Numerical Fluid Dynamics: Methods and Computations (Forum for Interdisciplinary Mathematics)

✍ Scribed by Dia Zeidan (editor), Jochen Merker (editor), Eric Goncalves Da Silva (editor), Lucy T. Zhang (editor)

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 323
• Edition: 1st ed. 2022
• Category: Library

✦ Synopsis

This book contains select invited chapters on the latest research in numerical fluid dynamics and applications. The book aims at discussing the state-of-the-art developments and improvements in numerical fluid dynamics. All the chapters are presented for approximating and simulating how these methods and computations interact with different topics such as shock waves, non-equilibrium single and two-phase flows, elastic human-airway, and global climate. In addition to the fundamental research involving novel types of mathematical sciences, the book presents theoretical and numerical developments in fluid dynamics. The contributions by well-established global experts in fluid dynamics have brought different features of numerical fluid dynamics in a single book.

The book serves as a useful resource for high-impact advances involving computational fluid dynamics, including recent developments in mathematical modelling, numerical methods such as finite volume, finite difference and finite element, symbolic computations, and open numerical programs such as OpenFOAM software. The book addresses interdisciplinary topics in industrial mathematics that lie at the forefront of research into new types of mathematical sciences, including theory and applications. This book will be beneficial to industrial and academic researchers, as well as graduate students, working in the fields of natural and engineering sciences. The book will provide the reader highly successful materials and necessary research in the field of fluid dynamics.

✦ Table of Contents

Preface
Contents
About the Editors
Structure Functions for Numerical Shocks
1 Introduction
2 Finite Scale Equations
2.1 Introducing the FSE
2.2 Model Equations for Numerical Simulation
2.3 Finite Scale Theory
3 Essentials of Shock Capturing
3.1 Lagrangian Codes (Artificial Viscosity)
3.2 Eulerian Codes; Nonoscillatory Differencing
4 The Numerical Laboratory
4.1 Lagrangian Calculation
4.2 Eulerian Calculation
4.3 Parameters
5 The Structure Function
5.1 Convergence Testing
5.2 Structure Function Construction
6 Analysis Models
6.1 Self-similar Analysis
6.2 Structure Function Metrics
7 The Standard Lagrangian Profiles
8 Overshoots and Oscillations
9 Pursuing the Analogy with Physical Shocks
9.1 Self-similar Analysis of the Full FSE
9.2 Finite Scale Analysis Models
10 Nonoscillatory Eulerian Profiles
11 Summary and Discussion
References
Generalized Probability Density Function of the Solution to the Random Burgers-Riemann Problem
1 Introduction
2 Random Solution
3 Generalized Probability Density Function
4 Numerical Computations
5 Discussion and Conclusions
References
Semi-analytical and Numerical Study on Equatorial Rossby Solitary Waves Under Non-traditional Approximation
1 Introduction
2 Nonlinear Equatorial Wave Model
2.1 Basic Mathematical Model
2.2 Model Derivation by Multiple-Scale Method
3 Solutions and Simulations
3.1 Solutions of the New Modified mZK Equation
3.2 Results and Discussions
4 Conservation Laws and Dynamical Analysis
5 Conclusions
References
High-Order Polynomial Recovery in Finite Element Advection Schemes
1 Introduction
2 Preliminaries
2.1 Jacobian Matrix
2.2 Transformation of Nodal Functions
2.3 Integral Transformation
2.4 Edges
3 Advection Scheme
4 Recovery
5 Numerical Tests
5.1 Rotational Convergence Test
5.2 Dry Compressible Euler Equations
6 Outlook
References
Breakdown of Morphing Continuum Approach for Flows Under Translational Nonequilibrium
1 Introduction
2 Morphing Continuum Theory
2.1 Boltzmann–Curtiss Description
2.2 A First-Order Approximation
2.3 Bulk Viscosity Model Based on the Boltzmann–Curtiss Distribution
2.4 Summary
3 Numerical Methodology
4 Validation of Morphing Continuum Approach: Sod Problem
5 Breakdown Analysis of MCT Approach
5.1 Criterion to the Continuum Breakdown
5.2 Argon: A Monatomic Gas
5.3 Nitrogen: A Diatomic Gas
6 Conclusion
References
Dynamics of Oscillatory Fluid Flow Inside an Elastic Human Airway
1 Introduction
2 Numerical Setup
2.1 Geometry Details
2.2 Meshing Details
2.3 Governing Equations
2.4 Numerical Schemes and Solver Details
2.5 Boundary Conditions
3 Grid Independence, Numerical Validation, and Verification
3.1 Grid Independence Study and Error Calculations
3.2 Validation of the Fluid Solver
3.3 Validation of the Structural Solver
3.4 Validation of FSI Framework
4 Results and Discussion
4.1 Three-Dimensional Development of Flow Field in Human Airways
4.2 Spatial and Temporal Evolution of the Velocity Field for a Breathing Cycle
4.3 Development of the Flow and Structural Characteristics Inside Human Airways
4.4 Effect of Reynolds Number of the Airflow on Structural Response
5 Conclusion
6 Limitation of the Study
References
Hyperbolic Balance Laws: Residual Distribution, Local and Global Fluxes
1 Introduction
2 Geometrical Notations
3 Example of Schemes and Conservation
4 Flux Formulation of Residual Distribution Schemes
5 Embedding Source Terms: Well Balancing and Global Fluxes
5.1 The One-Dimensional Case
5.2 Multiple Dimensions, Beyond Second Order and Other Extensions
6 Time Dependent Problems
6.1 Preliminaries: Global Fluxes, Time Derivative and Mass Matrices
6.2 Generalization
6.3 Unsteady Problems and Well Balanced on Dynamic Meshes
7 Examples
7.1 Some Examples of Compressible Flows Simulations
7.2 Shallow Water and the Lake At Rest State State
7.3 Shallow Water and Moving Equilibria
7.4 Shallow Water with Dry Areas
8 Conclusion and Outlook
References
An Energy-Splitting High-Order Numerical Method for Multi-material Flows
1 Introduction
2 Derivation of Two-Material Compressible Flow Models with Instantaneous Pressure and Velocity Equilibrium
2.1 The Seven-Equation Model
2.2 Six-Equation Reduced Models with Velocity Relaxation Limit
2.3 A Five-Equation Reduced Model with Pressure Relaxation Limit
2.4 A Novel Reduced Model
3 Numerical Approaches for Two-Material Flow Models with Instantaneous Pressure and Velocity Equilibrium
3.1 Conventional Godunov-Type Schemes for the Five-Equation Reduced Model
3.2 Fractional Step Method for the Non-equilibrium Model
3.3 Finite Volume Methods for the Novel Reduced Model
4 Numerical Results
4.1 Test of Volume Fraction Positivity
4.2 Two-Fluid Shock-Tube Problem
4.3 Shock-Interface Interaction
4.4 Shock-Bubble Interactions
4.5 Two-Fluid Richtmyer-Meshkov Instability
4.6 Water-Air Shock-Interface Interaction Problems
5 Discussion
References
An ADER-LSTDG Scheme for the Numerical Simulation of a Global Climate Model
1 Introduction
2 Physical Motivation
3 Mathematical Model
3.1 The Energy Balance Model (EBM)
3.2 Deep Ocean-EBM Coupled Model
4 Numerical Scheme
4.1 Spatial WENO Reconstruction
4.2 High-Order One-Step Time Discretization: ADER-LSTDG Approach
5 Assessment of the Numerical Scheme
6 Numerical Results
7 Conclusions
References
Efficient Experimental and Numerical Methods for Solving Vertical Distribution of Sediments in Dam-Break Flows
1 Introduction
2 Experimental Setup for Attaining Vertical Distribution of Sediments in Dam-Break Flows
3 Mathematical Models for Vertical Distribution of Sediments in Dam-Break Flows
4 Numerical Methods for Vertical Distribution of Sediments in Dam-Break Flows
4.1 Spatial Discretization
5 Experimental and Numerical Results
6 Conclusions
References