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Nomenclature.tex
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Nomenclature.tex
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\section*{Nomenclature}\label{sec:nomenclature}
\subsection*{Operators}
\subsection*{Algebraic operations}
\begin{tabular}{l l}
$\T{Q}$ & Transpose of a tensor\\
$\inv{Q}$ & Inverse of a tensor\\
$\av{q}$ & Average component of a quantity\\
$\fluc{q}$ & Fluctuating component of a quantity\\
$\norm{q}$ & Norm of a quantity\\
$\prim{q}$ & Quantity being expressed in primitive variables
\end{tabular}
\subsection*{Representation of scalars, tensors and other quantities}
\begin{tabular}{l l}
$\s{q}$ & Scalar quantity\\
$\v{q}$ & Vector quantity\\
$\m{Q}$ & Matrix quantity\\
$\tensor{Q}$ & Tensor quantity\\
$\abs{q}$ & Norm of a vector\\
$\c{Q,q}$ & Continous quantity\\
$\d{Q,q}$ & Discrete quantity\\
$\it{q}$ & Iteration index in the optimization loop\\
$\its{q}$ & Iteration index in the staggered algorithm\\
$\fic{Q}$ & Fictious entity\\
$\order{n}$ & Order of magnitude
\end{tabular}
\subsection*{Analytic operations}
\begin{tabular}{l l}
$\derivtime{q}$ & First time derivative at a fixed reference position\\
$\dderivtime{q}$ & Second time derivative at a fixed refrence position\\
$\pdfrac{q_1}{q_2}$ & Partial derivative of one argument with respect to the other\\
$\ppdfrac{q_1}{q_2}$ & Second partial derivative of one argument with respect to the other\\
$\mfrac{q_1}{q_2}$ & Material time derivative
\end{tabular}
\subsection*{Symbols}
\subsubsection*{Numerical formulation}
\begin{tabular}{l l}
$\fstate$ & Fluid state vector\\
$\fstatead$ & Adjoint fluid state vector\\
$\fstaterans$ & Augumented fluid state vector in the RANS formulation\\
$\fstateprim$ & Primitive fluid state vector\\
$\mpos$ & Fluid mesh position\\
$\mms$ & Fluid mesh motion\\
$\mmsad$ & Adjoint fluid mesh motion\\
$\ifaceprojStoF$ & Interface projection matrix from structure to fluid mesh\\
$\ifaceprojFtoS$ & Interface projection matrix from fluid to structure mesh\\
$\EOSfluid$ & State equation of the fluid\\
$\EOSstruct$ & State equation of the structure\\
$\EOSmesh$ & State equation of the mesh motion\\
$\dresidual$ & Discrete fluid residual\\
$\structdisp$ & Structure displacement\\
$\structdispad$ & Adjoint structure displacement\\
$\jactwo$ & Second order Jacobian of the flux\\
$\jacale$ & Jacobian of the mesh motion\\
$\fluxmatconv$ & Convective part of the flux matrix\\
$\fluxmatdiff$ & Diffusive part of the flux matrix\\
$\fload$ & Fluid load\\
$\sload$ & Structure load\\
$\cellvolmat$ & Diagonal matrix with vell volumes\\
$\turbulencesource$ & Source term in the \ac{RANS} equations\\
$\turbparamvec$ & Additional fluid state variables introduced by the turbulence model
\end{tabular}
\subsubsection*{Fluid Mechanics}
\begin{tabular}{l l}
$\dens$ & Density\\
$\pres$ & Pressure\\
$\totpres$ & Total pressure\\
$\fluidvel$ & Fluid velocity vector\\
$\machnum$ & Mach number\\
$\energyint$ & Internal energy\\
$\energytot$ & Total energy\\
$\sspeed$ & Speed of sound\\
$\fluxesconv$ & Convective fluxes\\
$\fluxesdiff$ & Diffusive fluxes\\
$\fluxesnum$ & Numerical flux\\
$\difftensor$ & Diffusive tensor\\
$\viscosdyn$ & Dynamic viscosity\\
$\viscoskin$ & Kinematic viscosity\\
$\nut$ & Turbulent eddy viscosity\\
$\reynolds$ & Reynolds number\\
$\fluidstrain$ & Deviatoric fluid strain tensor\\
$\fluidstress$ & Deviatoric fluid stress tensor\\
$\thermcond$ & Thermal conductivity of the fluid\\
$\temp$ & Fluid temperature\\
$\specheatratio$ & Specific heat ratio\\
$\eye$ & Identity matrix\\
$\roeavgfunc$ & Averaging function associated with the Roe flux\\
$\fluxjac$ & Flux Jacobian\\
$\jaceigvals$ & Diagonal matrix that contains the eigenvalues of the jacobian matrix of $\fluxmatconv$\\
$\jaceigvecs$ & Matrix that contains the eigenvectors of the jacobian matrix of $\fluxmatconv$\\
$\roeavgmat$ & Averaging matrix of the Roe flux\\
$\heatflux$ & Heat flux vector
\end{tabular}
\subsubsection*{Discretization}
\begin{tabular}{l l}
$\vertex$ & Mesh vertex\\
$\vertexset$ & Set of vertices\\
$\elementset$ & Set of elements related to vertex i\\
$\primmesh$ & Primal mesh\\
$\dualcell$ & Dual cell\\
$\dualmesh$ & Dual mesh\\
$\normal$ & Normal vector\\
$\wnormal$ & Weighted normal\\
$\normalx$ & x-component of the cell normal\\
$\normaly$ & y-component of the cell normal\\
$\normalz$ & z-component of the cell normal
\end{tabular}
\subsubsection*{Optimization}
\begin{tabular}{l l}
$\physvars$ & Physical design parameters\\
$\costfunc$ & Target cost function\\
$\optcrit$ & Optimization criterion\\
$\optcrits$ & Vector of optimization criteria\\
$\absvar$ & Abstract optimization variable\\
$\absvars$ & Vector of abstract optimization variables\\
$\Lagfunc$ & Lagrangian function of the optimization problem\\
$\tolsa$ & Specified tolerance in the Sensitivity analysis\\
$\eqctr$ & Equality constraints\\
$\numeqctr$ & Number of equality constraints\\
$\lagmultseq$ & Lagrange multipliers of the equality constraints\\
$\neqctr$ & Non-equality constraints\\
$\numneqctr$ & Number of non-equality constraints\\
$\lagmultsneq$ & Lagrange multipliers of the inequality constraints\\
$\lift$ & Lift of an airfoil\\
$\drag$ & Drag of an airfoil\\
$\aoa$ & Angle of attack
\end{tabular}
\subsubsection*{Sturctural Analysis}
\begin{tabular}{l l}
$\disp$ & Displacement vector\\
$\dispvec$ & Discrete displacement vector\\
$\ifacedispvec$ & Interface displacement vector\\
$\motion$ & Mesh motion\\
$\stiffmat$ & \ac{FE} stiffness matrix
\end{tabular}