(CGNS Documentation Home Page)
(Steering Committee Charter)
(Overview and EntryLevel Document)
(A User's Guide to CGNS)
(MidLevel Library)
(Standard Interface Data Structures)
(SIDS File Mapping Manual)
(CGIO User's Guide)
(Parallel CGNS User's Guide)
(ADF Implementation)
(HDF5 Implementation)
(Python Implementation)
(CGNS Tools and Utilities)
(Introduction)
(Design Philosophy of Standard Interface Data Structures)
(Conventions)
(BuildingBlock Structure Definitions)
(DataArray Structure Definitions)
(Hierarchical Structures)
(Grid Coordinates, Elements, and Flow Solution)
(Multizone Interface Connectivity)
(Boundary Conditions)
(Governing Flow Equations)
(TimeDependent Flow)
(Miscellaneous Data Structures)
(Conventions for DataName Identifiers)
(Structured TwoZone Flat Plate Example)
3 Conventions
3.1 Data Structure Notation Conventions
The intellectual content of the CGNS database is defined in terms of Clike
notation including typedefs and structures. The database is made up of
entities, and each entity has a type associated with it. Entities include such
things as the dimensionality of the grid, an array of grid coordinates, or a
zone that contains all the data associated with a given region.
Entities are defined in terms of types, where a type can be an
integer or a collection of elements (a structure) or a hierarchy of
structures or other similar constructs.
The terminology "instance of an entity" is used to refer to an entity that
has been assigned a value or whose elements have been assigned values. The
terminology "specific instance of a structure" is also used in the following
sections. It is short for an instance of an entity whose type is a structure.
Names of entities and types are constructed using conventions typical
of Mathematica
[Mathematica 3.0, Wolfram Research,
Inc. , Champaign, IL (1996)].
Names or identifiers contain no spaces and capitalization is used to
distinguish individual words making up a name; names are casesensitive.
The character "/" should be avoided in names, as well as the names
"." and "..", as these have
special meaning when referencing elements of a structure entity.
An entity name cannot exceed 32 characters.
The following notational conventions are employed:
 ! 
 comment to end of line

 _t 
 suffix used for naming a type

 ; 
 end of a definition, declaration, assignment or entity instance

 = 
 assignment (takes on the value of)

 := 
 indicates a type definition (typedef)

 [ ] 
 delimiters of an array

 { } 
 delimiters of a structure definition

 {{ }} 
 delimiters of an instance of a structure entity

 < > 
 delimiters of a structure parameter list

 int 
 integer

 real 
 floatingpoint number

 char 
 character

 bit 
 bit

 Enumeration( ) 
 indicates an enumeration type

 Data( ) 
 indicates an array of data, which may be multidimensional

 List( ) 
 indicates a list of entities

 Identifier( ) 
 indicates an entity identifier

 LogicalLink( ) 
 indicates a logical link

 / 
 delimiter for element of a structure entity

 ../ 
 delimiter for parent of a structure entity

 (r) 
 designation for a required structure element

 (o) 
 designation for an optional structure element

 (o/d) 
 designation for an optional structure element with default if absent

An enumeration type is a set of values identified by names; names of
values within a given enumeration declaration must be unique.
An example of an enumeration type is the following:
Enumeration( Dog, Cat, Bird, Frog )
This defines an enumeration type which contains four values.
Data() identifies an array of given dimensionality and size in
each dimension, whose elements are all of a given data type.
It is written as,
Data( DataType, Dimension, DimensionValues[] ) ;
Dimension is an integer, and DimensionValues[] is an
array of integers of size Dimension.
Dimension and DimensionValues[] specify the
dimensionality of the array and its size in each dimension.
DataType specifies the data type of the array's elements;
it may consist of one of the following: int, real,
char or bit.
For multidimensional arrays, FORTRAN indexing conventions are used.
Data() is formulated to map directly onto the data section of
an ADF node.
A typedef establishes a new type and defines it in terms of previously
defined types.
Types are identified by the suffix "_t", and the symbol
":=" is used to establish a type definition (or typedef).
For example, the above enumeration example can be used in a typedef:
Pet_t := Enumeration( Dog, Cat, Bird, Frog ) ;
This defines a new type Pet_t, which can then be used to
declare a new entity, such as,
Pet_t MyFavoritePet ;
By the above typedef and declaration, MyFavoritePet is an
entity of type Pet_t and can have the values Dog,
Cat, Bird or Frog.
A specific instance of MyFavoritePet is setting it equal to one
of these values (e.g., MyFavoritePet = Bird).
A structure is a type that can contain any number of elements, including
elements that are also structures.
An example of a structure type definition is:
Sample_t :=
{
int Dimension ; (r)
real[4] Vector ; (o)
Pet_t ObnoxiousPet ; (o)
} ;
where Sample_t is the type of the structure.
This structure contains three elements, Dimension,
Vector and ObnoxiousPet, whose types are int,
real[4] and Pet_t, respectively.
The type int specifies an integer, and real[4]
specifies an array of reals that is onedimensional with a length of
four.
The "(r)" and "(o)" notation in the right margin is
explained below.
Given the definition of Sample_t, entities of this type can
then be declared (e.g., Sample_t Sample1;).
An example of an instance of a structure entity is given by,
Sample_t Sample1 =
{{
Dimension = 3 ;
Vector = [1.0, 3.45, 2.1, 5.4] ;
ObnoxiousPet = Dog ;
}} ;
Note the different functions played by single braces "{" and
double braces "{{".
The first is used to delimit the definition of a structure type; the
second is used to delimit a specific instance of a structure entity.
Some structure type definitions contain arbitrarily long lists of other
structures or types.
These lists will be identified by the notation,
List( Sample_t Sample1 ... SampleN ) ;
where Sample1 ... SampleN is the list of structure names or
identifiers, each of which has the type Sample_t.
Within each list, the individual structure names are userdefined.
In the CGNS database it is sometimes necessary to reference the name or
identifier of a structure entity.
References to entities are denoted by Identifier(), whose
single argument is a structure type.
For example,
Identifier(Sample_t) SampleName ;
declares an entity, SampleName, whose value is the identifier
of a structure entity of type Sample_t.
Given this declaration, SampleName could be assigned the value
Sample1 (i.e., SampleName = Sample1).
It is sometimes convenient to directly identify an element of a specific
structure entity.
It is also convenient to indicate that two entities with different names
are actually the same entity.
We borrow UNIX conventions to indicate both these features, and make the
analogy that a structure entity is a UNIX directory and its elements are
UNIX files.
An element of an entity is designated by "/"; an example is
Sample1/Vector).
The structure entity that a given element belongs to is designated
"../".
A UNIXlike logical link that specifies the sameness of two apparently
different entities is identified by LogicalLink(); it has one
argument.
An example of a logical link is as follows: Suppose a specific
instance of a structure entity contains two elements that are of type
Sample_t; call them SampleA and SampleB.
The statement that SampleB is actually the same entity as
SampleA is,
SampleB = LogicalLink(../SampleA) ;
The argument of LogicalLink() is the UNIXlike "path name" of
the entity with which the link is made.
In this document, LogicalLink() and the direct specification
of a structure element via "/" and "../" are actually
seldom used.
These language elements are never used in the actual definition of a
structure type.
Structure type definitions include three additional syntactic/semantic
notions.
These are parameterized structures, structurerelated functions, and the
identification of required and optional fields within a structure.
As previously stated, one of our design objectives is to minimize
duplication of information within the CGNS database.
To meet this objective, information is often stored in only one location
of the hierarchy; however, that information is typically used in other
parts of the hierarchy.
A consequence of this is that it may not be possible to decipher all
the information associated with a given entity in the hierarchy without
knowledge of data contained in higher level entities.
For example, the grid size of a zone is stored in one location
(in Zone_t), but is needed in
many substructures to define the size of grid and solutiondata arrays.
This organization of information must be reflected in the language
used to describe the database. First, parameterized structures are
introduced to formalize the notion that information must be passed down the
hierarchy. A given structure type is defined in terms of a list of parameters
that precisely specify what information must be obtained from the structure's
parent. These structuredefining parameters play a similar role to
subroutine parameters in C or FORTRAN and are used to define fields within
the structure; they are also passed onto substructures. Parameterized
structures are also loosely tied to templates in C++.
Parameterized structures are identified by the delimiters
< > enclosing the list of parameters.
Each structure parameter in a structuretype definition consists of a
type and an identifier.
Examples of parameterized structure type definitions are:
NewSample_t< int Dimension, int Fred > :=
{
int[Dimension] Vector ; (o)
Pet_t ObnoxiousPet ; (o)
Stuff_t<Fred> Thingy ; (o)
} ;
Stuff_t< int George > :=
{
real[George] IrrelevantStuff ; (r)
} ;
NewSample_t and Stuff_t are parameterized structure
types.
Dimension and Fred are the structure parameters of
NewSample_t.
George is the structure parameter of Stuff_t.
All structure parameters in this example are of type int.
Thingy is a structure entity of type Stuff_t; it uses
the parameter Fred to complete its declaration.
Note the use of George and Fred in the above example.
George is a parameter in the definition of Stuff_t;
Fred is an argument in the declaration of an entity of type
Stuff_t.
This mimics the use of parameters in function definitions in C.
A second language feature required to cope with the cascade of information
within the hierarchy is structurerelated functions. For example, the size
of an array within a given structure may be a function of one or more of the
structuredefining parameters, or the array size may be a function of an
optional field within the structure. No new syntax is provided to
incorporate structurerelated functions; they are instead described in terms
of their return values, dependencies, and functionality.
An additional notation used in structure typedefs is that each element
or field within a structure definition is identified as required,
optional, or optional with a default if absent; these are designated by
"(r)", "(o)", and "(o/d)", respectively, in
the right margin of the structure definition.
These designations are included to assist in implementation of the data
structures into an actual database and can be used to guide mapping of
data as well as error checking.
"Required" fields are those essential to the interpretation of the
information contained within the data structure. "Optional" fields
are those that are not necessary but potentially useful, such as
documentation.
"Defaultedoptional" fields are those that take on a known default if
absent from the database.
In the example of Sample_t above, only the element
Dimension is required.
Both elements Vector and ObnoxiousPet are optional.
This means that in any specific instance of the structure, only
Dimension must be present.
An alternative instance of the entity Sample1 shown above is
the following:
Sample_t Sample1 =
{{
Dimension = 4 ;
}} ;
None of the entities and types defined in the above examples are actually
used in the definition of the SIDS.
As a final note, the reader should be aware that the SIDS is a
conceptual description of the form of the data.
The actual location of data in the file is determined by the file
mapping, defined by the appropriate
File Mapping Manual.
3.2 Structured Grid Notation and Indexing Conventions
A grid is defined by its vertices. In a 3D structured grid, the volume
is the ensemble of cells, where each cell is the hexahedron region defined
by eight nearest neighbor vertices. Each cell is bounded by six faces, where
each face is the quadrilateral made up of four vertices. An edge links two
nearestneighbor vertices; a face is bounded by four edges.
In a 2D structured grid, the notation is more ambiguous. Typically, the
quadrilateral area composed of four nearestneighbor vertices is referred to
as a cell. The sides of each cell, the line linking two vertices, is either
a face or an edge. In a 1D grid, the line connecting two vertices is a cell.
A structured multizone grid is composed of multiple regions
called zones, where each zone includes all the vertices, cells,
faces, and edges that constitute the grid in that region.
Indices describing a 3D grid are ordered (i,j,k);
(i,j) is used for 2D and (i) for 1D.
Cell centers, face centers, and edge centers are indexed by the minimum
i, j, and k indices of the connecting vertices.
For example, a 2D cell center (or face center on a 3D grid) would have
the following convention:
In addition, the default beginning vertex for the grid in a given zone
is (1,1,1); this means the default beginning cell center of the grid in
that zone is also (1,1,1).
A zone may contain gridcoordinate or flowsolution data defined
at a set of points outside the zone itself.
These are referred to as "rind" or ghost points and may be associated
with fictitious vertices or cell centers.
They are distinguished from the vertices and cells making up the grid
within the zone (including its boundary vertices), which are referred to
as "core" points.
The following is a 2D zone with a single row of rind vertices
at the minimum and maximum ifaces.
The grid size (i.e., the number of core vertices in each direction) is
5×4.
Core vertices are designated by a bullet, and rind vertices by
"×".
Default indexing is also shown for the vertices.
For a zone, the minimum faces in each coordinate direction are
denoted imin, jmin and kmin; the maximum faces
are denoted imax, jmax and kmax.
These are the minimum and maximum core faces.
For example, imin is the face or grid plane whose core vertices
have minimum i index (which if using default indexing is 1).
3.3 Unstructured Grid Element Numbering Conventions
The major difference in the way structured and unstructured
grids are recorded is the element definition.
In a structured grid, the elements can always be recomputed easily
using the computational coordinates, and therefore they are usually
not written in the data file.
For an unstructured grid, the element connectivity cannot be easily
built, so this additional information is generally added to the data file.
The element information typically includes the element type or shape,
and the list of nodes for each element.
In an unstructured zone, the nodes are ordered from 1 to N,
where N is the number of nodes in the zone.
An element is defined as a group of one or more nodes, where each node
is represented by its index.
The elements are indexed from 1 to M within a zone, where M
is the total number of elements defined for the zone.
CGNS supports eight element shapes  points, lines,
triangles, quadrangles,
tetrahedra, pentahedra,
pyramids, and hexahedra.
Elements describing a volume are referred to as 3D
elements.
Those defining a surface are 2D elements.
Line and point elements are called 1D and
0D elements, respectively.
In a 3D unstructured mesh, the cells are defined using
3D elements, while the boundary patches may be
described using 2D elements.
The complete element definition may include more than just the cells.
Each element shape may have a different number of nodes, depending on
whether linear, quadratic, or cubic interpolation is used.
Therefore the name of each type of element is composed of two parts;
the first part identifies the element shape, and the second part the
number of nodes.
The following table summarizes the element types supported in CGNS.
Element Types in CGNS

Dimensionality 
 Shape 
 Linear 
 Quadratic 
 Cubic 
 Quartic


 
 Interpolation 
 Interpolation 
 Interpolation 
 Interpolation


0D 
 Point 
 NODE 
 NODE 
 NODE 
 NODE

1D 
 Line 
 BAR_2 
 BAR_3 
 BAR_4 
 BAR_5

2D 
 Triangle 
 TRI_3 
 TRI_6 
 TRI_9, TRI_10 
 TRI_12, TRI_15


 Quadrangle 
 QUAD_4 
 QUAD_8, QUAD_9 
 QUAD_12, QUAD_16 
 QUAD_P4_16, QUAD_25

3D 
 Tetrahedron 
 TETRA_4 
 TETRA_10 
 TETRA_16, TETRA_20 
 TETRA_22, TETRA_34, TETRA_35


 Pyramid 
 PYRA_5 
 PYRA_13, PYRA_14 
 PYRA_21, PYRA_29, PYRA_30 
 PYRA_P4_29, PYRA_50, PYRA_55


 Pentahedron 
 PENTA_6 
 PENTA_15, PENTA_18 
 PENTA_24, PENTA_38, PENTA_40 
 PENTA_33, PENTA_66, PENTA_75


 Hexahedron 
 HEXA_8 
 HEXA_20, HEXA_27 
 HEXA_32, HEXA_56, HEXA_64 
 HEXA_44, HEXA_98, HEXA_125


General polyhedral elements can be recorded using the CGNS
generic element types NGON_n and NFACE_n.
See the Elements_t structure
definition for more detail.
The ordering of the nodes within an element is important.
Since the nodes in each element type could be ordered in multiple ways,
it is necessary to define numbering conventions.
The following sections describe the element numbering conventions
used in CGNS.
Like a structured zone, an unstructured zone may contain
gridcoordinates or flowsolution data at points outside of the zone
itself, through the use of ghost or "rind" points and elements.
However, unlike for structured zones, rind data for unstructured zones
cannot be defined implicitly (i.e., via indexing conventions alone).
In other words, when using rind with unstructured zones, the rind grid
points and their element connectivity information should always be
given.
3.3.1 1D (Line) Elements
1D elements represent geometrically a line (or bar).
The linear form, BAR_2, is composed of two nodes at each extremity
of the line.
The quadratic form, BAR_3, has an additional node located at
the middle of the line.
The cubic form of the line, BAR_4, contains two nodes
interior to the endpoints.
The quartic form of the line, BAR_5, contains three nodes
interior to the endpoints.
Linear and Quadratic Elements
 BAR_2

 BAR_3

Edge Definition
Oriented edge  
Corner nodes  
Mid node 
E1  
N1,N2  
N3 
Cubic Elements
 BAR_4

Edge Definition
Oriented edge  
Corner nodes  
Mid nodes 
E1  
N1,N2  
N3,N4 
Quartic Elements
 BAR_5

Edge Definition
Oriented edge  
Corner nodes  
Mid nodes 
E1  
N1,N2  
N3,N4,N5 
Note that nodes are uniformly spaced on all edges for all higher order elements.
3.3.2 2D (Surface) Elements
2D elements represent a surface in either 2D or 3D space.
Note that in physical space, the surface need not be planar, but
may be curved.
In a 2D mesh the elements represent the cells themselves; in a 3D
mesh they represent faces.
CGNS supports two shapes of 2D elements  triangles
and quadrangles.
The normal vector of a 2D element is computed using the cross product
of a vector from the first to second node, with a vector from the first
to third node.
The direction of the normal is such that the three vectors
(i.e., ,
, and
) form a righthanded triad.
In a 2D mesh, all elements must be oriented the same way; i.e., all
normals must point toward the same side of the mesh.
3.3.2.1 Triangular Elements
Six types of triangular elements are supported in CGNS, TRI_3,
TRI_6, TRI_9, TRI_10, TRI_12, and TRI_15.
TRI_3 elements are composed of three nodes located at the
three geometric corners of the triangle.
TRI_6 elements have three additional nodes located at the
middles of the three edges.
The cubic forms of triangular elements, TRI_9 and TRI_10
contain two interior nodes along each edge, and an interior face node
in the case of TRI_10.
The quartic forms of triangular elements, TRI_12 and TRI_15
contain three interior nodes along each edge, and three interior face nodes
in the case of TRI_15.
Linear and Quadratic Elements
 TRI_3

 TRI_6

Edge Definition
Oriented edges  
Corner nodes  
Mid node 
E1  
N1,N2  
N4 
E2  
N2,N3  
N5 
E3  
N3,N1  
N6 
 
Face Definition
Face  
Corner nodes  
Midedge nodes  
Oriented edges 
F1  
N1,N2,N3  
N4,N5,N6  
E1,E2,E3 

Cubic Elements
 TRI_9

 TRI_10

Edge Definition
Oriented edges  
Corner nodes  
Mid nodes 
E1  
N1,N2  
N4,N5 
E2  
N2,N3  
N6,N7 
E3  
N3,N1  
N8,N9 
 
Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface node  
Oriented edges 
F1  
N1,N2,N3  
N4,N5,N6,N7,N8,N9  
N10  
E1,E2,E3 

Notes
 N1,...,N10 
 Grid point identification number.
Integer ≥ 0 or blank, and no two values may be the same.
Grid points N1, N2, and N3 are in
consecutive order about the triangle.

 E1,E2,E3 
 Edge identification number.

 F1 
 Face identification number.

Quartic Elements
 TRI_12

 TRI_15

Edge Definition
Oriented edges  
Corner nodes  
Mid nodes 
E1  
N1,N2  
N4,N5,N6 
E2  
N2,N3  
N7,N8,N9 
E3  
N3,N1  
N10,N11,N12 
 
Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface node  
Oriented edges 
F1  
N1,N2,N3  
N4,N5,N6,N7,N8,N9,N10,N11,N12  
N13,N14,N15  
E1,E2,E3 

Notes
 N13 
 Is located at the centroid of subtriangle N1N5N11.

 N14 
 Is located at the centroid of subtriangle N2N8N5.

 N151 
 Is located at the centroid of subtriangle N3N11N8.

3.3.2.2 Quadrilateral Elements
CGNS supports seven types of quadrilateral elements, QUAD_4,
QUAD_8, QUAD_9, QUAD_12, QUAD_16, QUAD_P4_16, and QUAD_25.
QUAD_4 elements are composed of four nodes located at the
four geometric corners of the quadrangle.
In addition, QUAD_8 and QUAD_9 elements have four
midedge nodes, and QUAD_9 adds a midface node.
The cubic forms of quadrilateral elements, QUAD_12 and QUAD_16
contain two interior nodes along each edge, and four interior face nodes
in the case of QUAD_16.
The quartic forms of quadrilateral elements, QUAD_P4_16 and QUAD_25
contain three interior nodes along each edge, and nine interior face nodes
in the case of QUAD_25.
Linear and Quadratic Elements
 QUAD_4

 QUAD_8


 QUAD_9


Edge Definition
Oriented edges  
Corner nodes  
Mid node 
E1  
N1,N2  
N5 
E2  
N2,N3  
N6 
E3  
N3,N4  
N7 
E4  
N4,N1  
N8 

Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface node  
Oriented edges 
F1  
N1,N2,N3,N4  
N5,N6,N7,N8  
N9  
E1,E2,E3,E4 
Cubic Elements
 QUAD_12

 QUAD_16

Edge Definition
Oriented edges  
Corner nodes  
Mid nodes 
E1  
N1,N2  
N5,N6 
E2  
N2,N3  
N7,N8 
E3  
N3,N4  
N9,N10 
E4  
N4,N1  
N11,N12 
Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface nodes  
Oriented edges 
F1  
N1,N2,N3,N4  
N5,N6,N7,N8,N9,N10,N11,N12  
N13,N14,N15,N16  
E1,E2,E3,E4 
Notes
 N1,...,N16 
 Grid point identification number.
Integer ≥ 0 or blank, and no two values may be the same.
Grid points N1, ..., N4 are in
consecutive order about the quadrangle.

 E1,...,E4 
 Edge identification number.

 F1 
 Face identification number.

Quartic Elements
 QUAD_P4_16

 QUAD_25

Edge Definition
Oriented edges  
Corner nodes  
Mid nodes 
E1  
N1,N2  
N5,N6,N7 
E2  
N2,N3  
N8,N9,N10 
E3  
N3,N4  
N11,N12,N13 
E4  
N4,N1  
N14,N15,N16 
Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface nodes  
Oriented edges 
F1  
N1,N2,N3,N4  
N5,N6,N7,N8,N9,N10,N11,N12,N13,N14,N15,N16  
N17,N18,N19,N20,N21,N22,N23,N24,N25  
E1,E2,E3,E4 
3.3.3 3D (Volume) Elements
3D elements represent a volume in 3D space, and constitute the cells
of a 3D mesh.
CGNS supports four different shapes of 3D elements 
tetrahedra, pyramids,
pentahedra, and hexahedra.
3.3.3.1 Tetrahedral Elements
CGNS supports seven types of tetrahedral elements, TETRA_4,
TETRA_10, TETRA_16, TETRA_20, TETRA_22, TETRA_34, and TETRA_35.
TETRA_4 elements are composed of four nodes located at the
four geometric corners of the tetrahedron.
TETRA_10 elements have six additional nodes, at the middle
of each of the six edges.
The cubic forms of tetrahedral elements, TETRA_16 and TETRA_20
contain two interior nodes along each edge, and four interior face nodes
in the case of TETRA_20.
The quartic forms of tetrahedral elements, TETRA_22, TETRA_34, and TETRA_35
contain three interior nodes along each edge, twelve interior face nodes
in the case of TETRA_34, and twelve interior face nodes plus one interior volume
node in the case of TETRA_35.
Linear and Quadratic Elements
 TETRA_4

 TETRA_10

Edge Definition
Oriented edges  
Corner nodes  
Mid node 
E1  
N1,N2  
N5 
E2  
N2,N3  
N6 
E3  
N3,N1  
N7 
E4  
N1,N4  
N8 
E5  
N2,N4  
N9 
E6  
N3,N4  
N10 
 
Face Definition
Face  
Corner nodes  
Midedge nodes  
Oriented edges 
F1  
N1,N3,N2  
N7,N6, N5  
E3,E2,E1 
F2  
N1,N2,N4  
N5,N9, N8  
E1, E5,E4 
F3  
N2,N3,N4  
N6,N10,N9  
E2, E6,E5 
F4  
N3,N1,N4  
N7,N8, N10  
E3, E4,E6 

Cubic Elements
 TETRA_16


 TETRA_20

Edge Definition
Oriented edges  
Corner nodes  
Mid nodes 
E1  
N1,N2  
N5,N6 
E2  
N2,N3  
N7,N8 
E3  
N3,N1  
N9,N10 
E4  
N1,N4  
N11,N12 
E5  
N2,N4  
N13,N14 
E6  
N3,N4  
N15,N16 
Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface node  
Oriented edges 
F1  
N1,N3,N2  
N10,N9,N8,N7,N6,N5  
N17  
E3,E2,E1 
F2  
N1,N2,N4  
N5,N6,N13,N14,N12,N11  
N18  
E1,E5,E4 
F3  
N2,N3,N4  
N7,N8,N15,N16,N14,N13  
N19  
E2,E6,E5 
F4  
N3,N1,N4  
N9,N10,N11,N12,N16,N15  
N20  
E3,E4,E6 
Notes
 N1,...,N20 
 Grid point identification number.
Integer ≥ 0 or blank, and no two values may be the same.
Grid points N1 ... N3 are in consecutive order about
one trilateral face.
The cross product of a vector going from N1 to N2,
with a vector going from N1 to N3, must result in a
vector oriented from face F1 toward N4.

 E1,...,E6 
 Edge identification number.
The edges are oriented from the first to the second node.
A negative edge (e.g., E1) means that the edge is used in
its reverse direction.

 F1,...,F4 
 Face identification number.
The faces are oriented so that the cross product of a vector
from its first to second node, with a vector from its first to
third node, is oriented outward.

Quartic Elements
 TETRA_22


 TETRA_34


 TETRA_35

Edge Definition
Oriented edges  
Corner nodes  
Mid nodes 
E1  
N1,N2  
N5,N6,N7 
E2  
N2,N3  
N8,N9,N10 
E3  
N3,N1  
N11,N12,N13 
E4  
N1,N4  
N14,N15,N16 
E5  
N2,N4  
N17,N18,N19 
E6  
N3,N4  
N20,N21,N22 
Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface node  
Oriented edges 
F1  
N1,N3,N2  
N13,N12,N11,N10,N9,N8,N7,N6,N5  
N23,N24,N25  
E3,E2,E1 
F2  
N1,N2,N4  
N5,N6,N7,N17,N18,N19,N16,N15,N14  
N26,N27,N28  
E1,E5,E4 
F3  
N2,N3,N4  
N8,N9,N10,N20,N21,N22,N19,N18,N17  
N29,N30,N31  
E2,E6,E5 
F4  
N3,N1,N4  
N11,N12,N13,N14,N15,N16,N22,N21,N20  
N32,N33,N34  
E3,E4,E6 
Notes
 N23 
 Is located at the centroid of subtriangle N1N12N6.

 N24 
 Is located at the centroid of subtriangle N2N6N9.

 N25 
 Is located at the centroid of subtriangle N3N9N12.

 N26 
 Is located at the centroid of subtriangle N1N6N15.

 N27 
 Is located at the centroid of subtriangle N2N18N6.

 N28 
 Is located at the centroid of subtriangle N4N15N18.

 N29 
 Is located at the centroid of subtriangle N2N9N18.

 N30 
 Is located at the centroid of subtriangle N3N21N9.

 N31 
 Is located at the centroid of subtriangle N4N18N21.

 N32 
 Is located at the centroid of subtriangle N3N12N21.

 N33 
 Is located at the centroid of subtriangle N1N15N12.

 N34 
 Is located at the centroid of subtriangle N4N21N15.

 N35 
 Is located at the centroid of the tetrahedron.

3.3.3.2 Pyramid Elements
CGNS supports nine types of pyramid elements, PYRA_5,
PYRA_13, PYRA_14, PYRA_21, PYRA_29,
PYRA_30, PYRA_P4_29, PYRA_50, and PYRA_55.
PYRA_5 elements are composed of five nodes located at the
five geometric corners of the pyramid.
In addition, PYRA_13 and PYRA_14 elements have a node
at the middle of each of the eight edges; PYRA_14 adds a node
at the middle of the quadrilateral face.
The cubic forms of pyramid elements, PYRA_21,
PYRA_29, and PYRA_30
contain two interior nodes along each edge, eight interior face nodes
in the case of PYRA_29 and PYRA_30, and an additonal
interior volume node for PYRA_30.
The quartic forms of pyramid elements, PYRA_P4_29, PYRA_50, and PYRA_55
contain three interior nodes along each edge, 21 interior face nodes
in the case of PYRA_50, and 21 interior face nodes and five additonal
interior volume nodes for PYRA_55.
Linear and Quadratic Elements
 PYRA_5

 PYRA_13


 PYRA_14


Edge Definition
Oriented edges  
Corner nodes  
Mid node 
E1  
N1,N2  
N6 
E2  
N2,N3  
N7 
E3  
N3,N4  
N8 
E4  
N4,N1  
N9 
E5  
N1,N5  
N10 
E6  
N2,N5  
N11 
E7  
N3,N5  
N12 
E8  
N4,N5  
N13 

Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface node  
Oriented edges 
F1  
N1,N4,N3,N2  
N9,N8, N7, N6  
N14  
E4,E3,E2,E1 
F2  
N1,N2,N5  
N6,N11,N10  
 
E1, E6,E5 
F3  
N2,N3,N5  
N7,N12,N11  
 
E2, E7,E6 
F4  
N3,N4,N5  
N8,N13,N12  
 
E3, E8,E7 
F5  
N4,N1,N5  
N9,N10,N13  
 
E4, E5,E8 
Cubic Elements
Edge Definition
Oriented edges  
Corner nodes  
Mid nodes 
E1  
N1,N2  
N6,N7 
E2  
N2,N3  
N8,N9 
E3  
N3,N4  
N10,N11 
E4  
N4,N1  
N12,N13 
E5  
N1,N5  
N14,N15 
E6  
N2,N5  
N16,N17 
E7  
N3,N5  
N18,N19 
E8  
N4,N5  
N20,N21 
Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface nodes  
Oriented edges 
F1  
N1,N4,N3,N2  
N13,N12,N11,N10,N9,N8,N7,N6  
N22,N25,N24,N23  
E4,E3,E2,E1 
F2  
N1,N2,N5  
N6,N7,N16,N17,N15,N14  
N26  
E1,E6,E5 
F3  
N2,N3,N5  
N8,N9,N18,N19,N17,N16  
N27  
E2,E7,E6 
F4  
N3,N4,N5  
N10,N11,N20,N21,N19,N18  
N28  
E3,E8,E7 
F5  
N4,N1,N5  
N12,N13,N14,N15,N21,N20  
N29  
E4,E5,E8 
Notes
 N1,...,N30 
 Grid point identification number.
Integer ≥ 0 or blank, and no two values may be the same.
Grid points N1 ... N4 are in consecutive order about
the quadrilateral face.
The cross product of a vector going from N1 to N2,
with a vector going from N1 to N3, must result in a
vector oriented from face F1 toward N5.

 E1,...,E8 
 Edge identification number.
The edges are oriented from the first to the second node.
A negative edge (e.g., E1) means that the edge is used in
its reverse direction.

 F1,...,F5 
 Face identification number.
The faces are oriented so that the cross product of a vector
from its first to second node, with a vector from its first to
third node, is oriented outward.

Quartic Elements
 PYRA_P4_29


 PYRA_50


 PYRA_55

Edge Definition
Oriented edges  
Corner nodes  
Mid nodes 
E1  
N1,N2  
N6,N7,N8 
E2  
N2,N3  
N9,N10,N11 
E3  
N3,N4  
N12,N13,N14 
E4  
N4,N1  
N15,N16,N17 
E5  
N1,N5  
N18,N19,N20 
E6  
N2,N5  
N21,N22,N23 
E7  
N3,N5  
N24,N25,N26 
E8  
N4,N5  
N27,N28,N29 
Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface nodes  
Oriented edges 
F1  
N1,N4,N3,N2  
N17,N16,N15,N14,N13,N12,N11,N10,N9,N8,N7,N6  
N30,N31,N32,N33,N34,N35,N36,N37,N38  
E4,E3,E2,E1 
F2  
N1,N2,N5  
N6,N7,N8,N21,N22,N23,N20,N19,N18  
N39,N40,N41  
E1,E6,E5 
F3  
N2,N3,N5  
N9,N10,N11,N24,N25,N26,N23,N22,N21  
N42,N43,N44  
E2,E7,E6 
F4  
N3,N4,N5  
N12,N13,N14,N27,N28,N29,N26,N25,N24  
N45,N46,N47  
E3,E8,E7 
F5  
N4,N1,N5  
N15,N16,N17,N18,N19,N20,N29,N28,N27  
N48,N49,N50  
E4,E5,E8 
Notes
 N39 
 Is located at the centroid of subtriangle N1N7N19.

 N40 
 Is located at the centroid of subtriangle N2N22N7.

 N41 
 Is located at the centroid of subtriangle N5N19N22.

 N42 
 Is located at the centroid of subtriangle N2N10N22.

 N43 
 Is located at the centroid of subtriangle N3N25N10.

 N44 
 Is located at the centroid of subtriangle N5N22N25.

 N45 
 Is located at the centroid of subtriangle N3N13N25.

 N46 
 Is located at the centroid of subtriangle N4N28N13.

 N47 
 Is located at the centroid of subtriangle N5N25N28.

 N48 
 Is located at the centroid of subtriangle N4N16N28.

 N49 
 Is located at the centroid of subtriangle N1N19N16.

 N50 
 Is located at the centroid of subtriangle N5N28N19.

 N51 
 Is located at the intersection of the line N5N30 and the face N18N21N24N27.

 N52 
 Is located at the intersection of the line N5N32 and the face N18N21N24N27.

 N53 
 Is located at the intersection of the line N5N34 and the face N18N21N24N27.

 N54 
 Is located at the intersection of the line N5N36 and the face N18N21N24N27.

 N55 
 Is located at the intersection of the line N5N38 and the face N20N23N26N29.

3.3.3.3 Pentahedral Elements
CGNS supports nine types of pentahedral elements, PENTA_6,
PENTA_15, PENTA_18, PENTA_24,
PENTA_38, PENTA_40,
PENTA_33, PENTA_66, and PENTA_75.
PENTA_6 elements are composed of six nodes located at the
six geometric corners of the pentahedron.
In addition, PENTA_15 and PENTA_18 elements have a node
at the middle of each of the nine edges; PENTA_18 adds a
node at the middle of each of the three quadrilateral faces.
The cubic forms of the pentahedral elements, PENTA_24,
PENTA_38, and PENTA_40
contain two interior nodes along each edge, fourteen interior face nodes
in the case of PENTA_38 and PENTA_40, and an additonal
two interior volume nodes for PENTA_40.
The quartic forms of the pentahedral elements,
PENTA_33, PENTA_66, and PENTA_75
contain three interior nodes along each edge, 33 interior face nodes
in the case of PENTA_66, and 33 interior face nodes and an additonal
nine interior volume nodes for PENTA_75.
Linear and Quadratic Elements
 PENTA_6

 PENTA_15


 PENTA_18


Edge Definition
Oriented edges  
Corner nodes  
Mid node 
E1  
N1,N2  
N7 
E2  
N2,N3  
N8 
E3  
N3,N1  
N9 
E4  
N1,N4  
N10 
E5  
N2,N5  
N11 
E6  
N3,N6  
N12 
E7  
N4,N5  
N13 
E8  
N5,N6  
N14 
E9  
N6,N4  
N15 

Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface node  
Oriented edges 
F1  
N1,N2,N5,N4  
N7, N11,N13,N10  
N16  
E1, E5,E7,E4 
F2  
N2,N3,N6,N5  
N8, N12,N14,N11  
N17  
E2, E6,E8,E5 
F3  
N3,N1,N4,N6  
N9, N10,N15,N12  
N18  
E3, E4,E9,E6 
F4  
N1,N3,N2  
N9, N8, N7  
 
E3,E2,E1 
F5  
N4,N5,N6  
N13,N14,N15  
 
E7, E8, E9 
Cubic Elements
 PENTA_24


 PENTA_38


 PENTA_40

Edge Definition
Oriented edges  
Corner nodes  
Mid nodes 
E1  
N1,N2  
N7,N8 
E2  
N2,N3  
N9,N10 
E3  
N3,N1  
N11,N12 
E4  
N1,N4  
N13,N14 
E5  
N2,N5  
N15,N16 
E6  
N3,N6  
N17,N18 
E7  
N4,N5  
N19,N20 
E8  
N5,N6  
N21,N22 
E9  
N6,N4  
N23,N24 
Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface nodes  
Oriented edges 
F1  
N1,N2,N5,N4  
N7,N8,N15,N16,N20,N19,N14,N13  
N26,N27,N28,N29  
E1,E5,E7,E4 
F2  
N2,N3,N6,N5  
N9,N10,N17,N18,N22,N21,N16,N15  
N30,N31,N32,N33  
E2,E6,E8,E5 
F3  
N3,N1,N4,N6  
N11,N12,N13,N14,N24,N23,N18,N17  
N34,N35,N36,N37  
E3,E4,E9,E6 
F4  
N1,N3,N2  
N12,N11,N10,N9,N8,N7  
N25  
E3,E2,E1 
F5  
N4,N5,N6  
N19,N20,N21,N22,N23,N24  
N38  
E7,E8,E9 
Notes
 N1,...,N40 
 Grid point identification number.
Integer ≥ 0 or blank, and no two values may be the same.
Grid points N1 ... N3 are in consecutive order about
one trilateral face.
Grid points N4 ... N6 are in order in the same
direction around the opposite trilateral face.

 E1,...,E9 
 Edge identification number.
The edges are oriented from the first to the second node.
A negative edge (e.g., E1) means that the edge is used in
its reverse direction.

 F1,...,F5 
 Face identification number.
The faces are oriented so that the cross product of a vector
from its first to second node, with a vector from its first to
third node, is oriented outward.

 N39 
 Is at the centroid of the triangle N13,N17,N15.

 N40 
 Is at the centroid of the triangle N14,N18,N16.

Quartic Elements
 PENTA_33


 PENTA_66


 PENTA_75

Edge Definition
Oriented edges  
Corner nodes  
Mid nodes 
E1  
N1,N2  
N7,N8,N9 
E2  
N2,N3  
N10,N11,N12 
E3  
N3,N1  
N13,N14,N15 
E4  
N1,N4  
N16,N17,N18 
E5  
N2,N5  
N19,N20,N21 
E6  
N3,N6  
N22,N23,N24 
E7  
N4,N5  
N25,N26,N27 
E8  
N5,N6  
N28,N29,N30 
E9  
N6,N4  
N31,N32,N33 
Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface nodes  
Oriented edges 
F1  
N1,N2,N5,N4  
N7,N8,N9,N19,N20,N21,N27,N26,N25,N18,N17,N16  
N37,N38,N39,N40,N41,N42,N43,N44,N45  
E1,E5,E7,E4 
F2  
N2,N3,N6,N5  
N10,N11,N12,N22,N23,N24,N30,N29,N28,N21,N20,N19  
N46,N47,N48,N49,N50,N51,N52,N53,N54  
E2,E6,E8,E5 
F3  
N3,N1,N4,N6  
N13,N14,N15,N16,N17,N18,N33,N32,N31,N24,N23,N22  
N55,N56,N57,N58,N59,N60,N61,N62,N63  
E3,E4,E9,E6 
F4  
N1,N3,N2  
N15,N14,N13,N12,N11,N10,N9,N8,N7  
N34,N35,N36  
E3,E2,E1 
F5  
N4,N5,N6  
N25,N26,N27,N28,N29,N30,N31,N32,N33  
N64,N65,N66  
E7,E8,E9 
Notes
 N34 
 Is located at the centroid of subtriangle N1N14N8.

 N35 
 Is located at the centroid of subtriangle N2N8N11.

 N36 
 Is located at the centroid of subtriangle N3N11N14.

 N64 
 Is located at the centroid of subtriangle N4N26N32.

 N65 
 Is located at the centroid of subtriangle N5N29N26.

 N66 
 Is located at the centroid of subtriangle N6N32N29.

 N67 
 Is located at the centroid of subtriangle N16N38N56.

 N68 
 Is located at the centroid of subtriangle N19N47N38.

 N69 
 Is located at the centroid of subtriangle N22N56N47.

 N70 
 Is located at the centroid of subtriangle N17N45N63.

 N71 
 Is located at the centroid of subtriangle N20N54N45.

 N72 
 Is located at the centroid of subtriangle N23N63N54.

 N73 
 Is located at the centroid of subtriangle N18N42N60.

 N74 
 Is located at the centroid of subtriangle N21N51N42.

 N75 
 Is located at the centroid of subtriangle N24N60N51.

3.3.3.4 Hexahedral Elements
CGNS supports nine types of hexahedral elements, HEXA_8,
HEXA_20, HEXA_27, HEXA_32,
HEXA_56, HEXA_64,
HEXA_44, HEXA_98, and HEXA_125.
HEXA_8 elements are composed of eight nodes located at the
eight geometric corners of the hexahedron.
In addition, HEXA_20 and HEXA_27 elements have a node
at the middle of each of the twelve edges; HEXA_27 adds a
node at the middle of each of the six faces, and one at the cell center.
The cubic forms of the hexahedral elements, HEXA_32,
HEXA_56, and HEXA_64
contain two interior nodes along each edge, 24 interior face nodes
in the case of HEXA_56 and HEXA_64, and an additonal
eight interior volume nodes for HEXA_64.
The quartic forms of the hexahedral elements,
HEXA_44, HEXA_98, and HEXA_125
contain three interior nodes along each edge, 54 interior face nodes
in the case of HEXA_98, and 54 interior face nodes and an additonal
27 interior volume nodes for HEXA_125.
Linear and Quadratic Elements
 HEXA_8

 HEXA_20


 HEXA_27


Edge Definition
Oriented edges  
Corner nodes  
Mid node 
E1  
N1,N2  
N9 
E2  
N2,N3  
N10 
E3  
N3,N4  
N11 
E4  
N4,N1  
N12 
E5  
N1,N5  
N13 
E6  
N2,N6  
N14 
E7  
N3,N7  
N15 
E8  
N4,N8  
N16 
E9  
N5,N6  
N17 
E10  
N6,N7  
N18 
E11  
N7,N8  
N19 
E12  
N8,N5  
N20 

Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface node  
Oriented edges 
F1  
N1,N4,N3,N2  
N12,N11,N10,N9  
N21  
E4,E3, E2, E1 
F2  
N1,N2,N6,N5  
N9, N14,N17,N13  
N22  
E1, E6, E9, E5 
F3  
N2,N3,N7,N6  
N10,N15,N18,N14  
N23  
E2, E7, E10,E6 
F4  
N3,N4,N8,N7  
N11,N16,N19,N15  
N24  
E3, E8, E11,E7 
F5  
N1,N5,N8,N4  
N13,N20,N16,N12  
N25  
E5,E12,E8, E4 
F6  
N5,N6,N7,N8  
N17,N18,N19,N20  
N26  
E9, E10, E11, E12 
Cubic Elements
Edge Definition
Oriented edges  
Corner nodes  
Mid nodes 
E1  
N1,N2  
N9,N10 
E2  
N2,N3  
N11,N12 
E3  
N3,N4  
N13,N14 
E4  
N4,N1  
N15,N16 
E5  
N1,N5  
N17,N18 
E6  
N2,N6  
N19,N20 
E7  
N3,N7  
N21,N22 
E8  
N4,N8  
N23,N24 
E9  
N5,N6  
N25,N26 
E10  
N6,N7  
N27,N28 
E11  
N7,N8  
N29,N30 
E12  
N8,N5  
N31,N32 
Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface nodes  
Oriented edges 
F1  
N1,N4,N3,N2  
N16,N15,N14,N13,N12,N11,N10,N9  
N33,N36,N35,N34  
E4,E3,E2,E1 
F2  
N1,N2,N6,N5  
N9,N10,N19,N20,N26,N25,N18,N17  
N37,N38,N39,N40  
E1,E6,E9,E5 
F3  
N2,N3,N7,N6  
N11,N12,N21,N22,N28,N27,N20,N19  
N41,N42,N43,N44  
E2,E7,E10,E6 
F4  
N3,N4,N8,N7  
N13,N14,N23,N24,N30,N29,N22,N21  
N45,N46,N47,N48  
E3,E8,E11,E7 
F5  
N1,N5,N8,N4  
N17,N18,N32,N31,N24,N23,N15,N16  
N49,N50,N51,N52  
E5,E12,E8,E4 
F6  
N5,N6,N7,N8  
N25,N26,N27,N28,N29,N30,N31,N32  
N53,N54,N55,N56  
E9,E10,E11,E12 
Notes
 N1,...,N64 
 Grid point identification number.
Integer ≥ 0 or blank, and no two values may be the same.
Grid points N1 ... N4 are in consecutive order about
one quadrilateral face.
Grid points N5 ... N8 are in order in the same
direction around the opposite quadrilateral face.

 E1,...,E12 
 Edge identification number.
The edges are oriented from the first to the second node.
A negative edge (e.g., E1) means that the edge is used in
its reverse direction.

 F1,...,F6 
 Face identification number.
The faces are oriented so that the cross product of a vector
from its first to second node, with a vector from its first to
third node, is oriented outward.

Quartic Elements
Edge Definition
Oriented edges  
Corner nodes  
Mid nodes 
E1  
N1,N2  
N9,N10,N11 
E2  
N2,N3  
N12,N13,N14 
E3  
N3,N4  
N15,N16,N17 
E4  
N4,N1  
N18,N19,N20 
E5  
N1,N5  
N21,N22,N23 
E6  
N2,N6  
N24,N25,N26 
E7  
N3,N7  
N27,N28,N29 
E8  
N4,N8  
N30,N31,N32 
E9  
N5,N6  
N33,N34,N35 
E10  
N6,N7  
N36,N37,N38 
E11  
N7,N8  
N39,N40,N41 
E12  
N8,N5  
N42,N43,N44 
Face Definition
Face  
Corner nodes  
Midedge nodes  
Midface nodes  
Oriented edges 
F1  
N1,N4,N3,N2  
N20,N19,N18,N17,N16,N15,N14,N13,N12,N11,N10,N9  
N45,N46,N47,N48,N49,N50,N51,N52,N53  
E4,E3,E2,E1 
F2  
N1,N2,N6,N5  
N9,N10,N11,N24,N25,N26,N35,N34,N33,N23,N22,N21  
N54,N55,N56,N57,N58,N59,N60,N61,N62  
E1,E6,E9,E5 
F3  
N2,N3,N7,N6  
N12,N13,N14,N27,N28,N29,N38,N37,N36,N26,N25,N24  
N63,N64,N65,N66,N67,N68,N69,N70,N71  
E2,E7,E10,E6 
F4  
N3,N4,N8,N7  
N15,N16,N17,N30,N31,N32,N41,N40,N39,N29,N28,N27  
N72,N73,N74,N75,N76,N77,N78,N79,N80  
E3,E8,E11,E7 
F5  
N1,N5,N8,N4  
N21,N22,N23,N44,N43,N42,N32,N31,N30,N18,N19,N20  
N81,N82,N83,N84,N85,N86,N87,N88,N89  
E5,E12,E8,E4 
F6  
N5,N6,N7,N8  
N33,N34,N35,N36,N37,N38,N39,N40,N41,N42,N43,N44  
N90,N91,N92,N93,N94,N95,N96,N97,N98  
E9,E10,E11,E12 
3.3.4 Unstructured Grid Example
Consider an unstructured zone in the shape of a cube, with each edge
of the zone having three nodes.
The resulting unstructured grid has a total of 27 nodes, as illustrated
in the exploded figure below.
Example Unstructured Cube (Exploded View)
This zone contains eight hexahedral cells, numbered 1 to 8, and the
cell connectivity is:

Element No. 
 Element Connectivity


1   1, 2, 5, 4, 10, 11, 14, 13

2   2, 3, 6, 5, 11, 12, 15, 14

3   4, 5, 8, 7, 13, 14, 17, 16

4   5, 6, 9, 8, 14, 15, 18, 17

5   10, 11, 14, 13, 19, 20, 23, 22

6   11, 12, 15, 14, 20, 21, 24, 23

7   13, 14, 17, 16, 22, 23, 26, 25

8   14, 15, 18, 17, 23, 24, 27, 26


In addition to the cells, the boundary faces could also be added to the
element definition of this unstructured zone.
There are 24 boundary faces in this zone, corresponding to element
numbers 9 to 32.
Each boundary face is of type QUAD_4.
The table below shows the element connectivity of each boundary face,
as well as the element number and face number of its parent cell.

Face 
 Element No. 
 Element Connectivity 
 Parent Cell 
 Parent Face


Left 
 9 
 1, 10, 13, 4 
 1 
 5


 10 
 4, 13, 16, 7 
 3 
 5


 11 
 10, 19, 22, 13 
 5 
 5


 12 
 13, 22, 25, 16 
 7 
 5

Right 
 13 
 3, 6, 15, 12 
 2 
 3


 14 
 6, 9, 18, 15 
 4 
 3


 15 
 12, 15, 24, 21 
 6 
 3


 16 
 15, 18, 27, 24 
 8 
 3

Bottom 
 17 
 1, 2, 11, 10 
 1 
 2


 18 
 2, 3, 12, 11 
 2 
 2


 19 
 10, 11, 20, 19 
 5 
 2


 20 
 11, 12, 21, 20 
 6 
 2

Top 
 21 
 7, 16, 17, 8 
 3 
 4


 22 
 8, 17, 18, 9 
 4 
 4


 23 
 16, 25, 26, 17 
 7 
 4


 24 
 17, 26, 27, 18 
 8 
 4

Back 
 25 
 1, 4, 5, 2 
 1 
 1


 26 
 2, 5, 6, 3 
 2 
 1


 27 
 4, 7, 8, 5 
 3 
 1


 28 
 5, 8, 9, 6 
 4 
 1

Front 
 29 
 19, 20, 23, 22 
 5 
 6


 30 
 20, 21, 24, 23 
 6 
 6


 31 
 22, 23, 26, 25 
 7 
 6


 32 
 23, 24, 27, 26 
 8 
 6


3.4 Multizone Interfaces
1to1 Abutting Interface
Mismatched Abutting Interface
Overset Interface
StructuredGrid Multizone Interface Types
The above figure shows three types of multizone interfaces, shown for
structured zones.
The first type is a 1to1 abutting interface, also referred to as
matching or C0 continuous.
The interface is a plane of vertices that are physically coincident
between the adjacent zones.
For structured zones, gridcoordinate lines perpendicular to the
interface are continuous from one zone to the next.
In 3D, a 1to1 abutting interface is usually a logically rectangular
region.
The second type of interface is mismatched abutting, where two zones
touch but do not overlap (except for vertices and cell faces on the grid
plane of the interface).
Vertices on the interface may not be physically coincident between the
two zones.
The figure identifies the vertices and face centers of the
left zone that lay on the interface.
Even for structured zones in 3D, the vertices of a zone that constitute
an interface patch may not form a logically rectangular region.
The third type of multizone interface is called overset and occurs when
two zones overlap; in 3D, the overlap is a 3D region.
For overset interfaces, one of the two zones takes precedence over the
other; this establishes which solution in the overlap region to retain
and which to discard.
The region in a given zone where the solution is discarded is called an
overset hole and the grid points outlining the hole are called fringe
points.
The figure depicts an overlap region between two zones.
The right zone takes precedence over the left zone, and the points
identified in the figure are the fringe points and oversethole points
for the left zone.
In addition, for the zone taking precedence, any bounding points (i.e.,
vertices on the bounding faces) of the zone that lay within the overlap
region must also be identified.
Overset interfaces may also include multiple layers of fringe points
outlining holes and at zone boundaries.
For the mismatched abutting and overset interfaces in the above figure,
the left zone plays the role of receiver zone and the right plays the
role of donor zone.