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customcommands.tex
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customcommands.tex
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\newcommand{\abbrevation}[2]{\newcommand{#1}{#2}}
\abbrevation{\SQP}{SQP} %Sequential Quatdratic Programming
%%==============================%
% OPERATORS
% Representation of scalars, tensors and other quantities
%==============================%
\newcommand{\s}[1]{#1} %Scalar quantity with{q}
\renewcommand{\v}[1]{\boldsymbol{#1}} %Vector quantity with{q}
\newcommand{\m}[1]{\boldsymbol{#1}} %Matrix quantity with{Q}
\newcommand{\tensor}[1]{\mathcal{\boldsymbol{#1}}} %Tensor quantity with{Q}
\newcommand{\abs}[1]{\lvert#1\rvert} %Norm of a vector with{q}
\renewcommand{\c}[1]{\mathnormal{#1}} %Continous quantity with{Q,q}
\renewcommand{\d}[1]{\mathrm{#1}} %Discrete quantity with{Q,q}
\renewcommand{\it}[1]{{#1}^{(k)}} %Iteration index in the optimization loop with{q}
\newcommand{\its}[1]{{#1}^{(n)}} %Iteration index in the staggered algorithm with{q}
\newcommand{\fic}[1]{\bar{#1}} %Fictious entity with{Q}
\newcommand{\order}[1]{\mathcal{O}(#1)} %Order of magnitude with{n}
\newcommand{\ito}[1]{{#1}^{(k)}} %Iteration index in the optimization loop with{q}
%these are operators that should not be in the list of symbols-------------------------------------------------
\newcommand{\itn}[1]{{#1}^{(0)}} %Iteration index 0 with{q}
\newcommand{\itss}[1]{{#1}^{(n+1)}} %Iteration index in thestaggered algorithm with{q}
\newcommand{\expression}[1]{\textit{#1}} %To mark a new term beein introduced with{q}
\newcommand{\dvec}[1]{\boldsymbol{\mathsf{#1}}} %Discrete vector represenation of a scalar field with{q}
\newcommand{\dmat}[1]{\boldsymbol{\mathsf{#1}}} %Discrete vector represenation of a tensor field with{q}
\newcommand{\cvec}[1]{\c{\v{#1}}} %Discrete vector represenation of a scalar field with{q}
\newcommand{\cmat}[1]{\c{\m{#1}}} %Discrete vector represenation of a tensor field with{q}
\newcommand{\nd}[1]{\bar{#1}} %Non-dimensionalization with{q}
\newcommand{\reference}[1]{ {#1}_{ref} } %Variable at reference state with{q}
\newcommand{\conv}[1]{{#1}^{c}} %Convective form of a quantity (quantity in ALE-description} with{q}
\newcommand{\stdy}[1]{{#1}^{0}} %Value at steady state with{q}
\newcommand{\scalar}[1]{\s #1} %Scalar quantity with{q}
\newcommand{\linepdfrac}[2]{\pd #1 / \pd #2} %Partial derivative of one argument with respect to the other with{q1&q2}
\newcommand{\dyadic}{\otimes} %Symbol for dyadic product with{q}
%these are symbols that should not be in the list of symbols--------------------------------------------------
\newcommand{\pd}{\mathrm{\partial}} %TODO check whether I need the partial or not
\newcommand{\0}{\textcolor{lightgrey}{0}}
\renewcommand{\vec}[1]{\boldsymbol{#1}} %Vector
\newcommand{\REF}{\textbf{REF}} %a
\newcommand{\fot}{\frac{1}{2}} %One half
%%==============================%
% OPERATORS
% Algebraic operations
%==============================%
\newcommand{\T}[1]{{#1}^{T}} %Transpose of a tensor with{Q}
\newcommand{\inv}[1]{ {#1}^{-1}} %Inverse of a tensor with{Q}
\newcommand{\av}[1]{\bar{#1}} %Average component of a quantity with{q}
\newcommand{\fluc}[1]{{#1}'} %Fluctuating component of a quantity with{q}
\newcommand{\norm}[1]{\left\lVert#1\right\rVert} %Norm of a quantity with{q}
\newcommand{\prim}[1]{\tilde{#1}} %Quantity being expressed in primitive variables with{q}
%%==============================%
% OPERATORS
% Analytic operations
%==============================%
\newcommand{\derivtime}[1]{\dot{#1}} %First time derivative at a fixed reference position with{q}
\newcommand{\dderivtime}[1]{\ddot{#1}} %Second time derivative at a fixed refrence position with{q}
\newcommand{\pdfrac}[2]{\frac{\pd #1}{\pd #2}} %Partial derivative of one argument with respect to the other with{q_1&q_2}
\newcommand{\ppdfrac}[2]{\frac{\pd^{2} #1}{\pd {#2}^{2}}} %Second partial derivative of one argument with respect to the other with{q_1&q_2}
\newcommand{\mfrac}[2]{\frac{D #1}{D #2}} %Material time derivative with{q_1&q_2}
\renewcommand{\tfrac}[2]{\frac{\mathrm{d} #1}{\mathrm{d} #2}} %First total derivative of one argument with respect to the other with{q1&q2}
%==============================
% SYMBOLS
% Numerical formulation
%==============================
\newcommand{\EOSstruct}{\mathcal{S}_{gov}} %State equation of the structure
\newcommand{\EOSmesh}{\mathcal{D}_{gov}} %State equation of the mesh motion
\newcommand{\EOSfluid}{\mathcal{F}_{gov}} %State equation of the fluid
\newcommand{\mpos}{\vec{x}} %Fluid mesh position
\newcommand{\mms}{\dot{\vec{x}}} %Fluid mesh motion
\newcommand{\mmsad}{\vec{a}_{\vec{x}}} %Adjoint fluid mesh motion
\newcommand{\fstate}{\vec{w}} %Fluid state vector
\newcommand{\fstatead}{\vec{a}_{\vec{w}}} %Adjoint fluid state vector
\newcommand{\fstateprim}{\prim{\fstate}} %Primitive fluid state vector
\newcommand{\dfstateprim}{\prim{\dfstate}} %Primitive fluid state vector
\newcommand{\dfstate}{\dvec{w}} %Discrete fluid state vector
\newcommand{\dresidual}{\dvec{R}} %Discrete fluid residual
\newcommand{\structdisp}{\vec{u}} %Structure displacement
\newcommand{\structdispad}{\vec{a}_{\vec{u}}} %Adjoint structure displacement
\newcommand{\fload}{\vec{P}_F} %Fluid load
\newcommand{\sload}{\vec{P}_T} %Structure load
\newcommand{\jactwo}{\tensor{H}_2} %Second order Jacobian of the flux
\newcommand{\jacale}{\tensor{J}} %Jacobian of the mesh motion
\newcommand{\ifaceprojFtoS}{\dmat{T}_p} %Interface projection matrix from fluid to structure mesh
\newcommand{\ifaceprojStoF}{\dmat{T}_u} %Interface projection matrix from structure to fluid mesh
\newcommand{\fstaterans}{\fstate_{RANS}} %Augumented fluid state vector in the RANS formulation
\newcommand{\turbparamvec}{\dvec{\chi}} %Additional fluid state variables introduced by the turbulence model
\newcommand{\turbulencesource}{\mathsf{S}} %Source term in the \ac{RANS} equations
\newcommand{\fluxmatconv}{\dresidual^{c}}%Convective part of the flux matrix
\newcommand{\fluxmatdiff}{\dmat{G}} %Diffusive part of the flux matrix
\newcommand{\cellvolmat}{\dmat{A}} %Diagonal matrix with cell volumes
\newcommand{\specificwork}{\vec{w}} %Specific work
\newcommand{\dmpos}{\dvec{x}} %Fluid mesh motion
\newcommand{\dmms}{\dot{\dvec{x}}} %Fluid mesh motion
\newcommand{\load}{\vec{P} } %Fluid load TODO
\newcommand{\turbulenceparam}{\chi} %Additional fluid state variable introduced by the turbulence model
\newcommand{\turbmat}{\dmat{S}} %Turbulence term
%==============================%
% SYMBOLS
% Optimization
%==============================%
\newcommand{\costfunc}{z} %Target cost function
\newcommand{\eqctr}{\vec{h}} %Equality constraints
\newcommand{\numeqctr}{n_{\vec{h}}} %Number of equality constraints
\newcommand{\neqctr}{\vec{g}} %Non-equality constraints
\newcommand{\numneqctr}{n_{\vec{g}}} %Number of non-equality constraints
\newcommand{\absvar}{s} %Abstract optimization variable
\newcommand{\absvars}{\vec{s}} %Vector of abstract optimization variables
\newcommand{\optcrit}{q} %Optimization criterium
\newcommand{\optcrits}{\vec{\optcrit}} %Vector of optimization criteria
\newcommand{\physvars}{\vec{d}} %Physical design parameters
\newcommand{\Lagfunc}{L} %Lagrangian function of the optimization problem
\newcommand{\lagmultseq}{\vec{\eta}} %Lagrange multipliers of the equality constraints
\newcommand{\lagmultsneq}{\vec{\gamma}} %Lagrange multipliers of the inequality constraints
\newcommand{\adjoints}{\vec{a}} %Adjoint solutions
\newcommand{\tolsa}{\epsilon^{SA}} %Specified tolerance in the Sensitivity analysis
\newcommand{\lift}{L} %Lift of an airfoil
\newcommand{\drag}{D} %Drag of an airfoil
\newcommand{\aoa}{\alpha_{\infty}} %Angle of attack
%==============================%
% SYMBOLS
% Fluid Mechanics
%==============================%
\newcommand{\fluxesconv}{\mathcal{F}} %Convective fluxes
\newcommand{\fluxesdiff}{\mathcal{G}} %Diffusive fluxes
\newcommand{\fluxesnum}{\boldsymbol{\mathsf{{\phi}}}} %Numerical flux
\newcommand{\roeavgmat}{\tensor{A}_{\text{Roe}}} %Averaging matrix of the Roe flux
\newcommand{\dens}{\rho} %Density
\newcommand{\pres}{p} %Static pressure
\newcommand{\totpres}{p_{tot}} %Total pressure
\newcommand{\fluidvel}{\vec{v}} %Fluid velocity vector
\newcommand{\fluidvelx}{{v_1}} %Fluid velocity in x-direction
\newcommand{\fluidvely}{{v_2}} %Fluid velocity in y-direction
\newcommand{\fluidvelz}{{v_3}} %Fluid velocity in z-direction
\newcommand{\energytot}{E} %Total energies
\newcommand{\energyint}{e} %Internal energy
\newcommand{\eye}{\dmat{I}} %Identity matrix
\newcommand{\fluidstrain}{\tensor{\epsilon}} %Deviatoric fluid strain tensor
\newcommand{\fluidstress}{\tensor{\tau}} %Deviatoric fluid stress tensor
\newcommand{\thermcond}{k} %Thermal conductivity of the fluid
\newcommand{\temp}{T} %Fluid temperature
\newcommand{\heatflux}{\vec{\heatfluxcomp}} %Heat flux vector
\newcommand{\viscosdyn}{\mu} %Dynamic viscosity
\newcommand{\viscoskin}{\nu} %Kinematic viscosity
\newcommand{\reynolds}{R_{e}} %Reynolds number
\newcommand{\specheatratio}{\gamma} %Specific heat ratio
\newcommand{\jac}{\mathcal{H}} %Jacobian matrix
\newcommand{\fluxjac}{\mathcal{A}} %Flux Jacobian
\newcommand{\jaceigvecs}{\tensor{P}} %Matrix that contains the eigenvectors of the jacobian matrix of $\fluxmatconv$
\newcommand{\jaceigvals}{\tensor{\Lambda}} %Diagonal matrix that contains the eigenvalues of the jacobian matrix of $\fluxmatconv$
\newcommand{\roeavgfunc}{\tensor{M}} %Averaging function associated with the Roe flux
\newcommand{\machnum}{M} %Mach number
\newcommand{\nut}{\mu_{t}} %Turbulent eddy viscosity
\newcommand{\difftensor}{\mathbb{K}} %Diffussive tensor
\newcommand{\sspeed}{c} %Speed of sound
\newcommand{\dpres}{\mathsf{p}} %Pressure
\newcommand{\fluidvelcomp}{v} %Fluid velocity vector
\newcommand{\fluidstresscomp}{\tau} %Deviatoric fluid stress tensor
\newcommand{\heatfluxcomp}{q} %Heat flux comopnenent
\newcommand{\shr}{\gamma} %Specific heat ratio
\newcommand{\M}{\machnum} %Mach number
%==============================%
% SYMBOLS
% Discretization
%==============================%
\newcommand{\dualcell}{\mathcal{C}} %Dual cell
\newcommand{\primmesh}{\mathcal{P}_{h}} %Primal mesh
\newcommand{\dualmesh}{\mathcal{D}_{h}} %Dual mesh
\newcommand{\normal}{\vec{n}} %Normal vector
\newcommand{\wnormal}{\vec{\nu}} %Weighted normal
\newcommand{\normalx}{n_1} %x-component of the cell normal
\newcommand{\normaly}{n_2} %y-component of the cell normal
\newcommand{\normalz}{n_3} %z-component of the cell normal
\newcommand{\vertex}{\boldsymbol{X}} %Mesh vertex
\newcommand{\vertexset}{\mathsf{\kappa}}%Set of vertices
\newcommand{\elementset}{\mathsf{\lambda}} %Set of elements related to vertex i
\newcommand{\testfunc}{\phi} %Variational test function
\newcommand{\eigval}{\lambda} %Eigen value
\newcommand{\valfboxsep}{0pt}
\newcommand{\valfboxrule}{1pt}
%%%==============================%
%%% SYMBOLS
%%% Fluid Analysis
%%%==============================%
%%\newcommand{\sate}{w}
%%\newcommand{•}{•}
%%\newcommand{•}{•}
%%\newcommand{•}{•}
%%\newcommand{\statevec}{\vec{\state}}
%==============================%
% SYMBOLS
% Sturctural Analysis
%==============================%
\newcommand{\stiffmat}{\dmat{K}} %\ac{FE} stiffness matrix
\newcommand{\disp}{u} %Displacement vector
\newcommand{\dispvec}{\dvec{\disp}} %Discrete displacement vector
\newcommand{\motion}{\vec{x}} %Mesh motion
\newcommand{\ifacedisp}{d} %Interface displacement
\newcommand{\ifacedispvec}{\dvec{\ifacedisp}} %Interface displacement
\newcommand{\strucstateq}{\mathcal{P}} %State equation of the structure
\newcommand{\fluidstateq}{\mathcal{F}} %State equation of the fluid
\newcommand{\mmsstateeq}{\mathcal{D}} %State equation of the mesh motion
%=============================================================================%
% Nassi-Schneidermann auxiliary commands %
%=============================================================================%
%commands for the text part of the dioagrams
%the bold command is typcally used for TODO
%there is now automatic line wrapping in strtuktex, so the second command is
% used if the text becomes too long
\newcommand{\nassitext}[2]{\makebox[#1\textwidth]{\textit{\textcolor{nassitextcolor}{\small #2}}\hfill}}
\newcommand{\nassitextbold}[2]{\makebox[#1\textwidth]{\textbf{\textit{\textcolor{nassitextcolor}{\small #2}}}\hfill}}
\newcommand{\nassitexttwolines}[3]{\nassitext{#1}{#2}\hspace*{\hsize}\linebreak \nassitext{\df2}{#3}}
\newcommand{\tablesix}[6]{
\begin{tabular}{|c|l|l|}
\hline
\parbox[t]{2mm}{\multirow{3}{*}{\rotatebox[origin=c]{90}{Eulerian}}} & Euler & #1 \\
\hhline{~--} & \ac{NSE} & #2 \\
\hhline{~--} & \ac{RANS} & #3 \\
\hline
\parbox[t]{2mm}{\multirow{3}{*}{\rotatebox[origin=c]{90}{ALE}}} & Euler & #4 \\
\hhline{~--} & \ac{NSE} & #5 \\
\hhline{~--} & \ac{RANS} & #6 \\
\hline
\end{tabular}
}
\newcommand{\tablestatederivs}[6]{
\begin{center}
\begin{tabular}{ m{0.45\textwidth} | m{0.45\textwidth} }\hline
\rowcolor{black!20}\Centering Dimensional & \Centering Non-Dimensional\\ \hline
#1 & #2 \\
#3 & #4 \\
#5 & #6 \\
\end{tabular}
\end{center}
}
%\newenvironment{salign}
% {
% \begingroup\makeatletter\def\f@size{8}\check@mathfonts
% \def\maketag@@@#1{\hbox{\m@th\large\normalfont#1}}
% \begin{align}
% }
% {
% \end{align}
% \endgroup
% }
\newcommand\question[1]{\textcolor{red}{\textbf{#1}}}
\newcommand\cellsize[1]{meas(#1)}