Implementation of Open Boundaries within a Two-Way Coupled SPH Model to Simulate Nonlinear Wave–Structure Interactions
Abstract
:1. Introduction
- Accurate wave generation and wave absorption through coupling an SPH solver to an FNPF solver using the open boundary formulation by Tafuni et al. [24],
- Having an online exchange of information in two directions between the SPH solver and the FNPF solver.
2. Smoothed Particle Hydrodynamics
2.1. SPH Fundamentals
2.2. Governing Equations
2.3. Delta-SPH Formulation
3. Boundary Conditions in DualSPHysics
3.1. Open Boundary Conditions
3.2. Fixed Boundary Condition with Pressure Correction
3.3. Comparison to the State-of-the-Art
4. Coupling Methodology Using DualSPHysics and OceanWave3D
4.1. Inlet Velocity Correction
4.2. Outlet Velocity Correction
4.3. Coupling Algorithm
5. 2D Coupled Model: Validation
5.1. DualSPHysics Solver Options
5.2. Results and Discussion
6. 3D Coupled Model: Proof-of-Concept
6.1. Experimental Set-up
6.2. Numerical Set-up
6.3. Results and Discussion
6.4. Computational Speed-up
6.5. Visual Comparison of Overtopping
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
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Quantity | Horizontal Velocity u | Vertical Velocity w | Surface Elevation η | Pressure p |
---|---|---|---|---|
inlet | Imp | No | Imp | Hyd |
outlet | Imp | No | Ext | Ext |
Time Integration Scheme | Verlet |
---|---|
Time Step | Variable (including CFL and viscosity) |
Kernel | Wendland |
Smoothing Length | |
Viscosity Treatment | Artificial () |
Equation of State | Tait equation |
Boundary Conditions | Open Boundary Conditions |
-SPH | Yes (-SPH = 0.1) |
Wave Height H [m] | 0.12 |
Wave Period T [s] | 1.2 |
Water Depth d [m] | 0.7 |
Wave Length L [m] | 2.17 |
Particle Size d [m] | 0.01 |
Domain Length [m] | 4.34 |
Domain Width W [m] | 1.0 |
WEC Diameter D [m] | 0.5 |
WEC Draft q [m] | 0.113 |
Wave Theory | Stokes 5th |
Time Step Algorithm | Verlet |
Artificial Viscosity | 0.01 |
-SPH | 0.1 |
One-Way Coupling | Full Model | Difference | |
---|---|---|---|
# Particles | 5,010,954 | 25,473,152 | 508% |
# Fluid Particles | 2,949,433 | 21,165,100 | 718% |
GPU Memory [MB] | 780 | 3941 | 505% |
Estimated Runtime [hr] | 35 | 144 | 411% |
Real Runtime [hr] | 91 | 375 | 411% |
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Verbrugghe, T.; Stratigaki, V.; Altomare, C.; Domínguez, J.M.; Troch, P.; Kortenhaus, A. Implementation of Open Boundaries within a Two-Way Coupled SPH Model to Simulate Nonlinear Wave–Structure Interactions. Energies 2019, 12, 697. https://doi.org/10.3390/en12040697
Verbrugghe T, Stratigaki V, Altomare C, Domínguez JM, Troch P, Kortenhaus A. Implementation of Open Boundaries within a Two-Way Coupled SPH Model to Simulate Nonlinear Wave–Structure Interactions. Energies. 2019; 12(4):697. https://doi.org/10.3390/en12040697
Chicago/Turabian StyleVerbrugghe, Tim, Vasiliki Stratigaki, Corrado Altomare, J. M. Domínguez, Peter Troch, and Andreas Kortenhaus. 2019. "Implementation of Open Boundaries within a Two-Way Coupled SPH Model to Simulate Nonlinear Wave–Structure Interactions" Energies 12, no. 4: 697. https://doi.org/10.3390/en12040697