Neuro-Network for Turbulent Mixing
Neuro-Network Forecasting of Turbulent Mixing Development Based on Wavelet-Analysis
Tech Area / Field
- INF-COM/High Performance Computing and Networking/Information and Communications
- PHY-NGD/Fluid Mechanics and Gas Dynamics/Physics
8 Project completed
Senior Project Manager
Glazova M B
FIAN Lebedev / Quantum Radiophysics Department of the Lebedev Physical Institute of Russian Academy of Sciences, Russia, Moscow
- Institute of Mathematical Modelling, Russia, Moscow\nVNIITF, Russia, Chelyabinsk reg., Snezhinsk
Project summaryThe aim of the Project: Development of a model of a hydrodynamic instability and turbulent mixing (HI and TM) on the basis of evolution of the steady-state formations -"fundamental events", in any complicate (2D and 3D) flows; development of methods for singling-out and formation of a library of these fundamental events; development of a prediction methods for the dynamics and characteristics of turbulent mixing. The practical goal of the Project will be a set of the forecasting software.
For the Project goals an adequate approach consists in using the wavelet-transformation for the analysis of complex phenomena and the search of steady-state images, and the use of neuro-network algorithms for a reconstruction of flow dynamics.
During the last few decades there was a steady interest to the problem of HI and TM evolution, which has a fundamental value for the issues of inertial thermonuclear fusion. The processes of HI and TM are irremovable, and the instability growth is unavoidable on principle, and development of the corresponding instabilities reduces the efficiency of thermonuclear burn. The solution of the above problem is important for a number of applications connected with turbulent diffusion, burn, atmosphere phenomena, astrophysical problems etc., and it is essential that the procedures for calculations of such processes should be elaborated. However, no satisfactory models have been up to now proposed.
Meanwhile, from the results of experiments and numerical simulations it follows that the flows arising due to development of HI and TM are accompanied by evolutionary stable formations (let us call them "fundamental events") connected with initial conditions at the points of discontinuity, or with a source of perturbations (nonhomogeneous shock wave or nonhomogeneous field of acceleration g®).
The HI and TM issues are especially interesting for complex multi-mode initial conditions or a multi-mode character of a source (SW, g®) both for classical and ICF problems. In this case, especially at a later non-linear stage of perturbation, the liquid flow has a fractal character. This problems being important and interesting is still far from a solution, especially for a three-dimensional case.
One can suppose that the dynamics of evolutionary-stable formation can be represented as a set of fundamental events. This can be illustrated by Fig. 1 where the phase of a shock wave transmission through an interface of two gases of different densities (Richtmyer-Meshkov instability) is shown. From initial form of the discontinuity one can easily see high-frequency and low-frequency components, and the final stage is a superposition of the HF-component made of a mixed layer and the LF-component that is slightly changed during the observation time.
A neuro-network analysis proposed for solution of the problem is a new and promising research method. Its main advantage over a conventional algorithmic approach is a possibility of self-adaptation to the input data, and a possibility of tuning by training. The neuronets are able to solve a wide variety of problems including those incorrectly formulated. By means of special selection of a neuronet design one can single out most " essential" features of an input signal, which is consistent with the Project goal. The examples of neuronet education that can be easily analysed are illustrated in Fig. 1.
It is supposed to perform a theoretical analysis of HI and TM development by a newly developed mechanism of a wavelet technology. This is a modification of the Fourier-transformation method, which allows the analysis of localized structures throughout different scales. In the work by N.Astafieva1 it is shown that the wavelet technology makes it possible to interpret a structure of such a complex dependence as a fractal (and even multi-fractal) signal, and S.Terekhov2 determined a mathematical relation between neuro-computer and wavelet-methods. We believe that a complex usage of the above approaches would comprise a new and unique method for the analysis of complex flows.
A common structure of the Project is the following. The wavelet analysis suggests the formation of a space of features supplied to the input of a neuro-network. Initial data for the wavelet analysis are to be generated by means of numerical experiments with the use of different codes developed at IMM in collaboration with FIAN, VNIITF, and the foreign collaborators (note the models developed by D.Youngs). The neuronet education aims at the prediction of instability development at different phases of turbulent mixing.
Apart from the problem of prediction it is planned to use a special kind of neuro-network, the self-organising Kohonen maps, destined for visualization and systematization of the calculation results. This will allow one, in particular, to perform a complex comparison of the numerical codes simultaneously for a great number of parameters. The Kohonen mapping of the calculation results will permit one to determine the metrics, and as a result, an idea of similarity between different numerical procedures and codes, and to determine their relative closeness to the experimental data.
The given Project is the practical-aimed development of the ISTC Project # 029-94 devoted to the calculation-theoretical models and methods of the HI and TM analysis, as well as the hydrodynamic codes, and the experimental results obtained3 (FIAN, IMM, VNIIEF). The Project also uses the works on neuro-computing and wavelet-analysis4 carried out by the Project participants (VNIITF, FIAN). This permits one to expect a successful execution of the main goal, i.e. the development of a new method for the analysis of complex flows.
The main expected results of the Project:
- Development of methods for a separation of evolutionary stable formations from the complex initial conditions;
- Classification of fundamental events and creation of the libraries;
- Determination of the additive (or close to them) characteristics of non-linear and turbulent formations which are necessary for a reconstruction of flows (possible variants: circulation, the mass of mixing layers and so on);
1 N.Astafieva, "Wavelet-analysis: theoretical foundations and examples of application", Usp.Fiz.Nauk, v. 166, N 11, pp. 1145-1170
2 S.Terekhov, "Orthogonal compact-wave (Wavelet) transforms and their applications", Preprint VNIITF, N 113, Snezhinsk, 1997
3 V.Rozanov, Project Coordinator, Final Technical Report on the ISTC Project #029-94 " The Research of hydrodynamic instabilities and turbulent mixing for optimization of laser target compression".
4 S.Shumsky, Project Coordinator, Final Technical Reports on the ISTC Project #031 -94" Development of a high capacity content addressed neural network memory".- Development of methods for a reconstruction of the flow dynamics on the basis of libraries of events, initial conditions, external conditions for acceleration and motion;
- Determination of the main characteristics of a mixing zone, the width, concentration profile, distribution of kinetic energy and so on.
- Creation of a software complex for a decomposition of the initial conditions into a set of fundamental events (FE) and for FE-based synthesis of a turbulent flow at any stage.
The Project results may find a variety of applications connected with hydrodynamically unstable flows and turbulence, including the optimization of the target design and compression problem in ICF. In addition, the proposed method can make a considerable contribution into the theory of turbulence and its application in astrophysics, turbulent diffusion, burning and atmospheric processes, simulation of turbulent flows for space and aviation technologies, the analysis of chemical reactions and the catalysis.
This Project will be carried out by the professional teams of specialists previously engaged in the weapon studies. Thus, the given Project, which continues the theme of the above ISTC Projects, is in full accordance with the ISTC goals.
Potential role of the foreign collaborators
The collaborators may render assistance in the performance and analysis of the complete calculations that are necessary for a consideration of the initial data for the analysis, in the verification of the developed methods and in the development of the practical applications of the elaborated methods.