Preface
Personal Memories and Tributes
Publications by Bong Jae Chung
Contents
Part I Theory
Natural Second-Order Regularity for Systems in the Case 1
1 Introduction
2 On the A-Approximation of an Operator and Its Properties
2.1 Notation
2.2 N-Functions
2.3 Nonlinear Operators with (p,δ)-Structure
2.4 Approximation of a Nonlinear Operator
3 On the Existence and Uniqueness of Regular Solutions for the Approximate Problem
3.1 Description and Properties of the Boundary
3.2 Regularity Results with Possible Dependencies on A
4 Estimates Uniform with Respect to A for the Solutions of the Approximate Problem
5 Passing to the Limit
6 On the Time-Dependent Problem
References
Three-Dimensional Velocity Field Using the Cross-Model Viscosity Function
1 Introduction
2 Governing Equations
3 Main Results and Simulations
3.1 Constant Mean Pressure Gradient
3.2 Nonconstant Mean Pressure Gradient
4 Conclusions
References
Small Forced Oscillation of a Rigid Body in a Viscous Liquid
1 Introduction
2 Preliminary Results
3 Main Result
References
Critical Density Triplets for the Arrestment of a Sphere Falling in a Sharply Stratified Fluid
1 Introduction
2 Setup and Governing Equations
2.1 Setup Description
2.2 Nondimensionalization
2.3 The Potential Energy
3 Experimental Methods and Results
3.1 Tank, Bath, and Camera Setup
3.2 Stratification Setup
3.3 Experimental Results
4 Critical Density and Energy Criterion
4.1 Zero Density Transition Layer Thickness
4.2 Nonzero Density Transition Layer Thickness
5 Conclusion and Discussion
Appendix
Numerical Method
References
Part II Computation
Numerical Investigation of Incompressible Fluid Flow in Planar Branching Channels
1 Introduction
2 Mathematical Model
2.1 Governing Equations
3 Numerical Methods
3.1 Artificial Compressibility Method
3.2 Finite Difference Solver
3.2.1 Immersed Boundary Method
3.2.2 Lax-Friedrichs Scheme
3.2.3 MacCormack Scheme
3.2.4 Numerical Stabilization
3.3 Finite Volume Solver
4 Numerical Simulations
4.1 Test Case Description
4.1.1 Domain Geometry
4.1.2 Boundary Conditions
4.2 Numerical Results
5 Conclusions and Remarks
References
Consistent C Element-Free Galerkin Method for Finite StrainAnalysis
1 Introduction
2 Interpolation
2.1 General Approach for Moving Least Squares
2.2 Quasi-Singular Weight Function
3 Discrete Equilibrium Equations
4 Hyperelasticity/Plasticity Using the Elastic Mandel Stress Tensor
4.1 Formulation
4.2 Constitutive Integration
4.3 Specific Yield Function
5 Numerical Tests
5.1 Straight Cantilever Beam with Closed-Form Solution
5.2 Billet Upsetting Test
5.3 Tension Test
6 Conclusions
Appendix
First and Second Variations of det[C]
References
Physics-Informed Bias Method for Multiphysics Machine Learning: Reduced Order Amyloid-β Fibril Aggregation
1 Multiphysics Modeling
1.1 Amylod-β Fibril Aggregation
1.2 Complex Multiphysics Modeling Costs
1.3 Amyloid-β Aggregation Model
2 Physics-Informed Machine Learning
2.1 Amyloid-β Fibril Aggregation
3 Case Study: Training Set Bias Method for Modeling Amyloid-β Aggregation
4 Conclusions
References
Reduced Order Model Closures: A Brief Tutorial
1 Introduction
2 A Crash Course in ROM Closure: A Toy Problem
3 Galerkin ROM (G-ROM)
4 The Closure Problem and Its Solution: The Closure Model
4.1 The Closure Problem
4.2 The Closure Model
4.2.1 The Ideal ROM (I-ROM)
4.2.2 Closure Model Construction
5 The Data-Driven Variational Multiscale ROM (D2-VMS-ROM)
5.1 Model Form Ansatz
5.2 Least Squares Problem
6 ROM Closures in Action: Numerical Results
7 Mathematical Foundations of ROM Closures
8 Conclusions and Outlook
References
Artificial Stress Diffusion in Numerical Simulations of Viscoelastic Fluid Flows
1 Introduction
1.1 Motivation
1.2 Artificial Diffusion Concept
1.3 Tensorial Stress Diffusion in Oldroyd-B-Like Models
1.4 Structure and Aim of This Work
2 Mathematical Model
2.1 Equations of Motion
2.2 Constitutive Relation: Oldroyd-B Model
2.3 Dimensionless Form of Equations
2.4 Boundary Conditions
2.5 Variational Formulation
3 Numerical Approximation
3.1 Discretization in Time: Convective Term
3.2 Discretization in Space
4 Artificial Stress Diffusion Implementation
5 Numerical Results
5.1 Constant Diffusion Coefficient
5.2 Time-Dependent Diffusion Coefficient
5.3 Time-Derivative-Dependent Diffusion Coefficient
5.4 Residual Diffusive Term
6 Conclusions and Remarks
References
Cellular Automata Describing Non-equilibrium Fluids with Non-mixing Substances
1 Introduction
2 Preliminaries and Definitions
2.1 Singular Perturbation and Pattern Stability
2.2 Assembly of CA Code Rules
2.3 Canonical Assembly of a CA Rule
3 Case Study: Rule 3E6IGS58S
3.1 Canonical Assembly of Rule 3E6IGS58S
3.2 Perturbations of the Canonical Assembly
4 Conclusions and Further Developments
References
Part III Experiments
Circular Causality and Function in Self-Organized Systems with Solid-Fluid Interactions
1 Introduction
2 Exemplary Dissipative Structures
2.1 The Electrical Self-Organized Foraging Implementation: E-SOFI
2.2 The Chemical Self-Organized Foraging Implementation: C-SOFI
3 Agent-Environment Reciprocities as a General Framework for Self-Organization
4 Conclusions
References
Hydrokinetic Energy Harvesting Potential of Triangular Prims and Cross Cylinders
1 Introduction
2 Methods
3 Results
3.1 Data Comparison from the Cross Cylinder Turbine Model
3.2 Results from the Cross Cylinder Turbine Models
3.3 Results from Triangular Prism with Straight Sides
3.4 Results from Triangular Prism with Curved Sides
3.5 Summary and Discussion
4 Conclusion
References
Part IV Applications
Fickian and Non-Fickian Transports in Ultrasound Enhanced Drug Delivery: Modeling and Numerical Simulation
1 Introduction
2 Coupling Acoustic Pressure with Drug Transport
3 Qualitative Behavior of the Total Mass
4 Stability Analysis
5 Numerical Simulations
6 Conclusions
References
Computational Analysis to Study the Efficiency of Shear-Activated Nano-Therapeutics in The Treatmentof Atherosclerosis
1 Introduction
2 Methods
2.1 Computational Fluid Dynamics (CFD) Analysis
2.2 Particle Trajectories
2.3 Breakup Criterion
2.4 Interpolation of Flow Data
2.5 Initial Conditions
2.6 Particle Ricochet Assumption
2.7 Convergence Test
3 Results
3.1 Optimal Breakup Threshold
3.2 Specific Density
3.3 Particle Diameter
3.4 Stenosis Shape and Location
4 Summary and Conclusion
References
Compressed CO2 Refrigeration for Energy Storage and CO2Utilization
1 Introduction
2 Heat Transfer Analysis
2.1 Parallel-Flow Heat Exchanger
2.2 Counter-Flow Heat Exchanger
3 Results and Discussions
4 Conclusions
References
A Two-Phase Model for Mucosal Aggregation and Clearance in the Human Tear Film
1 Introduction
2 Theoretical Model
2.1 The Fluid Model
2.2 Phase I: Mucoadhesion and Wrapping Mechanics
2.2.1 Adhesion Mechanics
2.2.2 Wrapping and Size of Aggregate
2.3 Phase II: The Particle Model
3 Computational Methods
3.1 The Fluid Model
3.2 The FSI Particle Model
4 Results
5 Discussion
References
