1. Separate 2D and 3D modes are supported.
2. ACRi solvers place the unknown variables at the element centers (cell centered formulation).
3. There are 3 basic types of unstructured grids:
   • Regular Unstructured: (See Mode 1 below) This supports only Hexagonal (3D) and Quad (2D) elements.
   • Hybrid Unstructured: (See Mode 2 below) Supported modes are: Triangles and Quads in 2D; Tetrahedrals, quad-based pyramids, triangle-based prisms and hex's in 3D.
   • Split Unstructured: (See Mode 3 below) This also supports only Hexagonal (3D) and Quad (2D) elements. However, one element may be connected to multiple elements on any given side.
4. Elements are numbered sequentially starting at 1. No other assumptions are made regarding element orientations or spatial location.
5. Local refinement (or split faces or hanging nodes) in the form of one to many connections is supported.
6. ACRi solvers do their own numbering of boundary elements. Hence, only "volume" elements should be specified in the connectivity data (quadrilaterals or triangles in 2D and tets, pyramids, prisms or hexahedra in 3D).
7. Internal regions and sub-domains are specified by lists of elements and referred to by name.
8. Boundaries are specified by lists of ordered pairs of element number, face number and referred to by name.
9. Periodic boundaries are specified by list of ordered pairs of matching boundary elements, (element#, face# , element#, face#) and are read in from files.
10. ACRi solvers also support cylindrical coordinate systems. In this mode element orientations are constrained as will be detailed later.

Figure 3: Relation between Vertex Numbers and Side Numbers for a Triangle illustrating the application of the right hand rule. (2D only).

Figure 4: Relation between Vertex Numbers and Side Numbers for a Tetrahedron illustrating the application of the right hand rule. (3D only).

Figure 5: Relation between Vertex Numbers and Side Numbers for a Pyramid illustrating the application of the right hand rule. (3D only).

Figure 6: Relation between Vertex Numbers and Side Numbers for a Triangular Prism illustrating the application of the right hand rule. (3D only).

MODE 3: Connectivity for Quad or Hex Elements with Split Sides

The vertex and element connectivity for the split elements is specified. This is a supplementary mode of the command to enable local grid refinement or adaptation of the mesh in selected parts of the domain, based on solution features. (Split sides are element sides with more than one attached neighboring element). It can be used in conjunction with Mode 1 but is not available with Mode 2 of the command.

By default all ACRi Software Tools assume that each element is connected to 4 other elements in 2D and 6 other element in 3D geometry. However if the grid is locally refined then a element may be split into multiple "child" elements and some of the elements may be connected to more than the default number of neighboring elements. This supplementary connectivity is specified in the following manner.

The 1st record in the file consists of a header with two numbers: the number of split elements and the total number of data items in the rest of the file. The header is followed by a number of sets of data equal to the number of split elements. The 1st record of each set consists of the element number that is split followed by a side index for each side (4 for 2D and 6 for 3D) of the element which denotes the number of neighboring elements (if > 1) connected to that face. The index is zero if there is only one element connected to the side (no split). This record is followed by a list of element numbers that adjoin the split side in the order of the side index. The final record of the set consists of the local side number (from 1 to 6) for the adjoining elements that are attached to the split side.

The entire file is read in using the following two FORTRAN statements:

READ(IFILE,*) N_SPLIT_M, N_ITEMS
READ(IFILE,*) ( N_SPL(K), K = 1, N_ITEMS )

EXAMPLE:

If the ( Mode 1 ) vertex connectivity for the above mesh is as follows:

Element #	Vertex Connectivity
1	1	2	6	5
2	2	3	7	6
3	3	4	8	7
4	5	6	10	9
5	6	20	17	18
6	7	8	12	11
7	9	10	14	13
8	10	11	15	14
9	11	12	16	15
10	20	7	19	17
11	17	19	11	21
12	18	17	21	10

Then the SPLIt connectivity command is:

CONNectivity SPLIT on file "SPLIT.CON."

Contents of the file SPLIT. CON are:

(the text on the right is for clarity and must NOT be present in the file)

4	36				! 4 Split elements; 36 numeric items follow
2					! Split Element Number
0	0	0	2		! Face # 4 is split in to 2 segments
5	10				! Element numbers that split face connects to
3	3				! Face #3 (of Element 5) and Face #3 (of Element 10)
4					! Split Element Number
0	2	0	0		! Face # 2 is split in to 2 segments
5	12				! Element numbers that split face connects to
1	1				! Face #1 (of Element 5) and Face #1 (of Element 12)
6					! Split Element Number
2	0	0	0		! Face #1 is split in to 2 segments
10	11				! Element numbers that split face connects to
2	2				! Face #2 (of Element 10) and Face #2 (of Element 11)
8					! Split Element Number
0	0	2	0		! Face #3 is split in to 2 segments
12	11				! Element numbers that split face connects to
4	4				! Face #4 (of Element 12) and Face #4 (of Element 12)

Region Selection (Version 4.00 and above)

A region can be selected by grouping a LIST of elements and giving them a unique name. In example 2, the elements 14, 18, 20, 22, 24 have been grouped into a list and given a name SAMPLE1 as follows:

LOCAte LIST ID=SAMPLE1 14, 18, 20, 22, 24

Subsequent operations can then select this region by name various purposes such as initialization, applying sources, etc. The name can be up to 8 characters long.

Boundary Selection (Version 4.00 and above)

Boundary surfaces can be selected by grouping them into a PAIRed list and giving them a unique name. In example 2, the right boundary is defined by:

LOCAte PAIR ID=RIGHTBC 5 , 2 ; 6 , 3 ; 7 , 3 ; 8 , 3 ; 9 , 3 ;

which consists of ordered pairs of element number, local face number. Recall that local face numbers are assigned based on the order of the vertices in the connectivity file. Boundary conditions can now be set based by referring to the name set on the LOCAte command. The name can be up to 8 characters long.

Periodic Pairs (Version 4.00 and above)

Periodic boundaries are defined by providing pairs of matching boundary faces in a file (typical extension .per).

Each line of the file contains four integers

Element No. Face No. Matching Element No. Matching Face No.

See Example 2.

Radial Coordinate System

In a cylindrical system, some restrictions on the element orientations apply such that faces 3 and 4 are perpendicular to the global R direction and, in 3D, faces 5 and 6 are perpendicular to the global THETA direction. A vector from the centroid of face 3 to the centroid of face 4 should be approximately aligned with the unit vector in the R direction at the element centroid.

Command Input

Command input is accomplished via the FREEFORM™ language. For CFDStudio™ users, these commands are generated automatically.

Commands start on column 1 of a line and consist of a keyword, modifiers, numeric, separator, terminator, and comment fields. The typical file extensions for the commands file are ".inp", or ".q1" (all lower case).

An unstructured mesh is processed using the GRID, CONNectivity, and COORdinate commands.

The syntax for the GRID command consists of the keyword GRID with modifiers UNST, THRE (for 3D only), and a numeric field denoting the number of elements.

Thus for a 2D problem with 30,000 elements, the command is:

GRID UNSTructured 30000 elements

and for a 3D problem with 300,000 elements,

GRID UNSTructured THREe-d 300000 elements

Note that only the first four characters in a keyword or modifier are significant. The rest of the input is usually retained to make use of the self documenting feature of the FREEFORM™ language.

The syntax for the CONNectivity command is:

CONNectivity 'case_name.cnc'

where the file name containing the connectivity data is enclosed in single quotes. The CONNectivity command accepts an optional modifier SPLIt to indicate that the specified file contains auxiliary connectivity data for local refinement, i.e.,

CONNectivity SPLIt 'case_name.blk'

The typical file extension for auxiliary connectivity is '.blk'. If the CONNectivity SPLIt command is present then the CONNectivity command should precede it and the CONNectivity command should occur after the GRID command as shown in Example 1.

The syntax for the COORdinate command is:

COORdinate VERTices X Y 'case_name.xyz'

for 2D (see Example 1 and Example 2) and

COORdinate VERTices X Y Z 'case_name.xyz'

for 3D. The COORdinate command also accepts an optional modifier CYLIndrical which forces the vertex coordinates to be interpreted as X , R in 2D and X, R, and THETA in 3D. The CYLIindrical modifier can be placed anywhere on the line containing the COORdinate keyword.

Regions are defined by grouping elements with the LOCAte LIST command as follows,

LOCAte LIST ID=NAME0001

followed by a list of integers denoting the desired elements. See Example 2.

Boundaries are defined by grouping boundary faces with the LOCAte PAIR command as follows,

LOCAte PAIR ID=NAME0002

followed by a list of ordered pairs of integers element#1, face#1, element#2, face#2, …. See Example 2.

The appropriate face numbers are listed in Table 1(a) for 2D and Table 1(b) for 3D.

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Example 1

Figure 2 below shows a typical unstructured mesh to be used for this example.

Figure 8: Ordering of the unknowns (element numbers in boxes), vertex numbers and face numbers. The arrangement of the elements forms an 'O' grid. Elements 1,3,5 and 9 have split faces formed due to local refinement. The arrows indicate the local '4' orientation of each element.

Vertex File, Example-1.xyz:

Vertex No.	X coordinate	Y coordinate for 2D
1	0.	0.
2	3.	0.
3	1.	1.
4	2.	1.
5	1.	2.
6	2.	2.
7	0.	3.
8	3.	3.
9	1.	0.
10	1.25	1.
11	2.0	0.
12	1.75	1.
13	1.5	3.
14	1.5	2.
15	1.0	1.5
16	2.0	1.5

 

Connectivity File, Example-1.cnc:

Element No.	vertex 1	vertex 2	vertex 3	vertex 4
1	3	4	16	15
2	1	9	10	3
3	2	8	6	4
4	8	13	14	6
5	7	1	3	5
6	9	11	12	10
7	11	2	4	12
8	13	7	5	14
9	5	15	16	6

 

Auxiliary Connectivity File, Example-1.blk: (Elements 1, 3, 5, and 9 have split faces or hanging nodes)
4	38
1
0	0	3	0
2	6	7
4	4	4
3
0	0	0	2
1	9
2	4
5
0	0	0	2
1	9
1	3
9
2	0	0	0
4	8
4	4

Commands in File "Example-1.inp":

GRID UNSTructured 9 elements

CONNectivity 'Example-1.cnc'

CONNectivity SPLIt 'Example-1.blk'

COORdinate X Y VERTices 'Example-1.xyz'

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Example 2

Figure. 9 below shows another unstructured mesh to be used for Example 2.

Figure 9. An example mesh to illustrate setting up boundary definitions. The faces labeled p1 .. p4 form periodic pairs. The circled elements are gathered into a sub-region using the "LOCAte LIST" command. The right boundary, composed of the elements with the arrow heads pointing to the boundary, is defined using a "LOCAte PAIR" command.

Coordinates File, Example-2.xyz:
1	0.0	0.0
2	0.2	0.0
3	0.4	0.0
4	0.6	0.0
5	0.8	0.0
6	1.0	0.0
7	0.0	0.1
8	0.2	0.1
9	0.4	0.1
10	0.6	0.1
11	0.8	0.1
12	1.0	0.1
13	0.0	0.2
14	0.2	0.2
15	0.4	0.2
16	0.6	0.2
17	0.8	0.2
18	1.0	0.2
19	0.0	0.3
20	0.2	0.3
21	0.4	0.3
22	0.6	0.3
23	0.8	0.3
24	1.0	0.3
25	0.0	0.4
26	0.2	0.4
27	0.4	0.4
28	0.6	0.4
29	0.8	0.4
30	1.0	0.4
31	0.0	0.5
32	0.2	0.5
33	0.4	0.5
34	0.6	0.5
35	0.8	0.5
36	1.0	0.5

 

Connectivity File, Example-2.cnc:
1	1	2	8	7
2	2	3	9	8
3	3	4	10	9
4	4	5	11	10
5	5	6	12	11
6	12	18	17	11
7	18	24	23	17
8	24	30	29	23
9	30	36	35	29
10	35	34	28	29
11	34	33	27	28
12	33	32	26	27
13	32	31	25	26
14	25	19	20	26
15	19	13	14	20
16	13	7	8	14
17	8	9	15	14
18	9	10	16	15
19	10	11	17	16
20	17	23	22	16
21	23	29	28	22
22	28	27	21	22
23	27	26	20	21
24	20	14	15	21
25	15	16	22	21

 

Periodic Pairs File, Example-2.per:
1	3	10	3
2	3	11	3
3	3	12	3
4	3	13	3

 

Commands in File "Example-2.inp":

GRID UNSTructured 25 elements CONNectivity 'Example-2.cnc' COORdinate VERTices X Y 'Example-2.xyz' PERIodic 'Example-2.per' LOCAte LIST ID=SAMPLE1

14, 18, 20, 22, 24

LOCAte PAIR ID=RIGHTBC

5, 2 ; 6, 3 ; 7, 3 ; 8, 3 ; 9, 3 ;