itopol

The itopol array stores the connections between the blocks. The basic idea behind the itopol data-structure is that the blocks communicate through common sub-faces. For instance in 2-D, each block consists of four faces numbered 1--4. The faces are divided into sub faces that are numbered from west to east and from south to north, see Fig. 10. The itopol array stores for each sub face the neighbouring block (0 if the sub face is external) and the corresponding neighbouring face and subface numbers. This means that:

• a sub face of a block is either fully external or fully internal
• an internal sub face of a block is also a sub face of another block (it may also be the sub face of another face of the same block in some special cases with periodic boundary conditions)

  
Figure 10: Directions and numbering of faces and sub faces

A sub face in 2-D is described by the index range where i denotes the number of a grid cell not the number of grid points. Because in a general 3-D case the sub faces may have complex shapes which are hard to represent, we restrict the shape of the sub faces:

In 3-D sub faces consist of grid cells in a rectangular index range

The itopol array consists of three parts:

Part I

contains information about parts II and III

Part II

contains the NSUBFACES array.

Part III

contains the SUBFACES array.

Part I:  

Pos. 1

nblocks

Pos. 2

nfaces (= 2*ndim)

Pos. 3

maxnsubfaces (maximum number of subfaces encountered on all faces)

Pos. 4

lensubface (current number of integers stored for each subface in the subfaces array)

Pos. 5

Start address of Part II

of this array

Pos. 6

Start address of Part III

of this array

Part II:    

Part II is of length nblocks*nfaces and stores the nsubfaces array:

integer nsubfaces(1:nblocks, 1:nfaces)

The value nsubfaces(i,j) is the number of subfaces at face j of block i.

Part III:    

Part III stores the actual multi-block topology in the subfaces array:

integer subfaces(1:nblocks, 1:nfaces, 1:maxnsubfaces, 1:lensubface)

The value subfaces(i,j,k,m) is the value of position m of the subface record for sub face k of face j of block i. The subface record is organized as follows:

Pos. 1

i1 (lower i index of sub face)

Pos. 2

i2 (upper i index of sub face)

Pos. 3

j1 (lower j index of sub face)

Pos. 4

j2 (upper j index of sub face)

Pos. 5

blockno (number of neighbouring block)

Pos. 6

faceno (number of neighbouring face number)

Pos. 7

subfaceno (number of neighbouring sub face number)

Pos. 8

iorient (relative orientation of the blocks)

tsign

Indicates wether or not the subface has opposite direction when seen from the neighbour. tsign=0 if these directions are the same and tsign = 1 if these directions are opposite.

nsign

indicates wether or not the sign must be changed when copying normal velocities (not fluxes) The normal velocity is the contravariant velocity component corresponding to normal component. It may therefore point both inward and outward.

relblockor

indicates the sign change in between this block and its neighbour. This quantity is used in combination with nsign to determine the sign change when copying normal fluxes: . relblockor=0 means no sign change, 1 means a sign change.