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1. Introduction to Aqwa Solver Theory
1.1. Aqwa General Capabilities
1.2. Axes Conventions
1.2.1. Fixed Reference Axes
1.2.2. Local Structure Axes
1.2.3. Local Articulation Axes
1.2.4. Axis Transformation and Euler Rotations
1.3. Direction and Phase Angle Conventions
2. Ocean Environmental Conditions
2.1. Ocean Waves
2.1.1. Regular Wave
2.1.1.1. Linear Regular Wave
2.1.1.2. Second Order Stokes Wave
2.1.1.3. Fifth Order Stokes Wave
2.1.2. Irregular Waves
2.1.2.1. Formulated Wave Spectra
2.1.2.1.1. JONSWAP Spectrum
2.1.2.1.2. Pierson-Moskowitz Spectrum
2.1.2.1.3. Gaussian Spectrum
2.1.2.1.4. Ochi-Hubble Spectrum
2.1.2.1.5. Bretschneider Spectrum
2.1.2.1.6. TMA Spectrum
2.1.2.2. User Defined Wave-Spectrum
2.1.2.3. Import Time History of Wave Elevation
2.1.2.4. Cross-Swell Waves
2.1.2.5. Spreading Sea
2.1.2.6. User-Defined Carpet Spectra
2.1.2.7. Wave Spectral Group
2.2. Wind
2.2.1. Uniform Wind
2.2.2. Wind Velocity Profile and Fluctuation
2.2.2.1. Ochi and Shin Wind Spectrum
2.2.2.2. API Wind Spectrum
2.2.2.3. NPD Wind Spectrum
2.2.2.4. ISO Wind Spectrum
2.2.2.5. User Defined Wind Spectrum
2.2.2.6. Import of a Time History of Wind Speed and Direction
2.3. Current
2.3.1. Uniform and Profiled Current
2.3.2. Wave and Current Interaction
3. Hydrostatics of Free-Floating Structures
3.1. Hydrostatic Forces and Moments
3.2. Hydrostatic Equilibrium
3.2.1. Free-Floating Hydrostatic Stability
3.2.2. Small Angle Stability
3.2.3. Large Angle Stability
3.3. Hydrostatic Stiffness Matrix
3.4. Hydrostatic Property of Floating Body with Internal Tanks
3.4.1. Local Internal Tank Axes and Combined COG
3.4.2. Internal Tank Basic Motions
3.4.3. Hydrostatic Force and Moment Due to Internal Tanks
3.4.4. Hydrostatic Stiffness Due to Internal Tanks
3.4.5. Small Angle Stability of Freely Floating Structure with Internal Tanks
3.4.6. Large Angle Stability of Freely Floating Structure with Internal Tanks
3.5. Free Trim Large Angle Stability
4. Hydrodynamic Radiation and Diffraction Analysis by Source Distribution Method
4.1. Radiation and Diffraction Wave Forces
4.1.1. General Formula in Zero Forward Speed Case
4.1.2. Source Distribution Method
4.1.3. Removal of Irregular Frequencies
4.1.4. Mesh Quality Check
4.2. Hydrodynamic Interaction
4.2.1. Extended Hydrodynamic Coefficient Matrices
4.2.2. Suspending Standing Waves
4.3. Corrections for Small Forward Speed
4.4. Response Amplitude Operators
4.5. Response Amplitude Operators with Additional Input
4.6. Disturbed Wave Elevation and Air Gap
4.7. Composite Source Distribution Method for Symmetric Structures
4.8. Generalized Hydrodynamic Damping
4.9. Radiation Wave Properties at Negative Encounter Frequency
4.10. Fictitious Damping at Small Magnitude of Encounter Frequency
4.11. Hydrodynamic Properties of Internal Tanks
4.12. Hydrodynamic Analysis with Moonpool Effects
4.12.1. Resonant Frequency of Water Motion within Moonpools
4.12.2. Prescribed Oscillatory Pressure Distribution Approach
4.12.3. Multi-region Matching Approach for Simulation of Moonpool Effects
4.12.4. Artificial Damping for Suspending Resonant Water Motion within Moonpools
4.12.5. Composite Source Distribution Method for Symmetric Moonpool Configuration
4.12.6. Extended Hydrodynamic Coefficient Matrices of a Hydrodynamic Interaction Structure Group with Moonpools
5. Second Order Wave Excitation Forces
5.1. Second Order Motion and Force
5.2. Unidirectional Mean Wave Drift Forces (Far Field Solution)
5.3. General QTF Coefficient Matrix in Multiple Directional Waves
5.4. Mean Wave Drift Forces (Near Field Solution)
5.5. Extended Newman's Approximation
5.6. Second Order Wave Potential and Its Simplification
6. Morison Element Forces
6.1. Morison Equation
6.2. Scale Factor for Model Test Simulation
6.3. Morison Elements in Frequency Domain Dynamic Response Analysis
6.4. Morison Drag Linearization
6.5. Effects of Morison Elements in Equilibrium and Static Stability Analysis
6.6. Effects of Morison Elements in a Time Domain Dynamic Response Analysis
6.7. Properties of Typical Morison Elements
7. Hull Drag and Damping
7.1. Current and Wind Hull Drag
7.2. Nonlinear Roll Damping
7.2.1. Nonlinear Bilge Vortex Shedding Damping
7.2.2. Bilge Keel Damping
7.2.3. User-Defined Quadratic Roll Damping
7.3. Yaw Rate Drag Force
7.4. Morison Hull Drag Force
7.5. Wave Drift Damping
8. Articulation and Constraint
8.1. Articulations Between Structures
8.1.1. Motion Restriction due to Articulation
8.1.2. Effect of Articulation Stiffness, Damping and Friction
8.2. Elimination of Freedoms at the Center of Gravity
9. Moorings and Fenders
9.1. Linear Elastic Cable
9.2. Pulley
9.2.1. Pulley with Sliding Friction
9.2.2. Pulley with Bearing Friction
9.3. Linear Drum Winch
9.4. Winch Line and Force Line
9.5. Weightless Nonlinear Mooring Line
9.5.1. Steel Wire
9.5.2. Polynomial Nonlinear Mooring Line
9.5.3. Nonlinear Mooring with 2-Dimensional Load Extension Database
9.6. Quasi-Static Composite Catenary Mooring Line
9.6.1. Catenary Segment with Influence of Axial Linear Elasticity
9.6.2. Catenary Segment with Influence of Axial Nonlinear Elasticity
9.6.3. Cable on Global Sloped Seabed
9.7. Dynamic Composite Catenary Mooring Line
9.8. Fender
9.8.1. Fixed Fender
9.8.2. Floating Fender
9.8.3. Fender Friction and Damping
10. Tethers
10.1. Mass and Stiffness Matrices
10.2. Boundary Conditions and Constraints
10.3. Total Applied Forces
10.4. Integration in Time of Motion Equation
10.5. Fatigue/Extreme Value Statistical Post-Processing for Towed Tethers
11. Equilibrium Estimation and Stability Analysis of Structure System
11.1. External Static Forces
11.2. Equilibrium Analysis
11.2.1. The Stiffness Matrix
11.2.2. Iteration Towards Equilibrium
11.3. Static Stability Analysis
11.4. Dynamic Stability Analysis
12. Frequency Domain Dynamic Simulation
12.1. Linearization
12.1.1. Wind Drag Linearization
12.1.2. Dynamic Cable Drag Linearization
12.1.3. Morison Element Drag Linearization
12.1.4. Current Hull Drag Linearization
12.1.5. Nonlinear Roll Damping Linearization
12.2. Response Spectral Density
12.3. Significant Value Calculation
13. Time Domain Dynamic Simulation
13.1. Radiation Force by Convolution Integration
13.2. Sloshing Forces by Convolution Integration
13.3. Optional Additional External Forces
13.4. Inertia Forces in Time Domain Analysis
13.5. Irregular Wave Responses with Slow Drift (Aqwa-Drift)
13.5.1. Wave Excitation Forces and Motion Equation
13.5.2. Motions at Drift Frequency
13.5.3. Motions at Drift and Wave Frequency
13.5.4. Initial Position and Transients
13.6. Motion Response in Severe Sea State (Aqwa-Naut)
13.6.1. Extended Wheeler Stretching Method
13.6.1.1. Wheeler Stretching for Regular Linear Airy Waves
13.6.1.2. Wheeler Stretching for Irregular Airy Waves
13.6.1.3. Extended Wheeler Stretching for Second Order Stokes Waves
13.6.2. Second Order Correction of Linear Irregular Waves
13.6.3. Wave Ramp
13.6.4. Hydrodynamic pressure and disturbed wave elevation
13.7. Nodal Motion Response
13.8. Morison Tube Element and Nodal Loads
13.8.1. Nodal Loads of Tube Elements in Space Frames
13.8.2. Nodal Loads of Tube Elements in Riser-Type Structures
13.9. Integration in Time of Motion Equation
13.10. Low Frequency Maneuvering Loads
14. Extended Functionalities
14.1. Effective Nodal Acceleration RAOs
14.2. Shear Force and Bending Moment along Axes
14.3. Splitting Force and Moment
14.4. Evaluation of Percentage of Critical Damping from Twang Test
14.5. Aqwa Parallel Processing Calculation
15. References