Numerical Simulation in Physics and Engineering: Trends and Applications: Lecture Notes of the XVIII ‘Jacques-Louis Lions’ Spanish-French School

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Preface Contents About the Editors An Introduction to Quasi-Static Aeroelasticity 1 Introduction 2 The Collapse of Tacoma Narrows Bridge 2.1 What Has Been Observed 2.2 The Strouhal Instability 2.3 The Resonance of a Bridge 2.4 The Buffting Phenomenon 2.5 Flutter Induced by a Coupling Between Two Eigenmodes 2.5.1 A Short Description of Flutter Phenomenon 2.5.2 Linear Stability Analysis 2.5.3 Discussion on the Apparition of the Flutter (Roots in λ Are Real or Complex Conjugate) 2.5.4 Graphic Interpretation of the Flutter 2.5.5 Discussion of the Flutter Phenomenon for the Tacoma Narrows Bridge 2.6 The Galloping of the Bridge and the Stall Flutter Phenomenon 2.7 Letter from W.P. Rodden to R. Scanlan About Tacoma 2.8 Answer from R. Scanlan to W.P. Rodden About Tacoma 2.9 The Stall Flutter Phenomenon in the Torsion of the Bridge 3 Generalization of the Apparent Wind Method 4 Assembly of Several Rigid Structures 5 Control Strategy for the Full System 5.1 The Cooperative Strategy 5.2 How to Compute the Limit of the Optimal Control When →0 5.3 The Non-cooperative Strategy 5.3.1 Existence (and Uniqueness) of an Exact Decentralized Control with Coordination 5.4 A Coordination Algorithm for the Decentralized Control 6 Limit Cycle of Oscillations 6.1 Definition of a Limit Cycle of Oscillations 6.2 Localisation of Limit Cycles of Oscillations 6.3 How to Find Invariant Sets? 7 Computation of the Limit Cycle 7.1 Canonical Formulation for (98) 7.2 Second Step: Elimination of Second Order Terms 7.3 Partial Elimination of Terms of Order 3 8 The Stall Flutter of a Model in a Wind Tunnel 8.1 The Measures from the Wind Tunnel 8.2 The Simple Mathematical Model Used 9 About the Added Mass Method 10 Conclusion References Computational Treatment of Interface Dynamics via Phase-Field Modeling 1 Introduction 1.1 Interface Dynamics in Computational Mechanics and the Phase-Field Method 1.2 Notational Conventions 2 Derivation of Phase-Field Models via Diffusification 2.1 A Classical Moving Boundary Problem for Solidification of Pure Materials 2.2 The Basis of Diffusification 2.3 The Phase-Field Model for Solidification 2.4 The Diffuse-Interface Transition Profile: Asymptotic Analysis 3 General Framework of Thermomechanics and Energy Dissipation for Phase-Field Models 3.1 The Idea Behind Thermomechanically-Consistent Phase-Field Modeling 3.2 Allen-Cahn and Cahn-Hilliard 3.2.1 Allen-Cahn Equation 3.2.2 Cahn-Hilliard Equation 3.3 Navier-Stokes-Cahn-Hilliard 4 The Diffuse Domain Approach 4.1 Derivation of a Diffuse Domain Model for a Standard Convection-Diffusion Problem 4.2 Diffuse Domain Method for Problems Posed on Evolving Surfaces 5 Numerical Examples 5.1 Solidification Model 5.2 Cahn-Hilliard Equation 5.3 Diffuse Domain Model References Consistent Internal Energy Based Schemes for the Compressible Euler Equations 1 Introduction 2 Derivation of the Numerical Schemes 2.1 A Basic Result on Convection Operators 2.2 Internal Energy Formulation 2.3 The Time Semi-discrete Pressure Correction Scheme 2.4 The Fully Discrete Pressure Correction Scheme 2.5 A Segregated Variant 2.6 A Numerical Test 3 Entropy 3.1 Meshes and Discrete Norms 3.2 Implicit Schemes 3.3 Explicit Schemes References Comparison and Analysis of Natural Laminar Flow Airfoil Shape Optimization Results at Transonic Regime with Bumps and Trailing Edge Devices Solved by Pareto Games and EAs 1 Introduction 2 NLF Airfoil Shape Design Optimization with Bump and TED Devices for Shock Wave Control 3 Comparison and Analysis of Optimization Results Using SCB and TED 3.1 Comparison and Analysis of Results: Advantages and Drawbacks of SCB and TED Devices 3.1.1 Comparing Efficiency of SCB Technology Versus TED Technology 3.1.2 Comparing the Design Quality Level of SCB Technology and TED Technology 3.2 Extension to the 3-D NLF Wing Design Optimization with 3-D SCB/TED Devices 4 Conclusion and Perspectives References Time-Parallel Algorithm for Two Phase Flows Simulation 1 Introduction 2 Model 2.1 Numerical Method 3 The Parareal Algorithm 3.1 Original Parareal Algorithm 3.2 Multistep Variant of Parareal 4 Test Case 4.1 About the Convergence 4.2 Speed-Up Performances 5 Conclusion References Modelling of Bedload Sediment Transport for Weak and Strong Regimes 1 Introduction 2 Proposed Model 2.1 Convergence to the Classical SVE System for Weak Regimes 2.2 Energy Balance References