- Fixed bug in memory saving for POD,
N_modesintroduced, it is now possible to define the number of modes to compute for POD, mPOD and DMD,- Randomised SVD implemented as standard solver for the eigenvalue problems,
- DMD implemented!
- Improved printed messages,
- Possibility to control the parameter SAT as a self variable of the class. This lets the user control the largest number of modes that will be computed in each scale
MODULO (MODal mULtiscale pOd) is a software developed at the von Karman Institute to perform Multiscale Modal Analysis of numerical and experimental data using the Multiscale Proper Orthogonal Decomposition (mPOD).
The theoretical foundation of the decomposition is described in
- M.A. Mendez, M. Balabane, J.-M. Buchlin, Multiscale Proper Orthogonal Decomposition of Complex Fluid Flows, Journal of Fluid Mechanics, Vol 870, July 2019, pp. 988-1036. The pre-print is available at https://arxiv.org/abs/1804.09646
Example of applications of the mPOD are shown in
- M.A. Mendez, M.T. Scelzo, J.-M. Buchlin, Multiscale Modal Analysis of an Oscillating Impinging Gas Jet, Experimental Thermal and Fluid Science, Vol 91, February 2018, pp. 256-276 (https://doi.org/10.1016/j.expthermflusci.2017.10.032).
- M.A. Mendez, A. Gosset, J.-M. Buchlin, Experimental Analysis of the Stability of the Jet Wiping Process, Part II: Multiscale Modal Analysis of the Gas Jet-Liquid Film Interaction, Experimental Thermal and Fluid Science, Vol 106, September 2019, pp. 48-67 (https://doi.org/10.1016/j.expthermflusci.2019.03.004).
- M.A. Mendez, D. Hess, B. Watz, J.-M. Buchlin. Multiscale Proper Orthogonal Decomposition (mPOD) of TR-PIV data--: a Case Study on Transient Flows, 13th International Symposium on Particle Image Velocimetry at Munich. An extended version of this article is currently in preparation.Measurement Science and Technology, June 2020, Vol 31, pp. 094014 (https://doi.org/10.1088/1361-6501/ab82be)
- D. Barreiro-Villaverde, A. Gosset and M.A. Mendez, On the dynamics of the jet wiping: Numerical simulations and modal analysis, Physics of Fluids, June 2021, Vol 33, pp.062114 (https://doi.org/10.1063/5.0051451)
- C. Esposito, M. A. Mendez, J. Steelant, M.R. Vetrano, Spectral and modal analysis of a cavitating flow through an orifice. Experimental Thermal and Fluid Science, February 2021, Vol 121, pp. 110251(https://doi.org/10.1016/j.expthermflusci.2020.110251)
The pre-prints of these articles are available from the RG page: https://www.researchgate.net/profile/Miguel_Mendez5
Currently, this repository contains five exercises. Of these, two are done both in Matlab and in Python, while the remaining ones are only available in Matlab. The exercises include 1D and 2D cases with both scalar and vectorial quantities.
All the codes so far assume that the dataset is equally spaced both in space (i.e. along a Cartesian grid) and in time. TR-PIV or video sequences satisfy these conditions easily. Other simple exercises using Finite Difference are also considered (ex.1, ex.2, ex. 3).
The proposed exercises are the following:
1- Decomposition of the velocity profile of a pulsating Poiseuille flow (1D, scalar). The theoretical background for the analytical solution is described in M.A. Mendez,J.-M Buchlin, VKI-TN 215, 2016, pdf available at https://www.researchgate.net/publication/304538821_Notes_on_2D_Pulsatile_Poiseuille_Flows_An_Introduction_to_Eigenfunction_Expansion_and_Complex_Variables_using_Matlab/stats. (Available in Python and Matlab)
2- Decomposition of a Synthetic Test case (Available only in Matlab)
3- Decomposition of the Vorticity field of a 2D simulation in Matlab. (Available only in Matlab)
4- Decomposition of a TR-PIV measurement of an impinging jet. (Available in Python and Matlab)
5- Decomposition of a TR-PIV measurement of a flow past a cylinder. (Available only in Matlab)
Exercises 2,3 and 4 are taken from the article at https://arxiv.org/abs/1804.09646 . Exercise 5 is available at https://arxiv.org/abs/2001.01971.
A standalone application is available in the section "Release" of this repository. This is equipped with a Graphical User Interface developed by D. Ninni and presented in
- D. Ninni and M.A. Mendez, MODULO: A software for Multiscale Proper Orthogonal Decomposition of data, Software X, Vol 12, December 2020, pp. 100622 (https://doi.org/10.1016/j.softx.2020.100622).
A series of Video tutorial of the GUI has been published on a youtube channel:
The most recent implementation of MODULO is available on a Python module, prepared by Lorenzo Schena: