I apologise beforehand if the question isn't well defined or is too broad, I'm just having some difficulty finding the information I need. I also apologise if this should have been asked on stack overflow.
I have computed some numerical solutions using spectral methods to some different hydrodynamics problems that I'm interested in. The solutions are given as time series arrays. For example, at each time $t = 1, \dots, n,$ the solution for the velocity field $v$ is an $m \times m$ array. I would like to analyse my system to determine as much information about it as possible. For example, in my 2D vortex simulations, I would like to numerically determine the dominant behaviour of the system, or numerically find/predict any splitting or merging of vortices, or perhaps find relationships between the different variables of the system etc. The problem is, I don't actually know of many computational methods that I can use to determine these kinds of behaviour. Some things I do know we can use (and have implemented) are
- Autocorrelation functions (in both time and space).
- Singular value decomposition (to determine dominant behaviour).
- Analysing the spectra of the solution (radially averaged bins, FFT).
- Basic statistical analysis, analysing fluctuation data.
- Coupling tracer particles/dyes into the DE system to observe phenomena.
- Visualisation of the numerical solutions.
Obviously, comparing the numerical solution with the analytical solution is also a useful technique, though most of the time this isn't possible in hydrodynamics.
I was hoping that there were more numerical techniques available that I could learn and use to study my system. So I was wondering if someone could let me know of any papers or books that detail approaches to analysing numerical solutions, or could list down some methods that they know of. Any help would be greatly appreciated.
I was given a review paper today by Jiang et al. which outlines nine numerical methods for detecing vortices, and also a paper by Jeong et al.. It is mostly these types of algorithms/computational methods that I am interested in using.