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Update OpenFAST_Algorithms document with corrections
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@andrew-platt
andrew-platt committed Oct 8, 2020
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59 changes: 39 additions & 20 deletions docs/OtherSupporting/OpenFAST_Algorithms/OpenFAST_Algorithms.tex
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Expand Up @@ -44,6 +44,7 @@ \section{Definitions and Nomenclature}
AeroDyn & AD & AD \\
ServoDyn & SrvD & SrvD \\
SubDyn & SD & SD \\
ExtPtfm & ExtPtfm & ExtPtfm \\
HydroDyn & HydroDyn & HD \\
MAP++ & MAPp & MAP \\
FEAMooring & FEAM & FEAM \\
Expand All @@ -52,7 +53,6 @@ \section{Definitions and Nomenclature}
InflowWind & IfW & IfW \\
IceFloe & IceFloe & IceF \\
IceDyn & IceD & IceD \\
SoilDyn & SlD & SlD \\
\end{tabular}
\caption{Abbreviations for modules in FAST v8}
\label{tab:Abbrev}
Expand Down Expand Up @@ -86,10 +86,10 @@ \section{Input-Output Relationships}
% SolveOption2a_Inp2BD
\State $\mathit{y\_ED} \gets \Call{ED\_CalcOutput}{\mathit{p\_ED},\mathit{u\_ED},\mathit{x\_ED},\mathit{xd\_ED},\mathit{z\_ED}}$
\State $\mathit{u\_BD} \gets \Call{TransferOutputsToInputs}{\mathit{y\_ED}}$
\State $\mathit{y\_BD} \gets \Call{BD\_CalcOutput}{\mathit{p\_BD},\mathit{u\_BD},\mathit{x\_BD},\mathit{xd\_BD},\mathit{z\_BD}}$

\State
% SolveOption2b_Inp2IfW
\State $\mathit{y\_BD} \gets \Call{BD\_CalcOutput}{\mathit{p\_BD},\mathit{u\_BD},\mathit{x\_BD},\mathit{xd\_BD},\mathit{z\_BD}}$
\State $\mathit{u\_AD}($no IfW$) \gets \Call{TransferOutputsToInputs}{\mathit{y\_ED}}$
\State $\mathit{u\_IfW} \gets \Call{TransferOutputsToInputs}{\mathit{y\_ED} at \mathit{u\_AD} nodes}$

Expand Down Expand Up @@ -120,6 +120,7 @@ \section{Input-Output Relationships}
% \State $\mathit{u\_BD} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$ % only if not BD_Solve_Option1
\State $\mathit{u\_HD} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State $\mathit{u\_SD} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State $\mathit{u\_ExtPtfm} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State $\mathit{u\_MAP} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State $\mathit{u\_FEAM} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State $\mathit{u\_MD} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
Expand All @@ -138,24 +139,22 @@ \section{Input-Output Relationships}
\end{algorithmic}
%\end{algorithm}

Note that inputs to $ElastoDyn$ before calling CalcOutput() in the first step are not set in CalcOutputs\_And\_SolveForInputs().
Instead, the $ElastoDyn$ inputs are set depending on where CalcOutputs\_And\_SolveForInputs() is called:
Note that inputs to \emph{ElastoDyn} before calling CalcOutput() in the first step are not set in CalcOutputs\_And\_SolveForInputs().
Instead, the \emph{ElastoDyn} inputs are set depending on where CalcOutputs\_And\_SolveForInputs() is called:
\begin{itemize}[noitemsep] %i don't like the double spaces between bulleted items.
\item At time 0, the inputs are the initial guess from $ElastoDyn$;
\item At time 0, the inputs are the initial guess from \emph{ElastoDyn};
\item On the prediction step, the inputs are extrapolated values from the time history of ElastoDyn inputs;
\item On the first correction step, the inputs are the values calculated in the prediction step;
\item On subsequent correction steps, the inputs are the values calculated in the previous correction step.
\end{itemize}


%\pagebreak %break here for now so that it doesn't look so strange
%\subsection {Input-Output Solve for $HydroDyn$, $SubDyn$, $MAP$, \\
% $FEAMooring$, $IceFloe$, and the Platform Reference Point Mesh in $ElastoDyn$}
\subsection {Input-Output Solve for \textit{HydroDyn}, \textit{SubDyn}, \textit{MAP},
\textit{FEAMooring}, \textit{IceFloe}, and the Platform Reference Point Mesh in \textit{ElastoDyn}}
\subsection {Input-Output Solve for \textit{HydroDyn}, \textit{SubDyn}, \textit{OrcaFlexInterface}, \textit{BeamDyn}, \textit{ExtPtfm}, \textit{MAP}, \textit{FEAMooring}, \textit{MoorDyn},
\textit{FEAMooring}, \textit{IceFloe}, \textit{IceDyn}, and the Platform Reference Point Mesh in \textit{ElastoDyn}}

This procedure implements Solve Option 1 for the accelerations and loads in
$HydroDyn$, $SubDyn$, $MAP$, $FEAMooring$, and $ElastoDyn$ (at its platform reference point mesh).
\emph{HydroDyn},\emph{SubDyn},\emph{MAP},\emph{FEAMooring},\emph{OrcaFlexInterface},\emph{MoorDyn}, \emph{BeamDyn}, \emph{ExtPtfm}, \emph{IceFloe}, \emph{IceDyn}, and \emph{ElastoDyn} (at its platform reference point mesh).
The other input-output relationships for these modules are solved using Solve Option 2.

%\begin{algorithm}[ht]
Expand All @@ -171,16 +170,17 @@ \section{Input-Output Relationships}
\State $\mathit{y\_IceF} \gets \Call{CalcOutput}{\mathit{p\_IceF},\mathit{u\_IceF},\mathit{x\_IceF},\mathit{xd\_IceF},\mathit{z\_IceF}}$
\State $\mathit{y\_IceD(:)} \gets \Call{CalcOutput}{\mathit{p\_IceD(:)},\mathit{u\_IceD(:)},\mathit{x\_IceD(:)},\mathit{xd\_IceD(:)},\mathit{z\_IceD(:)}}$
\State
\State\Comment{Form $u$ vector using loads and accelerations from $\mathit{u\_HD}$, $\mathit{u\_BD}$ $\mathit{u\_SD}$, and platform reference input from $\mathit{u\_ED}$}
\State\Comment{Form $u$ vector using loads and accelerations from $\mathit{u\_HD}$, $\mathit{u\_BD}$, $\mathit{u\_SD}$, $\mathit{u\_Orca}$, $\mathit{u\_ExtPtfm}$, and platform reference input from $\mathit{u\_ED}$}
\State
\State $u \gets \Call{u\_vec}{\mathit{u\_HD},\mathit{u\_SD},\mathit{u\_ED}}$
\State $u \gets \Call{u\_vec}{\mathit{u\_HD},\mathit{u\_SD},\mathit{u\_ED},\mathit{u\_BD},\mathit{u\_Orca},\mathit{u\_ExtPtfm}}$
\State $k \gets 0$
\Loop\Comment{Solve for loads and accelerations (direct feed-through terms)}
\State $y\_ED \gets \Call{ED\_CalcOutput}{\mathit{p\_ED},\mathit{u\_ED},\mathit{x\_ED},\mathit{xd\_ED},\mathit{z\_ED}}$
\State $y\_SD \gets \Call{SD\_CalcOutput}{\mathit{p\_SD},\mathit{u\_SD},\mathit{x\_SD},\mathit{xd\_SD},\mathit{z\_SD}}$
\State $y\_HD \gets \Call{HD\_CalcOutput}{\mathit{p\_HD},\mathit{u\_HD},\mathit{x\_HD},\mathit{xd\_HD},\mathit{z\_HD}}$
\State $y\_BD \gets \Call{BD\_CalcOutput}{\mathit{p\_BD},\mathit{u\_BD},\mathit{x\_BD},\mathit{xd\_BD},\mathit{z\_BD}}$
\State $y\_Orca \gets \Call{Orca\_CalcOutput}{\mathit{p\_Orca},\mathit{u\_Orca},\mathit{x\_Orca},\mathit{xd\_Orca},\mathit{z\_Orca}}$
\State $\mathit{y\_ExtPtfm} \gets \Call{CalcOutput}{\mathit{p\_ExtPtfm},\mathit{u\_ExtPtfm},\mathit{x\_ExtPtfm},\mathit{xd\_ExtPtfm},\mathit{z\_ExtPtfm}}$

\If{ $k \geq k\_max$}
\State exit loop
Expand All @@ -189,6 +189,8 @@ \section{Input-Output Relationships}
\State$\mathit{u\_BD\_tmp} \gets \Call{TransferMeshMotions}{y\_ED}$
\State$\mathit{u\_MAP\_tmp} \gets \Call{TransferMeshMotions}{y\_ED}$
\State$\mathit{u\_FEAM\_tmp} \gets \Call{TransferMeshMotions}{y\_ED}$
\State$\mathit{u\_Orca\_tmp} \gets \Call{TransferMeshMotions}{y\_ED}$
\State$\mathit{u\_MD\_tmp} \gets \Call{TransferMeshMotions}{y\_ED}$
\State$\mathit{u\_IceF\_tmp} \gets \Call{TransferMeshMotions}{y\_SD}$
\State$\mathit{u\_IceD\_tmp(:)} \gets \Call{TransferMeshMotions}{y\_SD}$
\State$\mathit{u\_HD\_tmp} \gets \Call{TransferMeshMotions}{y\_ED,y\_SD}$
Expand All @@ -197,10 +199,10 @@ \section{Input-Output Relationships}
& \Call{TransferMeshMotions}{\mathit{y\_ED}} \\
& \cup \Call{TransferMeshLoads}{}(\!
\begin{aligned}[t]
& \mathit{y\_SD}, \\
& \mathit{y\_HD},\mathit{u\_HD\_tmp}, \\
& \mathit{y\_IceF},\mathit{u\_IceF\_tmp}) \\
& \mathit{y\_IceD(:)},\mathit{u\_IceD\_tmp(:)}) \\
& \mathit{y\_SD}, \\
& \mathit{y\_HD}, \mathit{u\_HD\_tmp}, \\
& \mathit{y\_IceF}, \mathit{u\_IceF\_tmp}, \\
& \mathit{y\_IceD(:)}, \mathit{u\_IceD\_tmp(:)}, \\
\end{aligned}
\end{aligned}$
\State$\mathit{u\_ED\_tmp} \gets \Call{TransferMeshLoads}{}( \!
Expand All @@ -212,7 +214,7 @@ \section{Input-Output Relationships}
\end{aligned}$

\State
\State$\mathit{U\_Residual} \gets u - \Call{u\_vec}{\mathit{u\_HD\_tmp},\mathit{u\_SD\_tmp},\mathit{u\_ED\_tmp}}$
\State$\mathit{U\_Residual} \gets u - \Call{u\_vec}{\mathit{u\_HD\_tmp},\mathit{u\_SD\_tmp},\mathit{u\_ED\_tmp},\mathit{u\_BD\_tmp},\mathit{u\_Orca\_tmp},\mathit{u\_ExtPtfm\_tmp}}$
\State

\If{ last Jacobian was calculated at least $\mathit{DT\_UJac}$ seconds ago }
Expand All @@ -235,16 +237,18 @@ \section{Input-Output Relationships}
\EndIf
\State
\State $u \gets u + \Delta u$
\State Transfer $u$ to $\mathit{u\_HD}$, $\mathit{u\_SD}$, and $\mathit{u\_ED}$\Comment{loads and accelerations only}
\State Transfer $u$ to $\mathit{u\_HD}$, $\mathit{u\_SD}$, $\mathit{u\_BD}$, $\mathit{u\_Orca}$, $\mathit{u\_ExtPtfm}$, and $\mathit{u\_ED}$\Comment{loads and accelerations only}
\State $k=k+1$

\EndLoop

\State\Comment{Transfer non-acceleration fields to motion input meshes}
\State

\State$\mathit{u\_BD}($not accelerations$) \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State$\mathit{u\_HD}($not accelerations$) \gets \Call{TransferMeshMotions}{\mathit{y\_ED},\mathit{y\_SD}}$
\State$\mathit{u\_SD}($not accelerations$) \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State$\mathit{u\_Orca}($not accelerations$) \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$ \State$\mathit{u\_ExtPtfm}($not accelerations$) \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State
\State $\mathit{u\_MAP} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State $\mathit{u\_MD} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
Expand All @@ -253,9 +257,8 @@ \section{Input-Output Relationships}
\State $\mathit{u\_IceD(:)} \gets \Call{TransferMeshMotions}{\mathit{y\_SD}}$

\EndProcedure

\end{algorithmic}
%\end{algorithm}


\subsection {Implementation of line2-to-line2 loads mapping}
The inverse-lumping of loads is computed by a block matrix solve for the distributed forces and moments,
Expand Down Expand Up @@ -340,6 +343,22 @@ \section{Solve Option 2 Improvements}
\State $\Call{AD\_UpdateStates}{\mathit{p\_AD},\mathit{u\_AD},\mathit{x\_AD},\mathit{xd\_AD},\mathit{z\_AD}}$
\State $\Call{SrvD\_UpdateStates}{\mathit{p\_SrvD},\mathit{u\_SrvD},\mathit{x\_SrvD},\mathit{xd\_SrvD},\mathit{z\_SrvD}}$
\State
% \begin Transfer_ED_to_HD_SD_BD_Mooring
% \State $\mathit{u\_ED}($not platform reference point$) \gets \Call{TransferOutputsToInputs}{y\_SrvD,y\_AD}$ %\Comment{sets all but platform reference point inputs}

% \State $\mathit{u\_BD} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$ % only if not BD_Solve_Option1
\State $\mathit{u\_HD} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State $\mathit{u\_SD} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State $\mathit{u\_ExtPtfm} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State $\mathit{u\_MAP} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State $\mathit{u\_FEAM} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State $\mathit{u\_MD} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State $\mathit{u\_Orca} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
% \end Transfer_ED_to_HD_SD_BD_Mooring
%%%%

\State

\State All other modules (used in Solve Option 1) advance their states
\EndProcedure
\end{algorithmic}
Expand Down

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