Campbell, S., Ilchmann, A., Mehrmann, V., Reis, T. (Eds.) Applications of Differential-Algebraic Equations: Examples and Benchmarks

New York: Springer, 2019. — 324 p.This volume encompasses prototypical, innovative and emerging examples and benchmarks of Differential-Algebraic Equations (DAEs) and their applications, such as electrical networks, chemical reactors, multibody systems, and multiphysics models, to name but a few. Each article begins with an exposition of modelling, explaining whether the model is prototypical and for which applications it is used. This is followed by a mathematical analysis, and if appropriate, a discussion of the numerical aspects including simulation. Additionally, benchmark examples are included throughout the text.
Mathematicians, engineers, and other scientists, working in both academia and industry either on differential-algebraic equations and systems or on problems where the tools and insight provided by differential-algebraic equations could be useful, would find this book resourceful.Preface of Applications of Differential-Algebraic Equations: Examples and BenchmarksExact Tracking
Approximate Tracking as Optimal Control
Asymptotic Tracking
Tracking with General Nonlinear DAEs
Some Needed Mathematics
Exact Tracking of General DAEs
Approximate Tracking of General DAEs
Asymptotic Tracking of General DAEs
An Example from Robotics
Stabilizing Feedback
Tracking Problem I as Inversion
Tracking Problem I as Stabilized Reduction
Tracking Using Optimal Control
Tracking Problem I as Optimal Control
Using Necessary Conditions
Concluding CommentsModeling Kinematic Joints
Contact Modeling
Path Constraints and Dynamic Inversion Control
A Mobile Robot
Prescribed Path for the Platform
Prescribed Path and Orientation for the Platform
Prescribed Path for the End Affector
Vehicle Moving on Prescribed Path
Identification of Road Profiles
Identification of Tyre Loads
Piecewise Defined DAEs and Dockings
ConclusionsOpen-Loop Control of Underactuated Mechanical Systems Using Servo-Constraints: Analysis and Some ExamplesGeneralized Coordinates
Servo-Constraints Approach
Relationship Between Relative Degree and Differentiation Index of Inverse Model DAEs
Index Reduction and Analysis Methods
Projection Approach
Using Redundant Coordinates for Servo-Constraints Approach
DAE Solver
Mass-on-Car System
Extension of Mass-on-Car System
Mass-Spring-Damper Chain
Influence of Actuator Model on the DAE IndexMaxwell's Equations
Boundary Conditions and Material Relations
Modelling of Excitations
Static and Quasistatic Fields
Electromagnetic Potentials
Domain and Grid
Maxwell's Grid Equations
Material Matrices
Differential Algebraic Equations
First-Order Formulation Time-Stepped by Leapfrog
A–Φ Formulations
Full Maxwell with Lorenz Gauge
Full Maxwell with Coulomb Gauge
Electroquasistatic Maxwell's Equations
Electric Scalar Potential ϕ-Formulation
Magnetic Vector Potential A-formulations
Electric Vector Potential T–Ω-formulation
Darwin Model
ψ–A A A A*-formulation of the Darwin Model
Discretisation of the Darwin Model
ConclusionsGas Network Benchmark Models
The Isothermal Euler Equations
Friction Factor
Gas Network
Pipes
Valves
Compressor/Ideal Compressor Unit
Control Valve
Node Conditions
Partial Differential Algebraic Equation
Network DAE
Pipeline Benchmark Model
Diamond Network
Gas Transportation Network – gas_N_A
Gas Transportation Network – gas_N_A (Derived from GasLib-)
Concluding Remarks
Code and Data AvailabilityTopological Index Analysis Applied to Coupled Flow NetworksA Network Model for Incompressible Flow Networks
Graphtheoretical Prerequisites
Solvability Results
Surrogate Model
A Model for Coupled Flow Networks
Topology Based Index Analysis for Coupled Flow Networks
Conclusion and DiscussionNonsmooth DAEs with Applications in Modeling Phase ChangesModeling Flash Processes with Nonsmooth DAEs
Nonsmooth Generalized Differentiation Index-One DAEs
Regularity and Consistency of Nonsmooth DAEs
Existence and Uniqueness of Solutions of Nonsmooth DAEs
Analysis and Simulation of Nonsmooth Flash Models
The Use of a Cubic Equation of State
Analysis and Simulation of the Cubic Equation of State Model
Structural Analysis
Regularity Analysis
Simulation
Unphysical Behavior from Common Modeling SimplificationsDerivation of the Navier-Stokes Equations for Incompressible Flows
Incompressibility and Mass Conservation
Balance of Momentum
The Navier-Stokes Equations for Incompressible Flows
Boundary Conditions
Formulation as Operator DAE
Semi-discrete Equations
Spatial Discretisation by Finite Elements
Finite Volumes and Finite Differences
Fully Discrete Approximation Schemes
Index and Causality of Discrete Systems
Common Time-Stepping Schemes as Index- AEs
Projection
SIMPLE Scheme: Implicit Pressure Correction
Artificial Compressibility
Derivative of the Constraint
Minimal Extension
Numerical Experiments
Time Integration with Half-Explicit EulerLinear Case
Nonlinear Case
Half-Explicit Euler
Projection Scheme