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

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