Algorithms Data Driven Methods And Analysis In Fluid Dynamics And Fluid Structure Interactions
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Algorithms, Data-driven Methods and Analysis in Fluid Dynamics and Fluid-Structure Interactions
For the first part, we study numerical methods for fluid-structure interactions (FSI). FSI problems are often too complex to solve analytically. On the other hand, numerically solving the whole system can be computaionally expensive. Our work focuses on stability-preserving reduced-order modeling techniques. A projection-based reduced-order modeling method is proposed and applied to the immersed boundary method (IBM) for biofluid systems. The reduced-order model (ROM) are derived from projecting the full-order model (FOM) on selected subspaces such that incompressibility and the Lyapunov stability are both preserved. We also address the practical issue of efficiently computing the reduced-order model using an interpolation technique. Next, a data-driven modeling approach for more general dynamics problem with latent variables is introduced without knowledge of the FOM. The data-driven model includes artificial latent variables in the state space, in addition to observed variables. We present a model framework where the stability of the coupled dynamics can be easily enforced. The model is implemented by recurrent cells and trained using back propagation through time. For both the projection-based method and the data-driven method, benchmark examples from order reductions are used to demonstrate the efficiency, robustness, and stability. Classic FSI problems are experimented to illustrate the accuracy and predictive capability of the proposed approaches. For the second part, we study the compressible Euler system for gas dynamics. We construct self-similar solutions to Riemann problems for the 1-dimensional isothermal Euler system. Such self-similar solutions always contain exactly two shock waves, necessarily generated at time $0_+$ and move apart along straight lines. We also provide physical interpretation of the solution structure, describing the behavior of the solution in the emerging wedge between the shock waves. We then move on to the 3-dimensional linearized Euler system. Radial solutions are used to construct examples of BV instability and $L^\infty$ blowup. Global existence of a class of radial solutions is shown using an argument based on scaling of the dependent variables, with variation estimates.
System- and Data-Driven Methods and Algorithms
Author: Peter Benner
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2021-11-08
An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques.
Data Driven Analysis and Modeling of Turbulent Flows
Data-driven Analysis and Modeling of Turbulent Flows provides an integrated treatment of modern data-driven methods to describe, control, and predict turbulent flows through the lens of both physics and data science.The book is organized into three parts:• Exploration of techniques for discovering coherent structures within turbulent flows, introducing advanced decomposition methods• Methods for estimation and control using data assimilation and machine learning approaches• Finally, novel modeling techniques that combine physical insights with machine learningThis book is intended for students, researchers, and practitioners in fluid mechanics, though readers from related fields such as applied mathematics, computational science, and machine learning will find it also of interest.• Exploration of techniques for discovering coherent structures within turbulent flows, introducing advanced decomposition methods• Methods for estimation and control using data assimilation and machine learning approaches• Finally, novel modeling techniques that combine physical insights with machine learning