## Simulation Progress

### Simulation Background

The CycWEC and wave-induced ﬂow ﬁeld are modeled using potential ﬂow theory. For an inviscid, incompressible, and irrotational ﬂow, the governing continuity equation simpliﬁes to the Laplace equation:

$\nabla^2\Phi=0$

The linearized free surface boundary condition is used to model the water surface. Subject to these kinematic and dynamic boundary conditions, the complex potential for a vortex moving under a free surface in the complex plane is:

$F(z,t)&=&\frac{\Gamma(t)}{2\pi i} ln\left(\frac{z-c(t)}{z-\bar{c}(t)}\right) &+&\frac{g}{\pi i}\int^{t}_{0}\int^{\infty}_{0} \frac{\Gamma(\tau)}{\sqrt{gk}}e^{-ik(z-\bar{c}(\tau))} &\times&sin\left[\sqrt{gk}(t-\tau)\right]dkd\tau$

Note: Please see scientific publications and references for full explanation and derivation

Besides a powerful numerical tool for the validation and evaluation of the novel CycWEC design, the simulation also provides:

• A means to compare and validate model vs. full scale behavior
• Exact solution of governing equations
• Energy conservation
• Spatial grid not needed
• Nominal solution times
• Powerful tool for WEC kinematic and dynamic design
• Submergence depth
• Number of blades and azimuthal positions