Overview
- This is the first monograph on the numerical analysis of oscillatory solutions to problems in fluid mechanics. It contains completely new ideas never published before
- An effective way of computation of objects as Young measures is presented based on an original adaptation of K-convergence
- The analytical part contains original results notably on the measure-valued strong uniqueness principle for various models of compressible fluid flows
Part of the book series: MS&A (MS&A, volume 20)
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Table of contents (14 chapters)
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Front Matter
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Mathematics of Compressible Fluid Flow: The State-of-the-Art
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Front Matter
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Generalized Solutions to Equations and Systems Describing Compressible Fluids
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Front Matter
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Numerical Analysis
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Front Matter
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Back Matter
Keywords
About this book
This book is devoted to the numerical analysis of compressible fluids in the spirit of the celebrated Lax equivalence theorem. The text is aimed at graduate students in mathematics and fluid dynamics, researchers in applied mathematics, numerical analysis and scientific computing, and engineers and physicists.
The book contains original theoretical material based on a new approach to generalized solutions (dissipative or measure-valued solutions). The concept of a weak-strong uniqueness principle in the class of generalized solutions is used to prove the convergence of various numerical methods. The problem of oscillatory solutions is solved by an original adaptation of the method of K-convergence. An effective method of computing the Young measures is presented. Theoretical results are illustrated by a series of numerical experiments.
Applications of these concepts are to be expected in other problems of fluid mechanics and related fields.
Authors and Affiliations
About the authors
Mária Lukáčová-Medviďová is professor for Applied Mathematics at the Johannes Gutenberg-University Mainz. She is a vice speaker of the Research Center Multiscale Simulation Methods for Soft Matter Systems and of the Mainz Institute for Multiscale Modeling. Her research interests lay in numerics and analysis of partial differential equations. She made important contributions to the development of structure-preserving schemes for hyperbolic conservation laws and hybrid multiscale methods for complex fluids. She received various awards, such as the Prize of the Czech Learned Society in 2002, Bronze Medal of the University of Košice in 2013, or the Gutenberg Research College Fellowship in 2020.
Hana Mizerová is an assistant professor at the Department of Mathematical Analysis and Numerical Mathematics of Comenius University in Bratislava, Slovakia. Her research focuses on numerical analysis of partial differential equations in fluid mechanics. In 2018, she was awarded the Seal of Excellence by the European Commission.
Bangwei She is a research worker at the Institute of Mathematics of the Czech Academy of Sciences. His research interests are in numerical analysis and scientific computing, particularly for partial differential equations with a focus on computational fluid dynamics.
Bibliographic Information
Book Title: Numerical Analysis of Compressible Fluid Flows
Authors: Eduard Feireisl, Mária Lukáčová-Medviďová, Hana Mizerová, Bangwei She
Series Title: MS&A
DOI: https://doi.org/10.1007/978-3-030-73788-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-73787-0Published: 18 December 2021
Softcover ISBN: 978-3-030-73790-0Published: 19 December 2022
eBook ISBN: 978-3-030-73788-7Published: 01 January 2022
Series ISSN: 2037-5255
Series E-ISSN: 2037-5263
Edition Number: 1
Number of Pages: LX, 482
Number of Illustrations: 1 b/w illustrations, 25 illustrations in colour
Topics: Analysis, Computational Mathematics and Numerical Analysis