Results: Panel results

Results on the body surface $\SB$ cannot be obtained using field points. Putting a field point close to $\SB$ may give unreliable results if the distance from $\SB$ is within a typical panel diameter.

OrcaWave therefore provides a separate set of panel results for the fluid pressure and/or velocity at the centroids of panels on the body surface $\SB$. These results are only available if the appropriate output option is selected.

Panel results can be very large data sets if your model has a large number of wave periods and headings. For this reason they are not included in the spreadsheet results tables but are instead accessed via the API (see the documentation for Python, Matlab, C++).

Panel pressure

Available if the output option for panel pressures is selected. The first-order complex pressure is given in terms of the total first-order potential, $\phi$, by \begin{equation}\label{eqPressureFromPotential} p(\vec X) = -\textrm{i}\omega\rho\phi(\vec X) \end{equation} Results at panel centroids are obtained directly from the solution of the potential formulation.

The units of panel pressure are $(F/L^2)/L$, where $F$ and $L$ denote the units of force and length, respectively.

Panel velocity

Available if the solve type includes the source formulation and the output option for panel velocities is selected. The first-order complex velocity is given in terms of the total first-order potential, $\phi$, by \begin{equation}\label{eqVelocityFromPotential} \vec{v}(\vec X) = \nabla\phi(\vec X) \end{equation} Results at panel centroids are obtained from \begin{equation} \begin{aligned} \nabla\phi(\vec X) & = \nabla\phi_I(\vec X) + 2\pi \Big\{\sigma_R(\vec{X}) + \sigma_S(\vec{X}) \Big\}\vec{n}(\vec X) + \int_{\SB} \Big\{\sigma_R(\vec{\xi}) + \sigma_S(\vec{\xi}) \Big\} \nabla_x G \ud S_{\xi} & & \vec{X} \in \SB \end{aligned} \end{equation}

The units of panel velocity are $(L/T)/L$, where $L$ and $T$ denote the units of length and time, respectively.

Decomposed panel results

Available if the output option for intermediate results is selected. The above panel results are decomposed into a contribution from the diffraction potential, $\phi_D$, and contributions from the components, $\phi_j$, of the radiation potential.

Decomposed panel pressure

In the case of pressure, results are available for:

• Diffraction panel pressure, $p_D$, defined by substituting $\phi_D$ for $\phi$ in (\ref{eqPressureFromPotential})
• Radiation panel pressure, $p_j$, defined by substituting $\phi_j$ for $\phi$ in (\ref{eqPressureFromPotential})

The panel pressure due to the total first-order potential can, of course, be constructed from these contributions \begin{equation} \begin{aligned} p(\vec X) & = p_D(\vec X) + \textrm{i} \omega \sum_{j} \xi_j p_j(\vec X) \end{aligned} \label{eqTotalPressureReconstruction} \end{equation} where $\xi_j$ are the displacement RAOs.

The units of $p_D$ are $(F/L^2)/L$. The units of $p_j$ are $FT/L^3$ and $FT/L^2$ for translation and rotation degrees of freedom, respectively. $F$, $L$ and $T$ denote the units of force, length and time, respectively.

Decomposed panel velocity

In an analogous fashion, diffraction panel velocity, $\vec{v}_D$, and radiation panel velocity, $\vec{v}_j$, are defined by substituting $\phi_D$ and $\phi_j$, respectively, for $\phi$ in (\ref{eqVelocityFromPotential}). The panel velocity can similarly be constructed from these contributions \begin{equation} \begin{aligned} \vec{v}(\vec X) & = \vec{v}_D(\vec X) + \textrm{i} \omega \sum_{j} \xi_j \vec{v}_j(\vec X) \end{aligned} \label{eqTotalVelocityReconstruction} \end{equation} The units of $\vec{v}_D$ are $(L/T)/L$. The units of $\vec{v}_j$ are $1$ and $L$ for translation and rotation degrees of freedom, respectively.

Decomposed infinite-frequency panel potential

Decomposed panel results are also available for the infinite-frequency limit of the radiation velocity potentials, $\phi_j$. The water pressure (\ref{eqPressureFromPotential}) does not approach a finite limit, so results are instead given for the velocity potential, $\phi_j$, on each panel.

The units of $\phi_j$ are $L$ and $L^2$ for translation and rotation degrees of freedom, respectively.