal (UNIX) or an Anaconda Prompt (Windows) window and change directory to spod_python. Run the following command line to install/upgrade the prerequisite Python packages.
pip install -r requirements.txt
Run the following script with Python 3 to load the data:
import h5py
import os
current_path = os.getcwd() # assuming Python launched in the 'spod_python' dir
data_path = os.path.join(current_path,'examples','bstep_data','bstepDDES.h5')
h5f = h5py.File(data_path,'r')
data = h5f['data'][:] # flow field data
dt = h5f['dt'][0] # unit in seconds
h5f.close()Run the following script to obtain SPOD results:
import spod
spod.spod(data,dt,current_path,weight='default',nOvlp='default',window='default',method='fast')
SPOD_LPf = h5py.File(os.path.join(current_path,'SPOD_LPf.h5'),'r') # load data from h5 format
L = SPOD_LPf['L'][:,:] # modal energy E(f, M)
P = SPOD_LPf['P'][:,:,:] # mode shape
f = SPOD_LPf['f'][:] # frequency
SPOD_LPf.close()Finally, run the following script to visualize the SPOD spectrum:
fig = spod.plot_spectrum(f,L,hl_idx=5)Expected results:
For more detailed postprocess examples including plotting mode shapes and flow field reconstructions, please refer to the examples.
SPOD is a memory-demanding algorithm. Before running it on your own case, please check if the memory requirement has been met. The table below helps estimate the memory usage of new cases. All data are obtained by running spod.spod in 'fast' mode.
| Case | Snapshot count | Data count / snapshot | Memory usage | CPU time |
|---|---|---|---|---|
| #1 | 2500 | 6825 | 0.77 GB | 2.5 s |
| #2 | 800 | 3580 | 0.29 GB | 0.4 s |
| #3 | 800 | 14320 | 0.56 GB | 1.6 s |
| #4 | 1701 | 7086 | 0.53 GB | 1.6 s |
| #5 | 1701 | 36377 | 2.20 GB | 8.6 s |
| #6 | 1701 | 468442 | 26.72 GB | 877.9 s |
| #7 | 1701 | 2407465 | 136.87 GB | 3645.5 s |
For fluid mechanics applications, the problem size can be reduced by selecting data every few grid points and time steps. This approach degrades the resolution in small scales but preserves that in the large scales. It is the large scales that are of interest to SPOD.
A memory-efficient SPOD algorithm named streaming SPOD [5] will be implemented in this package in later versions.
. |-- examples | |-- bstep_data | | |-- singlevar_results | | |-- multivar_results | | |-- bstepDDES.h5 | |-- comp_data | | |-- singlevar_results | | |-- compDDES.h5 | |-- jet_data | | |-- singlevar_results | | |-- jetLES.h5 | |-- 00_jet_single_var.py | |-- 01_bstep_single_var.py | |-- 02_bstep_multi_var.py | |-- 03_comp_single_var.py |-- LICENSE |-- requirements.txt |-- SPOD_quickstart_result.png |-- SPOD_schematic.png |-- spod.py
- spod.py: main script of spod_python
- SPOD_schematic.png: graphical illustration of SPOD algorithm
- SPOD_quickstart_result.png: SPOD energy spectrum of the quick start case
- requirements.txt: a list of prerequisite Python libraries
- LICENSE: license file
- examples
- bstep_data
- singlevar_results: postprocess results of the single variable case
- multivar_results: postprocess results of the multiple variable case
- bstepDDES.h5: flow field and grid data (HDF5 format)
- comp_data
- singlevar_results: postprocess results of the single variable case
- compDDES.h5: pressure and grid data of a compressor rotor blade (HDF5 format)
- jet_data
- singlevar_results: postprocess results of the single variable case
- jetLES.h5: flow field and grid data (HDF5 format)
- 00_jet_single_var.py: tutorial script for single variable SPOD of the jet case
- 01_bstep_single_var.py: tutorial script for single variable SPOD of the backward-facing step case
- 02_bstep_multi_var.py: tutorial script for multiple variable SPOD of the backward-facing step case
- 03_comp_single_var.py: tutorial script for single variable SPOD of the compressor rotor blade case
- bstep_data
[1] He, X., Fang, Z., Vahdati, M. & Rigas, G., (2021). Spectral proper orthogonal decomposition of compressor tip leakage flow. ETC Paper No. ETC2021-491. (under review) [preprint]
[2] He, X., Zhao, F., & Vahdati, M. (2021). Detached eddy simulation: recent development and application to compressor tip leakage flow. ASME Paper No. GT2021-59077. (under review) [preprint]
[3] Brès, G. A., Jordan, P., Jaunet, V., Le Rallic, M., Cavalieri, A. V., Towne, A., Lele, S., Colonius, T., & Schmidt, O. T. (2018). Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets. Journal of Fluid Mechanics, 851, 83-124. [DOI]
[4] Towne, A., Schmidt, O. T., & Colonius, T. (2018). Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. Journal of Fluid Mechanics, 847, 821-867. [DOI]
[5] Schmidt, O. T., & Towne, A. (2019). An efficient streaming algorithm for spectral proper orthogonal decomposition. Computer Physics Communications, 237, 98-109. [DOI]
[6] Schmidt, O. T., & Colonius, T. (2020). Guide to spectral proper orthogonal decomposition. AIAA Journal, 58(3), 1023-1033. [DOI]