Mathematical Modeling of Large-Scale and Complex Problems in Fluid Dynamics and Other Physical Processes
A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".
Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 346
Special Issue Editor
Interests: mathematical modeling; CFD; high-order numerical simulation; flow stability problems; pattern formation; perturbation analysis of interfacial instability; turbulence model; multiscale modeling; high-performance computing; deep learning; medical imaging and inverse problems
Special Issue Information
Dear Colleagues,
Many large-scale problems in computational fluid dynamics (CFD) such as uncertainty quantification, Bayesian inversion, wave instability, inverse problems, data assimilation and differential-equation-constrained optimization are considered very challenging computationally as they require many expensive numerical solutions for the corresponding differential equations.
Several techniques such as perturbation analysis, machine learning and statistical approaches for CFD are playing a key role in pushing the progress of our knowledge in these important areas. They are widely used in computing nonlinear, multidimensional processes in fluid dynamics, in studies of turbulence and hydrodynamic instabilities, in medical imaging, and in medicine and other natural sciences. Entropy generation and fluid dynamics due to shear stresses in turbulent channel flows are challenging subjects rich in physics and practical applications. Machine learning models can approximate physics calculations very quickly, but at the cost of accuracy. Using a machine learning approach inside traditional fluid simulations can improve both the accuracy and speed, even in examples that are very different from the training data. This approach opens the door to applying machine learning to large-scale physical modeling tasks such as airplane design and climate prediction.
The developments related to the new generations of high-performance supercomputing and machine learning are opportunities to advance the field of CFD in accelerating direct numerical simulations, improving turbulence closure modeling, and developing enhanced reduced-order models. Many efforts have focused on the development and the analysis of efficient computational tools for mathematical modeling of the stability of shear flows and their transition to turbulence, and have described numerical simulations. This progress will continue to be driven by an increasing availability of high-quality data, high-performance computing, and a better understanding and applications of these emerging techniques. The goal of this Special Issue is to fundamentally improve our scientific understanding in all of these areas. Specific topics could include machine learning approaches; mathematical and multiscale modeling; and numeric, high-performance computing (HPC) and parallel computing to solve challenging fluid dynamical problems, which can be applied to a wide range of problems including transitional shear flows, turbulence, hypersonic flows, etc., with particular interest in academic research and industrial applications.
This Special Issue of Entropy will focus on these topics and on the development of novel, efficient approaches to quantify entropy and to predict the nonlinear evolution of unstable flow structures. Furthermore, methods of physical analysis rooted in statistical physics should be considered to provide conceptual insights into these questions. These insights will yield connections between deep learning and diverse physical and mathematical topics, including dynamical phase transitions, chaos, random matrix theory, probability, and nonequilibrium statistical physics. Indeed, the fields of statistical physics and machine learning have long enjoyed a rich history of strongly coupled interactions, and recent advances at the intersection of statistical physics and deep learning suggest these interactions will only deepen going forward.
Dr. Ahmed Kaffel
Guest Editor
Manuscript Submission Information
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Keywords
- mathematical modeling
- computational fluid dynamics
- entropy
- statistical physics
- numerical simulation
- hydrodynamic instability
- turbulence
- multiscale modeling
- high-performance computing
- machine learning
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