# Numerical modeling

__Rigid body model__: Newton´s second law is used to obtain the dynamics of the structure as a rigid solid with six degrees of freedom: three translations and three rotations. Thus, it is necessary to know the inertia matrix of the platform and calculate all the forces and moments that act on it.__Hydrostatic and hydrodynamic models__: with the hydrostatic model, we obtain the combination of buoyancy and gravity forces acting on the device due to the stiffness matrix. For the calculation of hydrodynamic forces, linear potential theory is used, characterizing the response of the platform with hydrodynamic coefficients obtained with the boundary element method (BEM).__Mooring system model__: to model the lines used in the mooring system, two options are considered. On the one hand, a quasi-static model that ignores the dynamic effects on the lines, based on the catenary equation and significantly faster, on the other hand a more elaborate dynamic model, based on the finite element method (FEM).__Oscillating water column model (OWC)__: this model is based on the hydrodynamic model mentioned above. In this case, the aperture on the top of the device is considered as a new degree of freedom: the free surface in the chamber. This also affects the rest of the hydrodynamic coefficients of the platform. Finally, the OWC’s energy extraction system (PTO) is modelled, so its energy production can be obtained.__Aerodynamic model (Semisubmersible)__: this model is used to obtain the influence of the wind turbine acting on the platform. The turbine speed is studied, so the forces and the production are obtained too.

Once all the submodels are defined, they are coupled together in a single model. To do this, at each time step, the position and the speed of the platform are used in the others submodels as boundary conditions to obtain its forces and momentum.

Calibration process

The hydrodynamic model, which is the base of the WEC motions solver, is based on potential flow theory. Because of that, there are some assumptions behind (e.g. inviscid flow, …) which are partially mitigated through empirical linear and non-linear damping coefficients acting as viscous forces that need to be calibrated through experimental results (Iturrioz et al 2017). This process has three steps for each configuration:

__STATIC OFFSET TESTS__: used to verify that the fairleads loads and displacements obtained with the numerical model and in the laboratory match.

**OWC**

Figure 3. OWC. Static offset: Positive Surge. Configuration 1. Force-Displacement

Figure 4. OWC. Static offset: Positive Surge. Configuration 1. Mooring Force-Displacement

**SEMISUBMERSIBLE**

Figure 5. Semisubmersible. Static offset: Negative Surge. Force-Displacement

Figure 6. Semisubmersible. Static offset: Positive Surge. Mooring Force-Displacement

__DECAY FREE AND MOORED TESTS__: used to verify that the fairleads loads and displacements obtained with the numerical model and in the laboratory match.

**OWC**

__Configuration C2__: Closed chamber.

(click to enlarge)

Figure 7. OWC. Calibration. Configuration C2. Decay free test. Heave

Figure 12. OWC. Calibration. Configuration C2. Decay moored test. Heave

__Configuration C1__: Open aperture.

Figure 16. OWC. Calibration. Configuration C1. Decay free test. Heave

Figure 21. OWC. Calibration. Configuration C1. Decay moored test. Sway

**SEMISUBMERSIBLE**

(click to enlarge)

Figure 26. Semisubmersible. Calibration. Decay free test. Heave

Figure 31. Semisubmersible. Calibration. Decay moored test. Heave

__TESTS WITH REGULAR WAVES__: these tests are used to validate the calibration process, verifying that the calibration is correct.

**OWC**

(click to enlarge)

Figure 35 OWC. Validation. Configuration C2. Regular waves: H=2.5m Tp=10s. Surge, Heave and Pitch

Figure 36. OWC. Validation. Configuration C1. Regular waves: H=2.5m Tp=10s. Surge, Heave and Pitch

Figure 37. OWC. Validation. Configuration C1. Regular waves: H=2.5m Tp=10s. Free surface and pressure inside the chamber

**SEMISUBMERSIBLE**

(click to enlarge)

Figure 38. Semisubmersible. Validation. Regular waves: H=2.5m Tp=8s

Figure 39. Semisubmersible. Validation. Regular waves: H=5m Tp=14s

Figure 40. Semisubmersible. Validation. Wind. F_{constant} =12m/s.

Figure 41.Semisubmersible. Validation. Wind. F_{constant} =12m/s. Mooring lines

Figure 42. Semisubmersible. Validation. Waves + Wind. F =16m/s, H=2.5m, T=10s

Figure 43. Semisubmersible. Validation. Waves + Wind. F =16m/s, H=2.5m, T=10s. Mooring lines