Identifiers or names can be attached to DataArray_t
entities to identify and describe the quantity being stored.
To facilitate communication between different application codes, we propose to establish a set of standardized dataname identifiers with fairly precise definitions.
For any identifier in this set, the associated data should be unambiguously understood. In essence, this section proposes standardized terminology for labeling CFDrelated data, including grid coordinates, flow solution, turbulence model quantities, nondimensional governing parameters, boundary condition quantities, and forces and moments.
We use the convention that all standardized identifiers denote scalar quantities; this is consistent with the intended use of the DataArray_t
structure type to describe an array of scalars.
For quantities that are vectors, such as velocity, their components are listed.
Included with the lists of standard dataname identifiers are the fundamental units of dimensions associated with that quantity.
The following notation is used for the fundamental units: \(M\) is mass, \(L\) is length, \(T\) is time, \(\Theta\) is temperature, \(\alpha\) is angle, and \(I\) is electric current.
These fundamental units are directly associated with the elements of the DimensionalExponents_t
structure.
For example, a quantity that has dimensions \(ML/T\) corresponds to MassExponent = +1
, LengthExponent = +1
, and TimeExponent = 1
.
Unless otherwise noted, all quantities in the following sections denote floatingpoint data types, and the appropriate DataType
structure parameter for DataArray_t
is real
.
Coordinate systems for identifying physical location are as follows:
System 
3D 
2D 

Cartesian 
\((x,y,z)\) 
\((x,y)\) or \((x,z)\) or \((y,z)\) 
Cylindrical 
\((r,\theta,z)\) 
\((r,\theta)\) 
Spherical 
\((r,\theta,\phi)\) 

Auxiliary 
\((\xi,\eta,\zeta)\) 
\((\xi,\eta)\) or \((\xi,\zeta)\) or \((\eta,\zeta)\) 
Associated with these coordinate systems are the following unit vector conventions:
\(x\)direction: \(\mathbf{e}_x\) 
\(r\)direction: \(\mathbf{e}_r\) 
\(\xi\)direction: \(\mathbf{e}_\xi\) 
\(y\)direction: \(\mathbf{e}_y\) 
\(\theta\)direction: \(\mathbf{e}_\theta\) 
\(\eta\)direction: \(\mathbf{e}_\eta\) 
\(z\)direction: \(\mathbf{e}_z\) 
\(\phi\)direction: \(\mathbf{e}_\phi\) 
\(\zeta\)direction: \(\mathbf{e}_\zeta\) 
Note that \(\mathbf{e}_r\), \(\mathbf{e}_\theta\) and \(\mathbf{e}_\phi\) are functions of position.
We envision that one of the “standard” coordinate systems (Cartesian, cylindrical or spherical) will be used within a zone (or perhaps the entire database) to define grid coordinates and other related data. The auxiliary coordinates will be used for special quantities, including forces and moments, which may not be defined in the same coordinate system as the rest of the data. When auxiliary coordinates are used, a transformation must also be provided to uniquely define them. For example, the transform from Cartesian to orthogonal auxiliary coordinates is,
where \(T\) is an orthonormal matrix (\(2\times2\) in 2D and \(3\times3\) in 3D).
In addition, normal and tangential coordinates are often used to define boundary conditions and data related to surfaces. The normal coordinate is identified as \(n\) with the unit vector \(\mathbf{e}_n\).
The dataname identifiers defined for coordinate systems are listed in the following table. All represent real DataTypes
, except for ElementConnectivity
and ParentData
, which are integer.
DataName Identifier 
Description 
Units 


\(x\) 
\(L\) 

\(y\) 
\(L\) 

\(z\) 
\(L\) 

\(r\) 
\(L\) 

\(\theta\) 
\(\alpha\) 

\(\phi\) 
\(\alpha\) 

Coordinate in direction of \(\mathbf{e}_n\) 
\(L\) 

Tangential coordinate (2D only) 
\(L\) 

\(\xi\) 
\(L\) 

\(\eta\) 
\(L\) 

\(\zeta\) 
\(L\) 

Transformation matrix (\(\mathbf{T}\)) 
\(\) 

Interpolation factors 
\(\) 

Nodes making up an element 
\(\) 

Element parent identification 
\(\) 
This section describes dataname identifiers for typical NavierStokes solution variables. The list is obviously incomplete, but should suffice for initial implementation of the CGNS system. The variables listed in this section are dimensional or raw quantities; nondimensional parameters and coefficients based on these variables are discussed in the section Nondimensional Parameters.
We use fairly universal notation for state variables. Static quantities are measured with the fluid at speed: static density (\(\rho\)), static pressure (\(p\)), static temperature (\(T\)), static internal energy per unit mass (\(e\)), static enthalpy per unit mass (\(h\)), entropy (\(s\)), and static speed of sound (\(c\)). We also approximate the true entropy by the function \(s_{app} = p / \rho^{\gamma}\) (this assumes an ideal gas). The velocity is \(\mathbf{q} = u \mathbf{e}_x + v \mathbf{e}_y + w \mathbf{e}_z\), with magnitude \(q = ( \mathbf{q} \cdot \mathbf{q})^{1/2}\). Stagnation quantities are obtained by bringing the fluid isentropically to rest; these are identified by a subscript “0”. The term “total” is also used to refer to stagnation quantities.
Conservation variables are density, momentum (\(\rho \mathbf{q} = \rho u \mathbf{e}_x + \rho v \mathbf{e}_y + \rho w \mathbf{e}_z\)), and stagnation energy per unit volume (\(\rho e_{0}\)).
For rotating coordinate systems, \(u\), \(v\), and \(w\) are the \(x\), \(y\), and \(z\) components of the velocity vector in the inertial frame; \(\mathbf{\omega}\) is the rotation rate vector; \(\mathbf{R}\) is a vector from the center of rotation to the point of interest; and \(\mathbf{w}_r = \mathbf{\omega} \times \mathbf{R}\) is the rotational velocity vector of the rotating frame of reference, with components \(w_{rx}\), \(w_{ry}\), and \(w_{rz}\).
Molecular diffusion and heat transfer introduce the molecular viscosity (\(\mu\)), kinematic viscosity (\(\nu\)) and thermal conductivity coefficient (\(k\)). These are obtained from the state variables through auxiliary correlations. For a perfect gas, \(\mu\) and \(k\) are functions of static temperature only.
The NavierStokes equations involve the strain tensor (\(\bar{\bar{S}}\)) and the shearstress tensor (\(\bar{\bar{\tau}}\)). Using indicial notation, the 3D Cartesian components of the strain tensor are,
and the stress tensor is,
where \((x_1,x_2,x_3) = (x,y,z)\) and \((u_1,u_2,u_3) = (u,v,w)\). The bulk viscosity is usually approximated as \(\lambda = − 2 \mu /3\).
Reynolds averaging of the NavierStokes equations introduce Reynolds stresses (\(−\rho(u′v′)_{ave}\), etc.) and turbulent heat flux terms (\(−\rho(u′e′)_{ave}\), etc.), where primed quantities are instantaneous fluctuations. These quantities are obtained from auxiliary turbulence closure models. Reynoldsstress models formulate transport equations for the Reynolds stresses directly; whereas, eddyviscosity models correlate the Reynolds stresses with the mean strain rate,
where \(\nu_t\) is the kinematic eddy viscosity. The eddy viscosity is either correlated to mean flow quantities by algebraic models or by auxiliary transport models. An example twoequation turbulence transport model is the \(k\)\(\epsilon\) model, where transport equations are formulated for the turbulent kinetic energy (\(k = [(u′u′)_{ave} + (v′v′)_{ave} + (w′w′)_{ave}] / 2\)) and turbulent dissipation (\(\epsilon\)).
Skin friction evaluated at a surface is the dot product of the shear stress tensor with the surface normal:
Note that skin friction is a vector.
The dataname identifiers defined for flow solution quantities are listed below.
Note that for some vector quantities, like momentum, the table only explicitly lists dataname identifiers for the \(x\), \(y\), and \(z\) components, and for the magnitude.
It should be understood, however, that for any vector quantity with a standardized data name “Vector
”, the following standardized data names are also defined:

\(x\)component of vector 

\(y\)component of vector 

\(z\)component of vector 

Radial component of vector 

\(\theta\)component of vector 

\(\phi\)component of vector 

Magnitude of vector 

Normal component of vector 

Tangential component of vector (2D only) 
Also note that some dataname identifiers used with multispecies flows include the variable string Symbol, which represents either the chemical symbol for a species, or a defined name for a mixture.
See the section describing the ChemicalKineticsModel
data structure for examples and a table of defined names.
DataName Identifier 
Description 
Units 


Potential: \(\nabla\phi = q\) 
\(L^{2}/T\) 

Stream function (2D): \(\nabla \times \psi = q\) 
\(L^{2}/T\) 

Static density (\(\rho\)) 
\(M/L^{3}\) 

Static pressure (\(p\)) 
\(M/(LT^{2})\) 

Static temperature (\(T\)) 
\(\Theta\) 

Static internal energy per unit mass (\(e\)) 
\(L^{2}/T^{2}\) 

Static enthalpy per unit mass (\(h\)) 
\(L^{2}/T^{2}\) 

Entropy (\(s\)) 
\(M L^{2}/(T^{2} \Theta)\) 

Approximate entropy (\(s_{app} = p / \rho^{\gamma}\)) 
\(L^{3\gamma−1}/(M^{\gamma−1} T^{2})\) 

Stagnation density (\(\rho_0\)) 
\(M/L^{3}\) 

Stagnation pressure (\(p_0\)) 
\(M/(LT^{2})\) 

Stagnation temperature (\(T_0\)) 
\(\Theta\) 

Stagnation energy per unit mass (\(e_0\)) 
\(L^{2}/T^{2}\) 

Stagnation enthalpy per unit mass (\(h_0\)) 
\(L^{2}/T^{2}\) 

Stagnation energy per unit volume (\(\rho e_0\)) 
\(M/(L T^{2})\) 

xcomponent of velocity (\(u = \mathbf{q} \cdot \mathbf{e}_x\)) 
\(L/T\) 

ycomponent of velocity (\(v = \mathbf{q} \cdot \mathbf{e}_y\)) 
\(L/T\) 

zcomponent of velocity (\(w = \mathbf{q} \cdot \mathbf{e}_z\)) 
\(L/T\) 

Radial velocity component (\(\mathbf{q} \cdot \mathbf{e}_r\)) 
\(L/T\) 

Velocity component in \(\theta\) direction (\(\mathbf{q} \cdot \mathbf{e}_\theta\)) 
\(L/T\) 

Velocity component in \(\phi\) direction (\(\mathbf{q} \cdot \mathbf{e}_\phi\)) 
\(L/T\) 

Velocity magnitude (\(q = (\mathbf{q} \cdot \mathbf{q})^{1/2}\)) 
\(L/T\) 

Normal velocity component (\(\mathbf{q} \cdot \mathbf{n}\)) 
\(L/T\) 

Tangential velocity component (2D) 
\(L/T\) 

Static speed of sound 
\(L/T\) 

Stagnation speed of sound 
\(L/T\) 

xcomponent of momentum (\(\rho u\)) 
\(M/(L^{2}T)\) 

ycomponent of momentum (\(\rho v\)) 
\(M/(L^{2}T)\) 

zcomponent of momentum (\(\rho w\)) 
\(M/(L^{2}T)\) 

Magnitude of momentum (\(\rho q\)) 
\(M/(L^{2}T)\) 

xcomponent of velocity, relative to rotating frame (\(u_{rx} = u − w_{rx}\)) 
\(L/T\) 

ycomponent of velocity, relative to rotating frame (\(u_{ry} = v − w_{ry}\)) 
\(L/T\) 

zcomponent of velocity, relative to rotating frame (\(u_{rz} = w − w_{rz}\)) 
\(L/T\) 

xcomponent of momentum, relative to rotating frame (\(\rho u_{rx}\)) 
\(M/(L^{2}T)\) 

ycomponent of momentum, relative to rotating frame (\(\rho u_{ry}\)) 
\(M/(L^{2}T)\) 

zcomponent of momentum, relative to rotating frame (\(\rho u_{rz}\)) 
\(M/(L^{2}T)\) 

Velocity magnitude in rotating frame (\(q_r = (u_{rx} + u_{ry} + u_{rz})^{1/2}\)) 
\(L/T\) 

Stagnation pressure in rotating frame 
\(M/(LT^{2})\) 

Stagnation energy per unit mass in rotating frame (\((e_{0})_r\)) 
\(L^{2}/T^{2}\) 

Stagnation energy per unit volume in rotating frame (\(\rho (e_{0})_r\)) 
\(M/(LT^{2})\) 

Stagnation enthalpy per unit mass in rotating frame, rothalpy 
\(L^{2}/T^{2}\) 

\((u^{2} + v^{2} + w^{2})/2 = q^{2}/2\) 
\(L^{2}/T^{2}\) 

\(\rho q^{2}/2\) 
\(M/(LT^{2})\) 

Sound intensity level in decibels, \(10 {log_{10}}(I/I_{ref}) = 20 {log_{10}}(p/p_{ref})\), where \(I\) is the sound power per unit area, \(I_{ref} = 10−12 watts/m^{2}\) is the reference sound power per unit area, \(p\) is the pressure wave amplitude, and \(p_{ref} = 2\times10^{−5}\ N/m^{2}\) is the reference pressure. 
\(\) 

Sound intensity (i.e., sound power per unit area, \(I\)) 
\(M/T^{3}\) 

\(\omega_x = \partial w/ \partial y − \partial v/ \partial z = \mathbf{\omega} \cdot \mathbf{e}_x\) 
\(T^{−1}\) 

\(\omega_y = \partial u/ \partial z − \partial w/ \partial x = \mathbf{\omega} \cdot \mathbf{e}_y\) 
\(T^{−1}\) 

\(\omega_z = \partial v/ \partial x − \partial u/ \partial y = \mathbf{\omega} \cdot \mathbf{e}_z\) 
\(T^{−1}\) 

\(\omega = (\mathbf{\omega} \times \mathbf{\omega})^{1/2}\) 
\(T^{−1}\) 

xcomponent of skin friction (\(\mathbf{\tau} \cdot \mathbf{e}_x\)) 
\(M/(LT^{2})\) 

ycomponent of skin friction (\(\mathbf{\tau} \cdot \mathbf{e}_y\)) 
\(M/(LT^{2})\) 

zcomponent of skin friction (\(\mathbf{\tau} \cdot \mathbf{e}_z\)) 
\(M/(LT^{2})\) 

Skin friction magnitude (\((\mathbf{\tau} \times \mathbf{\tau})^{1/2}\)) 
\(M/(LT^{2})\) 

Velocity angle (\(arccos(u/q) \in [0, \pi]\)) 
\(\alpha\) 

\(arccos(v/q)\) 
\(\alpha\) 

\(arccos(w/q)\) 
\(\alpha\) 

xcomponent of velocity unit vector (\(\mathbf{q} \cdot \mathbf{e}_x / q\)) 
\(\) 

ycomponent of velocity unit vector (\(\mathbf{q} \cdot \mathbf{e}_y / q\)) 
\(\) 

zcomponent of velocity unit vector (\(\mathbf{q} \cdot \mathbf{e}_z / q\)) 
\(\) 

Mass flow normal to a plane (\(\rho \mathbf{q} \cdot \mathbf{n}\)) 
\(M/(L^{2}T)\) 

Kinematic viscosity (\(\nu = \mu/\rho\)) 
\(L^{2}/T\) 

Molecular viscosity (\(\mu\)) 
\(M/(LT)\) 

Kinematic eddy viscosity (\(\nu_t\)) 
\(L^{2}/T\) 

Eddy viscosity (\(\mu_t\)) 
\(M/(LT)\) 

Thermal conductivity coefficient (\(k\)) 
\(ML/(T^{3}\Theta)\) 

Powerlaw exponent (\(n\)) in molecular viscosity or thermal conductivity model 
\(\) 

Sutherland’s Law constant (\(T_{s}\)) in molecular viscosity or thermal conductivity model 
\(\Theta\) 

Reference temperature (\(T_{ref}\)) in molecular viscosity or thermal conductivity model 
\(\Theta\) 

Reference viscosity (\(\mu_{ref}\)) in molecular viscosity model 
\(M/(LT)\) 

Reference thermal conductivity (\(k_{ref}\)) in thermal conductivity model 
\(ML/(T^{3}\Theta)\) 

Ideal gas constant (\(R = c_p − c_v\)) 
\(L^{2}/(T^{2}\Theta)\) 

Specific heat at constant pressure (\(c_p\)) 
\(L^{2}/(T^{2}\Theta)\) 

Specific heat at constant volume (\(c_v\)) 
\(L^{2}/(T^{2}\Theta)\) 

Reynolds stress \(−\rho (u′u′)_{ave}\) 
\(M/(LT^{2})\) 

Reynolds stress \(−\rho (u′v′)_{ave}\) 
\(M/(LT^{2})\) 

Reynolds stress \(−\rho (u′w′)_{ave}\) 
\(M/(LT^{2})\) 

Reynolds stress \(−\rho (v′v′)_{ave}\) 
\(M/(LT^{2})\) 

Reynolds stress \(−\rho (v′w′)_{ave}\) 
\(M/(LT^{2})\) 

Reynolds stress \(−\rho (w′w′)_{ave}\) 
\(M/(LT^{2})\) 

Molecular weight for species Symbol 
\(\) 

Heat of formation per unit mass for species Symbol 
\(L^{2}/T^{2}\) 

Fuel/air mass ratio 
\(\) 

Reference temperature for the heat of formation 
\(\Theta\) 

Mass of species Symbol, divided by total mass 
\(\) 

Laminar viscosity of species Symbol 
\(M/(LT)\) 

Thermal conductivity of species Symbol 
\(ML/(T^{3}\Theta)\) 

The ratio \(\beta = h / e = \int_{T_{ref}}^{T} c_{p} dT / \int_{T_{ref}}^{T} c_{v} dT\) for the mixture 
\(\) 

The gas constant of the mixture divided by the freestream gas constant, \(Z = R / R_{\infty}\) 
\(\) 

Vibrationalelectronic excitation energy per unit mass 
\(L^{2}/T^{2}\) 

Heat of formation per unit mass for the entire mixture, \(H = \sum_{i=1}^{n} Y_i H_i\), where \(n\) is the number of species, \(Y_i\) is the mass fraction of species \(i\), and \(H_i\) is the heat of formation for species \(i\) at the reference temperature 
\(L^{2}/T^{2}\) 

Vibrational electron temperature 
\(\Theta\) 

Density of species Symbol 
\(M/L^{3}\) 

Number of moles of species Symbol divided by the total number of moles for all species 
\(\) 

Voltage 
\(ML^{2}/TI\) 

xcomponent of electric field vector 
\(ML/TI\) 

ycomponent of electric field vector 
\(ML/TI\) 

zcomponent of electric field vector 
\(ML/TI\) 

xcomponent of magnetic field vector 
\(I/L\) 

ycomponent of magnetic field vector 
\(I/L\) 

zcomponent of magnetic field vector 
\(I/L\) 

xcomponent of current density vector 
\(I/L^{2}\) 

ycomponent of current density vector 
\(I/L^{2}\) 

zcomponent of current density vector 
\(I/L^{2}\) 

Electrical conductivity 
\(ML/T^{3}I^{2}\) 

xcomponent of Lorentz force vector 
\(ML/T^{2}\) 

ycomponent of Lorentz force vector 
\(ML/T^{2}\) 

zcomponent of Lorentz force vector 
\(ML/T^{2}\) 

Joule heating 
\(ML^{2}/T^{2}\) 

Reference length \(L\) 
\(L\) 
This section lists dataname identifiers for typical Reynoldsaveraged NavierStokes turbulence model variables. Turbulence model solution quantities and model constants present a particularly difficult nomenclature problem  to be precise we need to identify both the variable and the model (and version) that it comes from. The list in the following table falls short in this respect.
DataName Identifier 
Description 
Units 


Distance to nearest wall 
\(L\) 

\(k = [(u′u′)_{ave} + (v′v′)_{ave} + (w′w′)_{ave}] / 2\) 
\(L^{2}/T^{2}\) 

\(\epsilon\) 
\(L^{2}/T^{3}\) 

\(\epsilon/k = \omega\) 
\(T^{−1}\) 

BaldwinBarth oneequation model \(R_T\) 
\(\) 

SpalartAllmaras oneequation model \(\nu_{SA}\) 
\(L^{2}/T\) 
CFD codes are rich in nondimensional governing parameters, such as Mach number and Reynolds number, and nondimensional flowfield coefficients, such as pressure coefficient. The problem with these parameters is that the definitions and conditions at which they are evaluated can vary from code to code. Reynolds number is particularly notorious in this respect.
These parameters have posed a difficult dilemma for us. Either we impose a rigid definition for each and force all database users to abide by it, or we develop some methodology for describing the particular definition that the user is employing. The first limits applicability and flexibility, and the second adds complexity. We have opted for the second approach, but we include only enough information about the definition of each parameter to allow for conversion operations. For example, the Reynolds number includes velocity, length, and kinematic viscosity scales in its definition (i.e., \(Re = VLR/\nu\)). The database description of Reynolds number includes these different scales. By providing these “definition components”, any code that reads Reynolds number from the database can transform its value to an appropriate internal definition. These definition components are identified by appending a “_” to the dataname identifier of the parameter.
Definitions for nondimensional flowfield coefficients follow: the pressure coefficient is defined as,
where \(\rho_{ref}q^{2}_{ref} / 2\) is the dynamic pressure evaluated at some reference condition, and \(p_{ref}\) is some reference pressure. The skin friction coefficient is,
where \(\mathbf{\tau}\) is the shear stress or skin friction vector. Usually, \(\mathbf{\tau}\) is evaluated at the wall surface.
The dataname identifiers defined for nondimensional governing parameters and flowfield coefficients are listed in the following table.
DataName Identifier 
Description 
Units 


Mach number: \(M = q/c\) 
\(\) 

Velocity scale (\(q\)) 
\(L/T\) 

Speed of sound scale (\(c\)) 
\(L/T\) 

Mach number relative to rotating frame: \(M_r = q_r /c\) 
\(\) 

Reynolds number: \(Re = VL_{R}/\nu\) 
\(\) 

Velocity scale (\(V\)) 
\(L/T\) 

Length scale (\(L_R\)) 
\(L\) 

Kinematic viscosity scale (\(\nu\)) 
\(L^{2}/T\) 

Prandtl number: \(Pr = \mu c_p/k\) 
\(\) 

Thermal conductivity scale (\(k\)) 
\(ML/(T^{3}\Theta)\) 

Molecular viscosity scale (\(\mu\)) 
\(M/(LT)\) 

Specific heat scale (\(c_p\)) 
\(L^{2}/(T^{2}\Theta)\) 

Turbulent Prandtl number, \(\rho \nu_t c_p/k_t\) 
\(\) 

Specific heat ratio: \(\gamma = c_p/c_v\) 
\(\) 

Specific heat at constant pressure (\(c_p\)) 
\(L^{2}/(T^{2}\Theta)\) 

Specific heat at constant volume (\(c_v\)) 
\(L^{2}/(T^{2}\Theta)\) 

\(c_p\) 
\(\) 

\(\mathbf{c_f} \cdot \mathbf{e}_x\) 
\(\) 

\(\mathbf{c_f} \cdot \mathbf{e}_y\) 
\(\) 

\(\mathbf{c_f} \cdot \mathbf{e}_z\) 
\(\) 

\(\rho_{ref} q^{2}_{ref} / 2\) 
\(M/(LT^{2})\) 

\(p_{ref}\) 
\(M/(LT^{2})\) 
Boundary condition specification for inflow/outflow or farfield boundaries often involves Riemann invariants or characteristics of the linearized inviscid flow equations. For an ideal compressible gas, these are typically defined as follows: Riemann invariants for an isentropic 1D flow are,
Characteristic variables for the 3D Euler equations linearized about a constant mean flow are,
where the characteristics and corresponding characteristic variables are
Characteristic 
\(\Delta_n\) 
\(W'_n\) 

Entropy 
\(u\) 
\(p′ − \rho′c^{2}\) 
Vorticity 
\(u\) 
\(v′\) 
Vorticity 
\(u\) 
\(w′\) 
Acoustic 
\(u \pm c\) 
\(p′ \pm u′ \rho c\) 
Primed quantities are linearized perturbations, and the remainder are evaluated at the mean flow. The only nonzero meanflow velocity component is \(u\). The dataname identifiers defined for Riemann invariants and characteristic variables are listed in the following table.
DataName Identifier 
Description 
Units 


\(u + 2c / (\gamma − 1)\) 
\(L/T\) 

\(u − 2c / (\gamma − 1)\) 
\(L/T\) 

\(p′ − \rho′ c^{2}\) 
\(M/(L T^{2})\) 

\(v′\) 
\(L/T\) 

\(w′\) 
\(L/T\) 

\(p′ + u′\rho c\) 
\(M/(L T^{2})\) 

\(p′ − u′\rho c\) 
\(M/(L T^{2})\) 
Conventions for dataname identifiers for forces and moments are defined in this section. Ideally, forces and moments should be attached to geometric components or less ideally to surface grids. Currently, the standard mechanism for storing forces and moments is generally through the ConvergenceHistory_t
node, either attached to the entire configuration (under CGNSBase_t
) or attached to a zone (under Zone_t
).
Given a differential force \(f\) (i.e., a force per unit area), the force integrated over a surface is,
where \(\mathbf{e}_x\), \(\mathbf{e}_y\) and \(\mathbf{e}_z\) are the unit vectors in the x, y and z directions, respectively. The moment about a point \(r_{0}\) integrated over a surface is,
Lift and drag components of the integrated force are,
where \(\mathbf{L}\) and \(\mathbf{D}\) are the unit vectors in the positive lift and drag directions, respectively.
Lift, drag and moment are often computed in auxiliary coordinate frames (e.g., wind axes or stability axes). We introduce the convention that lift, drag and moment are computed in the \((\xi, \eta, \zeta)\) coordinate system. Positive drag is assumed parallel to the \(\xi\)direction (i.e., \(\mathbf{D} = \mathbf{e}_\xi\)); and positive lift is assumed parallel to the \(\eta\)direction (i.e., \(\mathbf{L} = \mathbf{e}_\eta\)). Thus, forces and moments defined in this auxiliary coordinate system are,
Lift, drag and moment coefficients in 3D are defined as,
where \(\rho_{ref}q^{2}_{ref} / 2\) is a reference dynamic pressure, \(S_{ref}\) is a reference area, and \(c_{ref}\) is a reference length. For a wing, \(S_{ref}\) is typically the wing area and \(c_{ref}\) is the mean aerodynamic chord. In 2D, the sectional force coefficients are,
where the forces are integrated along a contour (e.g., an airfoil crosssection) rather than a surface.
The dataname identifiers and definitions provided for forces and moments and their associated coefficients are listed in the table below. For coefficients, the dynamic pressure and length scales used in the normalization are provided.
DataName Identifier 
Description 
Units 


\(F_x = \mathbf{F} \cdot \mathbf{e}_x\) 
\(ML/T^{2}\) 

\(F_y = \mathbf{F} \cdot \mathbf{e}_y\) 
\(ML/T^{2}\) 

\(F_z = \mathbf{F} \cdot \mathbf{e}_z\) 
\(ML/T^{2}\) 

\(F_r = \mathbf{F} \cdot \mathbf{e}_r\) 
\(ML/T^{2}\) 

\(F_\theta = \mathbf{F} \cdot \mathbf{e}_\theta\) 
\(ML/T^{2}\) 

\(F_\phi = \mathbf{F} \cdot \mathbf{e}_\phi\) 
\(ML/T^{2}\) 

\(L\) or \(L'\) 
\(ML/T^{2}\) 

\(D\) or \(D'\) 
\(ML/T^{2}\) 

\(M_x = \mathbf{M} \cdot \mathbf{e}_x\) 
\(ML^{2}/T^{2}\) 

\(M_y = \mathbf{M} \cdot \mathbf{e}_y\) 
\(ML^{2}/T^{2}\) 

\(M_z = \mathbf{M} \cdot \mathbf{e}_z\) 
\(ML^{2}/T^{2}\) 

\(M_r = \mathbf{M} \cdot \mathbf{e}_r\) 
\(ML^{2}/T^{2}\) 

\(M_\theta = \mathbf{M} \cdot \mathbf{e}_\theta\) 
\(ML^{2}/T^{2}\) 

\(M_\phi = \mathbf{M} \cdot \mathbf{e}_\phi\) 
\(ML^{2}/T^{2}\) 

\(M_\xi = \mathbf{M} \cdot \mathbf{e}_\xi\) 
\(ML^{2}/T^{2}\) 

\(M_\eta = \mathbf{M} \cdot \mathbf{e}_\eta\) 
\(ML^{2}/T^{2}\) 

\(M_\zeta = \mathbf{M} \cdot \mathbf{e}_\zeta\) 
\(ML^{2}/T^{2}\) 

\(x_0 = \mathbf{r}_0 \cdot \mathbf{e}_x\) 
\(L\) 

\(y_0 = \mathbf{r}_0 \cdot \mathbf{e}_y\) 
\(L\) 

\(z_0 = \mathbf{r}_0 \cdot \mathbf{e}_z\) 
\(L\) 

\(C_L\) or \(c_l\) 
\(\) 

\(C_D\) or \(c_d\) 
\(\) 

\(\mathbf{C_M} \cdot \mathbf{e}_x\) or \(\mathbf{c_m} \cdot e_x\) 
\(\) 

\(\mathbf{C_M} \cdot \mathbf{e}_y\) or \(\mathbf{c_m} \cdot e_y\) 
\(\) 

\(\mathbf{C_M} \cdot \mathbf{e}_z\) or \(\mathbf{c_m} \cdot e_z\) 
\(\) 

\(\mathbf{C_M} \cdot \mathbf{e}_r\) or \(\mathbf{c_m} \cdot e_r\) 
\(\) 

\(\mathbf{C_M} \cdot \mathbf{e}_\theta\) or \(\mathbf{c_m} \cdot \mathbf{e}_\theta\) 
\(\) 

\(\mathbf{C_M} \cdot \mathbf{e}_\phi\) or \(\mathbf{c_m} \cdot \mathbf{e}_\phi\) 
\(\) 

\(\mathbf{C_M} \cdot \mathbf{e}_\xi\) or \(\mathbf{c_m} \cdot \mathbf{e}_\xi\) 
\(\) 

\(\mathbf{C_M} \cdot \mathbf{e}_\eta\) or \(\mathbf{c_m} \cdot \mathbf{e}_\eta\) 
\(\) 

\(\mathbf{C_M} \cdot \mathbf{e}_\zeta\) or \(\mathbf{c_m} \cdot \mathbf{e}_\zeta\) 
\(\) 

\(\rho_{ref} q^{2}_{ref} / 2\) 
\(M/(LT^{2})\) 

\(S_{ref}\) 
\(L^{2}\) 

\(c_{ref}\) 
\(L\) 
Dataname identifiers related to timedependent flow include those associated with the storage of grid coordinates and flow solutions as a function of time level or iteration. Also included are identifiers for storing information defining both rigid and arbitrary (i.e., deforming) grid motion.
DataName Identifier 
Data Type 
Description 
Units 



Time values 
\(T\) 


Iteration values 
\(\) 


Number of zones used for each recorded step 
\(\) 


Number of families used for each recorded step 
\(\) 


Names of zones used for each recorded step 
\(\) 


Names of families used for each recorded step 
\(\) 


Names of RigidGridMotion structures used for each recorded step for a zone 
\(\) 


Names of ArbitraryGridMotion structures used for each recorded step for a zone 
\(\) 


Names of GridCoordinates structures used for each recorded step for a zone 
\(\) 


Names of FlowSolution structures used for each recorded step for a zone 
\(\) 


Physical coordinates of the origin before and after a rigid grid motion 
\(L\) 


Rotation angles about each axis of the translated coordinate system for rigid grid motion 
\(\alpha\) 


Grid velocity vector of the origin translation for rigid grid motion 
\(L/T\) 


Rotation rate vector about the axis of the translated coordinate system for rigid grid motion 
\(\alpha /T\) 


\(x\)component of grid velocity 
\(L/T\) 


\(y\)component of grid velocity 
\(L/T\) 


\(z\)component of grid velocity 
\(L/T\) 


\(r\)component of grid velocity 
\(L/T\) 


\(\theta\)component of grid velocity 
\(\alpha /T\) 


\(\phi\)component of grid velocity 
\(\alpha /T\) 


\(\xi\)component of grid velocity 
\(L/T\) 


\(\eta\)component of grid velocity 
\(L/T\) 


\(\zeta\)component of grid velocity 
\(L/T\) 