This open access book introduces the fundamentals of the space–time conservation element and solution element (CESE) method, which is a novel numerical approach for solving equations of physical conservation laws. It highlights the recent progress to establish various improved CESE schemes and its engineering applications. With attractive accuracy, efficiency, and robustness, the CESE method is particularly suitable for solving time-dependent nonlinear hyperbolic systems involving dynamical evolutions of waves and discontinuities. Therefore, it has been applied to a wide spectrum of problems, e.g., aerodynamics, aeroacoustics, magnetohydrodynamics, multi-material flows, and detonations. This book contains algorithm analysis, numerical examples, as well as demonstration codes. This book is intended for graduate students and researchers who are interested in the fields such as computational fluid dynamics (CFD), mechanical engineering, and numerical computation.
Author(s): Chih-Yung Wen, Yazhong Jiang, Lisong Shi
Series: Engineering Applications of Computational Methods, 13
Publisher: Springer
Year: 2023
Language: English
Pages: 143
City: Singapore
Preface
Contents
1 Introduction
1.1 Background
1.2 History of the CESE Method
1.3 Main Features of the CESE Method
1.4 Outline of the Book
References
2 Non-dissipative Core Scheme of CESE Method
2.1 Space–Time Integral Form of Governing Equations
2.2 Definitions of Conservation Elements and Solution Elements
2.3 Non-dissipative Core Scheme: a Scheme
References
3 CESE Schemes with Numerical Dissipation
3.1 a–α Scheme
3.2 Courant–Number–Insensitive Scheme
3.3 Upwind CESE Scheme
3.3.1 Construction of Upwind CESE Scheme
3.3.2 Scheme for Linear Scalar Convection Equation
3.3.3 Scheme for Euler Equations
3.3.4 Remarks on Upwind CESE Method
3.4 Comparison of Different CESE Schemes
3.5 Numerical Examples
References
4 Multi-dimensional CESE Schemes
4.1 CESE Schemes on Cartesian Meshes
4.1.1 The Improved a-α CESE Scheme
4.1.2 CNI CESE Scheme
4.1.3 Upwind CESE Scheme
4.2 CESE Schemes on Unstructured Meshes
4.2.1 a-α CESE Scheme
4.2.2 CNI CESE Scheme
4.2.3 Upwind CESE Scheme
4.3 Numerical Examples
References
5 High-Order CESE Schemes
5.1 Construction of High-Order CESE Schemes
5.1.1 Construction of a Third-Order 1D CESE Scheme
5.1.2 Construction of a Third-Order 2D CESE Scheme on Uniform Mesh
5.1.3 Construction of a Third-Order 2D CESE Scheme on Unstructured Mesh
5.2 Numerical Examples
References
6 Numerical Features of CESE Schemes
6.1 Stability
6.2 Efficiency
6.3 Accuracy
References
7 Application: Compressible Multi-fluid Flows
7.1 Richtmyer–Meshkov Instability
7.2 Rayleigh–Taylor Instability
7.3 Shock Refraction
7.4 Shock–Gas-Bubble Interaction
7.5 Shock–Water-Droplet Interaction
References
8 Application: Detonations
8.1 Gaseous Detonations
8.1.1 Ignition of Detonations
8.1.2 Dynamics of Detonations
8.1.3 Rotating Detonation Waves
8.2 Two-Phase Detonations
References
9 Other Applications
9.1 Hypersonic Aerodynamics
9.2 Aeroacoustics
9.3 Solid Dynamics
9.4 Magnetohydrodynamics
References
10 Summary
Appendix
