Appendix A Conventions for Data-Name Identifiers

• A.1 Coordinate Systems
• A.2 Flowfield Solution
• A.3 Turbulence Model Solution
• A.4 Nondimensional Parameters
• A.5 Characteristics and Riemann Invariants Based on 1-D Flow
• A.6 Forces and Moments
• A.7 Time-Dependent Flow

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 data-name 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 CFD-related 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 data-name 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, Θ is temperature, α 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 floating-point data types, and the appropriate DataType structure parameter for DataArray_t is real.

A.1 Coordinate Systems

Coordinate systems for identifying physical location are as follows:

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,

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 e_n.

The data-name identifiers defined for coordinate systems are listed in the following table. All represent real DataTypes, except for ElementConnectivity and ParentData, which are integer.

A.2 Flowfield Solution

This section describes data-name identifiers for typical Navier-Stokes 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 (ρ), 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 / ρ^γ (this assumes an ideal gas). The velocity is q = ue_x + ve_y + we_z, with magnitude q = (q ⋅ 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 (ρq = ρue_x + ρve_y + ρwe_z), and stagnation energy per unit volume (ρe₀).

For rotating coordinate systems, u, v, and w are the x, y, and z components of the velocity vector in the inertial frame; ω is the rotation rate vector; R is a vector from the center of rotation to the point of interest; and w_r = ω × 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 (μ), kinematic viscosity (ν) and thermal conductivity coefficient (k). These are obtained from the state variables through auxiliary correlations. For a perfect gas, μ and k are functions of static temperature only.

The Navier-Stokes equations involve the strain tensor () and the shear-stress tensor (). Using indicial notation, the 3-D Cartesian components of the strain tensor are,

Reynolds averaging of the Navier-Stokes equations introduce Reynolds stresses (−ρ(u′v′)_ave, etc.) and turbulent heat flux terms (−ρ(u′e′)_ave, etc.), where primed quantities are instantaneous fluctuations. These quantities are obtained from auxiliary turbulence closure models. Reynolds-stress models formulate transport equations for the Reynolds stresses directly; whereas, eddy-viscosity models correlate the Reynolds stresses with the mean strain rate,

Skin friction evaluated at a surface is the dot product of the shear stress tensor with the surface normal:

The data-name identifiers defined for flow solution quantities are listed below.

Note that for some vector quantities, like momentum, the table only explicitly lists data-name 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:

	VectorX		x-component of vector
	VectorY		y-component of vector
	VectorZ		z-component of vector
	VectorR		Radial component of vector
	VectorTheta		θ-component of vector
	VectorPhi		φ-component of vector
	VectorMagnitude		Magnitude of vector
	VectorNormal		Normal component of vector
	VectorTangential		Tangential component of vector (2-D only)

Also note that some data-name identifiers used with multi-species 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.

A.3 Turbulence Model Solution

This section lists data-name identifiers for typical Reynolds-averaged Navier-Stokes 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.

A.4 Nondimensional Parameters

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 = VL_R/ν. 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 data-name identifier of the parameter.

Definitions for nondimensional flowfield coefficients follow: the pressure coefficient is defined as,

The data-name identifiers defined for nondimensional governing parameters and flowfield coefficients are listed in the following table.

A.5 Characteristics and Riemann Invariants Based on 1-D Flow

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 1-D flow are,

A.6 Forces and Moments

Conventions for data-name 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,

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 (ξ, η, ζ) coordinate system. Positive drag is assumed parallel to the ξ-direction (i.e., D = e_ξ); and positive lift is assumed parallel to the η-direction (i.e., L = e_η). Thus, forces and moments defined in this auxiliary coordinate system are,

Lift, drag and moment coefficients in 3-D are defined as,

The data-name 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.

A.7 Time-Dependent Flow

Data-name identifiers related to time-dependent 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.