Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids (CISM International Centre for Mechanical Sciences, 599)

✍ Scribed by Laura De Lorenzis (editor), Alexander Düster (editor)

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 225
• Category: Library

✦ Synopsis

The book examines innovative numerical methods for computational solid and fluid mechanics that can be used to model complex problems in engineering. It also presents innovative and promising simulation methods, including the fundamentals of these methods, as well as advanced topics and complex applications. Further, the book explores how numerical simulations can significantly reduce the number of time-consuming and expensive experiments required, and can support engineering decisions by providing data that would be very difficult, if not impossible, to obtain experimentally. It also includes chapters covering topics such as particle methods addressing particle-based materials and numerical methods that are based on discrete element formulations; fictitious domain methods; phase field models; computational fluid dynamics based on modern finite volume schemes; hybridizable discontinuous Galerkin methods; and non-intrusive coupling methods for structural models.

✦ Table of Contents

Preface
Contents
Discrete Element Methods: Basics and Applications in Engineering
Introduction
Governing Equations
Constitutive Modeling of the Particle Phase
Normal Contact Model
Tangential Contact Model
Rolling Resistance Model
DEM Solver
Time Integration
Search Algorithms
Example: Silo Discharge
DEM Using Parallel Solvers
Solver DEMFLOW
Numerical Test: Medium Number of Cores
Numerical Test: Large Number of Cores
Conclusion
References
Adaptive Integration of Cut Finite Elements and Cells for Nonlinear Structural Analysis
Introduction
The Finite Cell Method
Weak Formulation
Discretization of the Weak Formulation
A Simple Linear Elastostatic Example
Standard Numerical Integration Schemes
Newton-Cotes Formulas (pq=n-1)
Gauss-Legendre Quadrature (pq=2n-1)
Adaptive Quadtree/Octree Quadrature Schemes
Numerical Integration Based on Moment Fitting
Moment Fitting Equations
Adaptive Moment Fitting
Treatment of Integration Points in the Fictitious Domain
Numerical Examples
J2 Flow Theory of Plasticity for Small Strains
J2 Flow Theory of Plasticity for Large Strains
Conclusions
Appendix
References
Numerical Implementation of Phase-Field Models of Brittle Fracture
Introduction
Formulation
Quasi-Static Evolution (Incremental Variational Problem)
Treatment of Irreversibility
Relaxed (Crack-Set' Irreversibility) Implicit (History-Field' Irreversibility)
Penalized
Examples
Solution Strategies
Staggered
Monolithic (Newton-Raphson with Line-Search)
Examples
Conclusions
References
Practical Computational Fluid Dynamics with the Finite Volume Method
Introduction
Governing Equations
Numerical Solution of Continuum Problems
Closure
Mesh Generation and Mesh Handling
Guidance on Mesh Generation
Mesh Types
Adaptive Mesh Refinement
FVM Mesh Quality Metrics
Dynamic Mesh Simulations
Closure
Finite Volume Discretisation
Generic Scalar Transport Equation
Numerical Discretisation
Rate of Change
Gradient
Convection
Diffusion
Source and Sink Terms
Numerical Boundary Conditions
Time Advancement
Closure
Pressure–Velocity Coupling
Governing Equations
Pressure Equation as a Schur Complement
Derivation of the Pressure Equation
Segregated Solution Algorithm: SIMPLE
Segregated Solution Algorithm: PISO
Block–Implicit Coupled Solution
Closure
Linear Equation Solvers
Finite Volume Matrix
Matrix Storage Formats
Matrix Properties
Definition of Residual
Direct Solvers
Iterative Solvers
Krylov Subspace Solvers
Preconditioning
Algebraic Multigrid
Block–Coupled Solution Algorithms
Closure
Examples
CFD for External Aerodynamics
Turbomachinery CFD
Biomedical CFD Simulations
Closure
References
Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems
Introduction
Incompressible Flows: Problem Statement
HDG Method for Oseen Flows
Functional and Discrete Approximation Setting
Strong Forms of the Local and Global Problems
Weak Forms of the Local and Global Problems
Discrete Forms and the Resulting Linear System
Local Postprocess of the Primal Variable
Numerical Examples
Stokes Flow
Oseen Flow
Navier-Stokes Flow
Appendix: Saddle-Point Structure of the Global Problem
Appendix: Implementation Details
References
Non Intrusive Global/Local Coupling Techniques in Solid Mechanics: An Introduction to Different Coupling Strategies and Acceleration Techniques
Introduction
Reference Model
Iterative Techniques Using the Global and the Local Models Separately
Local Model
Global Model
Basic Fixed Point Iterative Technique
Basic Fixed Point with Relaxation
Use of Overlap
Illustrations
Application of the Previous Results
Comments on Other Iterative Algorithms
3D Example
Conclusion
References