Numerical Methods for Flows: FEF 2017 Selected Contributions (Lecture Notes in Computational Science and Engineering, 132)

✍ Scribed by Harald van Brummelen (editor), Alessandro Corsini (editor), Simona Perotto (editor), Gianluigi Rozza (editor)

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 358
• Category: Library

✦ Synopsis

This book includes selected contributions on applied mathematics, numerical analysis, numerical simulation and scientific computing related to fluid mechanics problems, presented at the FEF-“Finite Element for Flows” conference, held in Rome in spring 2017. Written by leading international experts and covering state-of-the-art topics in numerical simulation for flows, it provides fascinating insights into and perspectives on current and future methodological and numerical developments in computational science. As such, the book is a valuable resource for researchers, as well as Masters and Ph.D students.

✦ Table of Contents

Preface
Contents
About the Editors
Simulation of Complex High Reynolds Flows with a VMS Method and Adaptive Meshing
1 Introduction
2 Whistling Study Through CFD
2.1 Numerical Resolution of the Navier–Stokes Equations
2.2 Immersed Boundaries and Automatic Anisotropic Adaptation
3 Whistling Simulations
3.1 Vortex Detection
3.2 Validation in a Simple Air Flow Benchmark
3.3 Industrial Application
4 Conclusions and Perspectives
References
Comparison of Coupled and Decoupled Solvers for Incompressible Navier–Stokes Equations Solved by Isogeometric Analysis
1 Introduction
2 NURBS Objects
3 Mathematical Model
3.1 Weak Formulation
3.2 Solution Methods
3.2.1 Coupled Approach
3.2.2 Decoupled Approach
3.3 Discretization
4 Computational Examples
4.1 Backward Facing Step
4.2 Kaplan Turbine
5 Conclusion
References
High-Order Isogeometric Methods for Compressible Flows
1 Introduction
2 High-Resolution Isogeometric Analysis
2.1 Model Problem
2.2 Galerkin Method
2.3 Algebraic Flux Correction
3 Numerical Results
4 Conclusions
References
High-Order Isogeometric Methods for Compressible Flows
1 Introduction
2 High-Resolution Isogeometric Analysis
2.1 Governing Equations
2.2 Spatial Discretization by Isogeometric Analysis
2.3 Temporal Discretization by Explicit Runge–Kutta Methods
2.4 Algebraic Flux Correction
3 Numerical Results
4 Conclusions
References
Simulations of Non-hydrostatic Flows by an Efficient and Accurate p-Adaptive DG Method
1 Introduction
2 Outline of the Numerical Method
3 Numerical Results
4 Conclusion
References
A Fully Semi-Lagrangian Method for the Navier–Stokes Equations in Primitive Variables
1 Introduction
2 The Fully Semi-Lagrangian Scheme
3 Numerical Tests
4 Conclusions and Future Developments
References
Mesh Adaptation for k-Exact CFD Approximations
1 Introduction
2 Features-, Goal-, Norm-Oriented Formulations
2.1 Feature-Based (FB) Adaptation
2.2 The Goal-Oriented (GO) Formulation
2.3 Numerical Corrector and Norm-Oriented (NO) Formulation
3 Estimates for k-Exact Approximations
3.1 Higher-Order (HO) Estimates
3.2 High-Order Accurate Unsteady Mesh Adaptation
4 Conclusions
References
Entropy Stable Discontinuous Galerkin Finite Element Moment Methods for Compressible Fluid Dynamics
1 Introduction
2 The Boltzmann Equation
2.1 Properties of the Collision Operator
2.2 Properties of the Linearized Collision Operator
2.3 Hydrodynamic Limits
2.4 Euler Equations
2.4.1 Navier–Stokes–Fourier Equations
3 Velocity-Space-Time Galerkin Approximation
3.1 Velocity Discretization of a Renormalized Boltzmann Equation
3.2 Space-Time Discontinuous Galerkin Approximation
3.2.1 Semi-discrete Discontinuous Galerkin Approximation
3.2.2 Entropy Stability
3.2.3 Fully-Discrete Discontinuous Galerkin Approximation
4 Numerical Results
5 Conclusions
References
Space-Time NURBS-Enhanced Finite Elements for Solving the Compressible Navier–Stokes Equations
1 Introduction
2 Quasi-Linear Form of the Navier–Stokes Equations
3 Stabilized Space-Time Finite Element Formulation
4 NURBS-Enhanced Finite Elements
5 Numerical Examples
5.1 Cylinder Flow
5.2 NACA0012 Airfoil
6 Concluding Remarks
References
Fluid Flow Simulation from Geometry Data Based on Point Clouds
1 Introduction
2 Volume Immersion
3 Immersion of Point Clouds
3.1 Distance Function to a Set of Points
3.2 Unit Metric Construction
3.3 Definition of the Neighbourhood
4 A Numerical Example
5 Conclusion
References
Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows
1 Introduction
2 Axioms
3 Constitutive Dependence
4 Deriving Constraints
5 Choices and Connections
6 Regularisation of the Asymptotic Model
7 Conclusion
References
On the Sensitivity to Model Parameters in a Filter Stabilization Technique for Advection Dominated Advection-Diffusion-Reaction Problems
1 Introduction
2 Problem Definition
2.1 Overview of Stabilization Techniques
3 A Filter Stabilization Technique
4 Numerical Results
5 Conclusions
References
One-Dimensional Line SIAC Filtering for Multi-Dimensions: Applications to Streamline Visualization
1 Introduction and Motivation
2 Background
3 Line SIAC Filters: Reducing the Filter Dimension
4 Numerical Results
5 Conclusions and Future Work
References
A High Performance Computing Framework for Finite Element Simulation of Blood Flow in the Left Ventricle of the Human Heart
1 Introduction
2 Computational Model
2.1 The Mathematical Model
2.2 Finite Element Approximation
2.3 Computational Tools
3 Results
3.1 Parallel Efficiency
3.2 Hemodynamics
4 Conclusion
References
Phase Field-Based Incompressible Two-Component Liquid Flow Simulation
1 Introduction
2 Navier–Stokes–Cahn–Hilliard Two-Phase Flow Model
3 Variational Formulation and Discretization
4 Application to the Rayleigh-Taylor Instability Problem
5 Summary and Conclusions
References
A Study on the Performance Portability of the Finite Element Assembly Process Within the Albany Land Ice Solver
1 Introduction
2 Albany Land Ice
2.1 Numerical Implementation Within the Albany Code
2.2 Finite Element Assembly
3 Performance Analysis
3.1 Architectures
3.2 Architecture Comparison
3.3 Scalability Study
4 Conclusions
References
A Multimesh Finite Element Method for the Stokes Problem
1 Introduction
2 Notation
3 Multimesh Finite Element Method
4 Implementation
5 Numerical Results
6 Discussion
References
A Variational Multi-Scale Anisotropic Mesh Adaptation Scheme for Aerothermal Problems
1 Introduction
2 Numerical Methods for the Thermal Resolution of the Impinging Jet Cooling
2.1 Variational Multi-Scale Scheme for the Convection-Diffusion Equation
2.2 A Posteriori Error Estimation on Solution's Subscales
3 Mesh Adaptation
3.1 Principles of Hessian Based Anisotropic Mesh Adaptation
3.2 A New Anisotropic Mesh Adaptation Technique Based on the Subscales Error Estimator
4 Results and Discussions
4.1 Test Case Description
4.2 Flow Dynamics, Localization of the Subscales Error and Resulting Meshes
5 Conclusions
References
Density-Based Inverse Homogenization with Anisotropically Adapted Elements
1 Introduction
2 A Density-Based Method for Topology Optimization
3 The Homogenization Procedure
3.1 The Direct Method
3.2 The Inverse Method
4 The Numerical Discretization
4.1 The Anisotropic Setting
4.2 The Adaptive Algorithm
5 Numerical Results
6 Conclusions
References
Bathymetry Reconstruction Using Inverse Shallow Water Models: Finite Element Discretization and Regularization
1 Introduction
2 Formulation of the Forward and Inverse Problems
3 Discretization of the SWE System
4 Numerical Results for the Inverse Problem
5 Conclusion and Outlook
References
Enabling Scalable Multifluid Plasma Simulations Through Block Preconditioning
1 Introduction
2 Governing Equations and Discretization
3 Block Preconditioner Definition
4 Computational Results
4.1 Current Pulse Test Problem
4.2 Soliton-Like Test Problem
5 Conclusion
References
The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: From Laminar to Turbulent Flows
1 Introduction
2 Projection Based ROMs
3 Stabilized Finite Element RB Reduced Order Method
4 Finite Volume POD-Galerkin Reduced Order Model
4.1 POD-Galerkin Projection Method
4.2 POD-Galerkin Reduced Order Model for Turbulent Flows
5 Numerical Results
5.1 Stabilized Finite Element Based ROM Results
5.2 Finite Volume POD-Galerkin-RBF ROM Results
6 Conclusion and Perspectives
References
Optimization Based Particle-Mesh Algorithm for High-Order and Conservative Scalar Transport
1 Introduction
2 Governing Equations and Problem Statement
2.1 Governing Equations
2.2 Definitions
2.3 Problem Statement
3 PDE-Constrained Particle-Mesh Interaction
3.1 Formulation
3.2 Conservation
3.3 Numerical Implementation
4 Numerical Examples
4.1 Convergence Study: Translation of Periodic Pulse
4.2 Application: Mass Conservative Rayleigh–Taylor Instability
5 Conclusions
References
Krylov Smoothing for Fully-Coupled AMG Preconditioners for VMS Resistive MHD
1 Introduction
2 Resistive MHD Model Equations and Discretization
3 Fully-Coupled Newton–Krylov Multigrid Preconditioned Solution Approach
4 Results and Discussion
4.1 3D Taylor-Green MHD Turbulent Vortex Decay
4.2 3D Island Coalescence
4.3 2D Compressible Tearing Mode
5 Conclusions
References
Double Layer Potential Density Reconstruction Procedure for 3D Vortex Methods
1 Introduction
2 Integral Equations Arising in Vortex Methods
3 Double Layer Potential Density Direct Reconstruction
4 Vortex Sheet Intensity Reconstruction
5 Numerical Results
6 Conclusion
References
Balancing Domain Decomposition Method on Additive Schwartz Framework for Multi-Level Implementation
1 Introduction
2 Overview of Methods
2.1 Iterative Substructuring Method
2.1.1 Neumann-Neumann Preconditioner
2.1.2 BDD
2.2 BDD on Additive Schwartz Framework
2.3 Multi-Level BDD on Additive Schwartz Framework
3 Numerical Examples
3.1 Cubic Model
3.2 Plate Model
4 Conclusions
References
Algebraic Dual Polynomials for the Equivalence of Curl-CurlProblems
1 Introduction
2 The Equivalent Curl-Curl Dual Problems
3 Primal Spectral Element Formulation
4 Dual Spectral Element Formulation
4.1 Duality in the Interior of the Domain
4.2 Duality in the Boundary
5 Discrete Formulation of the Curl-Curl Problem
5.1 The Neumann Problem
5.2 The Dirichlet Problem
5.3 The Equivalence Condition
5.4 Equality of Norms
6 Test Case
7 Conclusions
References
Multiple-Precision Iterative Methods for Solving Complex Symmetric Electromagnetic Systems
1 Introduction
2 Multiple-Precision Complex Number Calculation
3 Mixed-Precision Iterative Methods
4 Numerical Experiments
5 Conclusion
References
Gradient-Based Limiting and Stabilization of Continuous Galerkin Methods
1 Introduction
2 Artificial Diffusion Operators
3 Limiting of Antidiffusive Terms
3.1 Nonlinear High-Order Stabilization
3.2 Recovery of Nodal Gradients
3.3 Recovery of Nodal Time Derivatives
4 Numerical Examples
References
High Order CG Schemes for KdV and Saint-Venant Flows
1 Introduction
2 SEM Approximation of the KdV Equation
3 EVM-Stabilized SEM of the Saint-Venant System
4 Sensitivity Study to the EVM Control Parameters
5 Comparison with a Second Order FV Computation
6 Conclusion
References