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Merge pull request #2 from jjonkman/f/SlD_Opt1_jac
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Fixed How SoilDyn is Called in the Glue Code
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@andrew-platt
andrew-platt authored Apr 20, 2020
2 parents 0a44146 + 8d0ece3 commit 4d64b4b
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55 changes: 39 additions & 16 deletions docs/OtherSupporting/OpenFAST_Algorithms/OpenFAST_Algorithms.tex
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Original file line number Diff line number Diff line change
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 Down Expand Up @@ -86,10 +87,10 @@ \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 @@ -120,11 +121,14 @@ \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 $\mathit{u\_MD} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$
\State $\mathit{u\_Orca} \gets \Call{TransferMeshMotions}{\mathit{y\_ED}}$

\State
\State $\mathit{y\_SD} \gets \Call{SD\_CalcOutput}{\mathit{p\_SD},\mathit{u\_SD},\mathit{x\_SD},\mathit{xd\_SD},\mathit{z\_SD}}$
\State $\mathit{u\_SlD} \gets \Call{TransferMeshPosition}{\mathit{y\_SD}}$
% \end Transfer_ED_to_HD_SD_BD_Mooring
%%%%
Expand All @@ -151,11 +155,11 @@ \section{Input-Output Relationships}


%\pagebreak %break here for now so that it doesn't look so strange
\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{SoilDyn}, \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
\emph{HydroDyn},\emph{SubDyn},\emph{MAP},\emph{FEAMooring},\emph{OrcaFlexInterface},\emph{MoorDyn},\emph{SoilDyn}, and\emph{ElastoDyn} (at its platform reference point mesh).
\emph{HydroDyn},\emph{SubDyn},\emph{MAP},\emph{FEAMooring},\emph{OrcaFlexInterface},\emph{MoorDyn},\emph{SoilDyn}, \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 @@ -172,17 +176,17 @@ \section{Input-Output Relationships}
\State $\mathit{y\_IceD(:)} \gets \Call{CalcOutput}{\mathit{p\_IceD(:)},\mathit{u\_IceD(:)},\mathit{x\_IceD(:)},\mathit{xd\_IceD(:)},\mathit{z\_IceD(:)}}$
\State $\mathit{y\_SlD} \gets \Call{CalcOutput}{\mathit{p\_SlD},\mathit{u\_SlD},\mathit{x\_SlD},\mathit{xd\_SlD},\mathit{z\_SlD}}$
\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 $y\_SlD \gets \Call{SlD\_CalcOutput}{\mathit{p\_SlD},\mathit{u\_SlD},\mathit{x\_SlD},\mathit{xd\_SlD},\mathit{z\_SlD}}$
\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 @@ -191,6 +195,8 @@ \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$\mathit{u\_SlD\_tmp} \gets \Call{TransferMeshMotions}{y\_SD}$
Expand All @@ -216,7 +222,7 @@ \section{Input-Output Relationships}
\end{aligned}$

\State
\State$\mathit{U\_Residual} \gets u - \Call{u\_vec}{\mathit{u\_HD\_tmp},\mathit{u\_SD\_tmp},\mathit{u\_ED\_tmp},\mathit{u\_SlD\_tmp}}$
\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 @@ -239,16 +245,18 @@ \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 @@ -260,13 +268,6 @@ \section{Input-Output Relationships}
\EndProcedure
\end{algorithmic}

\paragraph{SoilDyn}
The motion inputs to \emph{SoilDyn} are the position and orientation of the mesh points. The \emph{SoilDyn} module expects changes in position to be in the order of $10^{-3}$~m, or angular changes of $10^{-4}$~radians or less throughout the duration of the simulation with response terms on the order of $10^{12}$~N/m (or N-m/radians).
To simplify the mathematics in the Jacobian, an Euler angle extraction is performed to get rotations about the $x$, $y$, and $z$ axis (the angles are small enough that order does not matter in this context). So the $u$ input vector for \emph{SoilDyn} is a 6-vector for each mesh point.
The resulting reaction forces from \emph{SoilDyn} are roughly characterized as $F_{\mathrm{react}} \approx k x$ where $k$ is a stiffness matrix and $x$ is the 6-vector of translational and rotational displacements (note that there may be some damping or drift terms, but of much lower magnitude).
This creates a situation where $\mathit{u_SD} \gets \mathit{y_SlD} \gets \mathit{y_SD}$ is a feed back loop of \emph{SubDyn} node displacements (stored in states) of a given mesh point directly through \emph{SoilDyn} to the input force on that node point. Without including this calculation in the Jacobian, the accelerations of the \emph{SubDyn} nodes will be missing the reaction force and likely cause non-convergence or large oscillations. For this reason we include the \emph{SoilDyn} input / output into the Jacobian. However this does cause some of the Jacobian to differ by as many as six orders of magnitude, which is numerically non-ideal for the solve.



\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 @@ -351,6 +352,28 @@ \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 $\Call{SD\_UpdateStates}{\mathit{p\_SD},\mathit{u\_SD},\mathit{x\_SD},\mathit{xd\_SD},\mathit{z\_SD}}$
\State $\mathit{y\_SD} \gets \Call{SD\_CalcOutput}{\mathit{p\_SD},\mathit{u\_SD},\mathit{x\_SD},\mathit{xd\_SD},\mathit{z\_SD}}$
\State $\mathit{u\_SlD} \gets \Call{TransferMeshPosition}{\mathit{y\_SD}}$
\State $\Call{SlD\_UpdateStates}{\mathit{p\_SlD},\mathit{u\_SlD},\mathit{x\_SlD},\mathit{xd\_SlD},\mathit{z\_SlD}}$

%%%%

\State

\State All other modules (used in Solve Option 1) advance their states
\EndProcedure
\end{algorithmic}
Expand Down
2 changes: 1 addition & 1 deletion modules/openfast-library/src/FAST_Solver.f90
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Original file line number Diff line number Diff line change
Expand Up @@ -5088,7 +5088,7 @@ SUBROUTINE SolveOption2b_Inp2IfW(this_time, this_state, p_FAST, m_FAST, ED, BD,
ErrMsg = ""


IF ( p_FAST%CompElast == Module_BD .AND. .NOT. BD_Solve_Option1 ) THEN
IF ( p_FAST%CompElast == Module_BD ) THEN
DO k=1,p_FAST%nBeams
CALL BD_CalcOutput( this_time, BD%Input(1,k), BD%p(k), BD%x(k,this_state), BD%xd(k,this_state),&
BD%z(k,this_state), BD%OtherSt(k,this_state), BD%y(k), BD%m(k), ErrStat2, ErrMsg2 )
Expand Down

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