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This book is an introduction to the use of machine learning and data-driven approaches in fluid simulation and animation, as an alternative to traditional modeling techniques based on partial differential equations and numerical methods – and at a lower computational cost. This work starts with a brief review of computability theory, aimed to convince the reader – more specifically, researchers of more traditional areas of mathematical modeling – about the power of neural computing in fluid animations. In these initial chapters, fluid modeling through Navier-Stokes equations and numerical methods are also discussed. The following chapters explore the advantages of the neural networks approach and show the building blocks of neural networks for fluid simulation. They cover aspects related to training data, data augmentation, and testing. The volume completes with two case studies, one involving Lagrangian simulation of fluids using convolutional neural networks and the other using Generative Adversarial Networks (GANs) approaches.

Differential equations. --- Artificial intelligence. --- Soft condensed matter. --- Computer simulation. --- Differential Equations. --- Artificial Intelligence. --- Fluids. --- Computer Modelling. --- Deep learning (Machine learning) --- Aprenentatge automàtic --- Mecànica de fluids --- Simulació per ordinador

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This book provides a successful solution to one of the central problems of mathematical fluid mechanics: the Leray’s problem on existence of a solution to the boundary value problem for the stationary Navier—Stokes system in bounded domains under sole condition of zero total flux. This marks the culmination of the authors' work over the past few years on this under-explored topic within the study of the Navier—Stokes equations. This book will be the first major work on the Navier—Stokes equations to explore Leray’s problem in detail. The results are presented with detailed proofs, as are the history of the problem and the previous approaches to finding a solution to it. In addition, for the reader’s convenience and for the self-sufficiency of the text, the foundations of the mathematical theory for incompressible fluid flows described by the steady state Stokes and Navier—Stokes systems are presented. For researchers in this active area, this book will be a valuable resource.

Functional analysis --- Differential equations --- differentiaalvergelijkingen --- functies (wiskunde) --- Differential equations. --- Functional analysis. --- Differential Equations. --- Functional Analysis. --- Mecànica de fluids --- Equacions de Navier-Stokes --- Dinàmica de fluids --- Anàlisi numèrica

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Fluid mechanics. --- Fluid mechanics --- Thermodynamics. --- Mathematical models. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Hydromechanics --- Continuum mechanics --- Mecànica de fluids --- Hidromecànica --- Mecànica dels medis continus --- Dinàmica de fluids --- Hidràulica --- Hidrodinàmica --- Fluids

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This volume explores state-of-the-art developments in theoretical and applied fluid mechanics with a focus on stabilization and control. Chapters are based on lectures given at the summer school “Fluids under Control”, held in Prague from August 23-27, 2021. With its accessible and flexible presentation, readers will be motivated to deepen their understanding of how mathematics and physics are connected. Specific topics covered include: Stabilization of the 3D Navier-Stokes system Flutter stabilization of flow-state systems Turbulence control Design through analysis Fluids Under Control will appeal to graduate students and researchers in both mathematics and physics. Because of the applications presented, it will also be of interest to engineers working on environmental and industrial issues.

Functional analysis --- Differential equations --- Fluid mechanics --- Engineering sciences. Technology --- differentiaalvergelijkingen --- functies (wiskunde) --- systeemtheorie --- systeembeheer --- mechanica --- Functional analysis. --- System theory. --- Control theory. --- Differential equations. --- Continuum mechanics. --- Functional Analysis. --- Systems Theory, Control. --- Differential Equations. --- Continuum Mechanics. --- Mecànica de fluids

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This title provides an up-to-date, lively and approachable introduction to the mathematical formalism, numerical techniques and applications of relativistic hydrodynamics. The topic is presented here in a form which will be appreciated both by students and researchers in the field. The book is especially recommended to astrophysicists, particle physicists and applied mathematicians.

Relativistic fluid dynamics. --- Hydrodynamics. --- Fluid dynamics --- Relativistic mechanics --- Relativity (Physics) --- Relativistic fluid dynamics --- Hydrodynamics --- Hidrodinàmica --- Dinàmica de fluids --- Mecànica de fluids --- Aerodinàmica --- Capa límit --- Equacions de Navier-Stokes --- Fluídica --- Fluïdització --- Magnetohidrodinàmica --- Ones de xoc --- Turbulència --- Vòrtexs --- Tixotropia --- Enginyeria hidràulica --- Mecànica --- Mecànica analítica --- Cavitació --- Ones --- Ones de gravetat --- Urodinàmica --- Viscositat