Mathematical Models of Fluid Dynamics: Modelling, Theory, Basic Numerical Facts – An Introduction

Without sacrificing scientific strictness, this introduction to the field guides readers through mathematical modeling, the theoretical treatment of the underlying physical laws and the construction and effective use of numerical procedures to describe the behavior of the dynamics of physical flow.
The book is carefully divided into three main parts:The design of mathematical models of physical fluid flowA theoretical treatment of the equations representing the models, as Navier–Stokes, Euler, and boundary layer equations, models of turbulence, in order to gain qualitative as well as quantitative insights into the processes of flow events, e.g. traffic models, models of tunnel fires etc.The construction and effective use of numerical procedures in order to find quantitative descriptions of concrete physical or technical fluid flow situation.
Both students and experts wanting to control or predict the behavior of fluid flows by theoretical and computational fluid dynamics will benefit from this combination of all relevant aspects in one handy volume.

Spis treści:
Preface to the Second Edition.
Preface to the First Edition.
1 Ideal Fluids.
1.1 Modeling by Euler’s Equations.
1.2 Characteristics and Singularities.
1.3 Potential Flows and (Dynamic) Buoyancy.
1.4 Motionless Fluids and Sound Propagation.
2 Weak Solutions of Conservation Laws.
2.1 Generalization of What Will Be Called a Solution.
2.2 Traffic Flow Example with Loss of Uniqueness.
2.3 The Rankine–Hugoniot Condition.
3 Entropy Conditions.
3.1 Entropy in the Case of an Ideal Fluid.
3.2 Generalization of the Entropy Condition.
3.3 Uniqueness of Entropy Solutions.
3.4 Kruzkov’s Ansatz.
4 The Riemann Problem.
4.1 Numeri cal Importance of the Riemann Problem.
4.2 The Riemann Problem for Linear Systems.
4.3 The Aw–Rascle Traffic Flow Model.
5 Real Fluids.
5.1 The Navier–Stokes Equations Model.
5.2 Drag Force and the Hagen–Poiseuille Law.
5.3 Stokes Approximation and Artificial Time.
5.4 Foundations of the Boundary Layer Theory and Flow Separation.
5.5 Stability of Laminar Flows.
5.6 Heated Real Gas Flows.
5.7 Tunnel Fires.
6 Proving the Existence of Entropy Solutions by Discretization Procedures.
6.1 Some Historical Remarks.
6.2 Reduction to Properties of Operator Sequences.
6.3 Convergence Theorems.
6.4 Example.
7 Types of Discretization Principles.
7.1 Some General Remarks.
7.2 Finite Difference Calculus.
7.3 The CFL Condition.
7.4 Lax–Richtmyer Theory.
7.5 The von Neumann Stability Criterion.
7.6 The Modified Equation.
7.7 Difference Schemes in Conservation Form.
7.8 The Finite Volume Method on Unstructured Grids.
7.9 Continuous Convergence of Relations.
8 A Closer Look at Discrete Models.
8.1 The Viscosity Form.
8.2 The Incremental Form.
8.3 Relations.
8.4 Godunov Is Just Good Enough.
8.5 The Lax–Friedrichs Scheme.
8.6 A Glimpse of Gas Dynamics.
8.7 Elementary Waves.
8.8 The Complete Solution to the Riemann Problem.
8.9 The Godunov Scheme in Gas Dynamics.
9 Discrete Models on Curvilinear Grids.
9.1 Mappings.
9.2 Transformation Relations.
9.3 Metric Tensors.
9.4 Transforming Conservation Laws.
9.5 Good Practice.
9.6 Remarks Concerning Adaptation.
10 Finite Volume Models.
10.1 D ifference Methods on Unstructured Grids.
10.2 Order of Accuracy and Basic Discretization.
10.3 Higher–Order Finite Volume Schemes.
10.4 Polynomial Recovery.
10.5 Remarks Concerning Non–polynomial Recovery.
10.6 Remarks Concerning Grid Generation.
Index.
Suggested Reading.

Nota biograficzna:

Rainer Ansorge studied Mathematics and Physics at the Free University and Technical University (TU) of Berlin, Germany. After positions as computational engineer at the Volkswagen Company (1956) he became Full Professor of Mathematics at the University of Hamburg, Germany (1969). He was one of the founders of the TU Hamburg–Harburg (1974–1986) and his scientific research activities are covering more than 20 countries. Prof. Ansorge is member of the European Academy of Sciences and Arts, of the New York Academy of Sciences and the GAMM.
Prof. Sonar is head of the group Partial Differential Equations at the Institute of Computational Mathematics of the University of Braunschweig. His main fields are: Numerics of the partial differential equations, numerical fluid mechanics and analysis of discrete data.

Okładka tylna:
Without sacrificing scientific strictness, this introduction to the field guides readers through mathematical modeling, the theoretical treatment of the underlying physical laws and the construction and effective use of numerical procedures to describe the behavior of the dynamics of physical flow.
The book is carefully divided into three main parts:The design of mathematical models of physical fluid flowA theoretical treatment of the equations representing the models, as Navier–Stokes, Euler, and boundary layer equations, models of turbulence, in order to gain qualitative as well as quantitative insights into the processes of flow events, e.g. traffic models, models of tunnel fires etc.The construction and effective use of numerical procedures in order to find quantitative descriptions of concrete physical or technical fluid flow situation.
Both students and experts wanting to control or predict the behavior of fluid flows by theoretical and computational fluid dynamics will benefit from this combination of all relevant aspects in one handy volume.