Content

1. Introduction
2. Files provided
3. Running a test example
4. Storing EIRENE triangular grids in IMAS
   
   1. Structure of EIRENE files keeping the grid
   2. Presentation of EIRENE grid in GGD
   3. Module  triangular_grid_modile 
   4. Module  triangular_grid_ids_io 
   5. Template files  save_grid.f90  and  recover_grid.f90
5. Storing the EIRENE input
6. Things to be done

1. Introduction

The Fortran routines described herein are intended to become a part of interface between the code EIRENE and the IMAS data structure. 

2. Files provided

The files listed below can be found in the public directory ~g2yyakov/public/eirene.

!!! To be updated

3. Running a test example

!!! To be updated. !!! You need to have installed GSL (GGD Standard Library).

1. Open the file  gsl_config.sh  and set the value of the variable HOME to the GSL source directory location.
2. Type
   module load imasenv    
3. Create the required IMAS entry:
   imasdb eirene 
4. Type 
   . ./gsl_config.sh 
5. Now you can compile the examples. Type
   make clean 
make save 
   OR type
   ifort triangular_grid_module.f90 trangular_grid_ids_io.f90 save_grid.f90 -o save_grid.exe ${PKG_PART  }
6. Run the program:
   ./save_grid.exe 
   The program puts the grid stored in the files soledge3x.* into the IDS  edge_profiles   of the IMAS database  eirene .
7. Type
   make recover 
   OR type
   ifort triangular_grid_module.f90 trangular_grid_ids_io.f90 recover_grid.f90 -o recover_grid.exe ${PKG_PART  }
8. Run the program:
   ./recover_grid.exe 
   Compare the new files  eirene.*   with the original files  soledge3x.* .

4. Storing EIRENE triangular grids in IMAS

The Fortran routines described herein take files containing the description of a triangular grid in native EIRENE format and store this grid in an IMAS IDS; on the other hand, they extract a stored grid description from IMAS and provide it in EIRENE format. At present, these routines have been tested only with the IDS's  edge_profiles and equilibrium.

The grid is stored in the IMAS subsystem called GGD (General Grid Description). This subsystem consists of two data sub-trees available in most IMAS IDS:  grid_ggd  and  ggd  .  The former contains the description of the grid itself; the latter, all quantities given with reference to this grid (for, value of electron temperature at all grid nodes, values of energy flux at all nodes at the divertor surface etc.). A more detailed description will be given in section 5. 

The files provided are intended to support storing triangular 2D grids in the  grid_ggd  structure. In the future (if required), they can be upgraded to support work with 3D grids consisting of a triangular 2D grid in the poloidal plane and a grid in the toroidal direction.

4.1. Structure of EIRENE files keeping the grid

There are three files describing the triangular grid used in EIRENE.

The file defining the grid nodes and their coordinates (soledge3x.npco_char in the provided example) starts with the number of nodes in the line 1. The rest of lines contain 3 number each: 
node index, R (or X) coordinate (cm), Z (or Y) coordinate (cm). 

The file defining the triangles in terms of its vertices (soledge3x.elemente  in the provided example) has the following structure. The line 1 contains the number of triangles. Each following line contains 4 integers:
triangle index, index of vertex 1 (in the grid node list), index of vertex 2, index of vertex 3.

The file describing the boundaries and neighbours of the triangles in terms of its vertices (soledge3x.neighbor  in the provided example) has the following structure. The line 1 contains the number of triangles. Each following line contains 12 integers:
triangle index, N₁, S₁, M₁, N₂, S₂, M₂, N₃, S₃, M₃,  ixtri  ,  iytri .

Here N_i  is the index of the neighbouring triangle on side i, S_i  is the index of this side in the triangle N_i, M_i  is the ‘material property’ of the side i,   ixtri  and  iytri  are not used now (they are zeros in this example). Note that side 1 connects vertices 1 and 2; side 2, vertices 2 and 3; side 3, vertices 3 and 1. The material property (MP) is an index referring to a surface model defined in the main EIRENE file. In particular, MP is 0 for transparent (i.e., internal) grid edges. The MP of boundary edges can have different positive values. In the provides example, there are boundary edges with MP = 1, 2, 3.

4.2. Presentation of EIRENE grid in GGD

We begin with brief overview of general principles of presentation of grids in the  grid_ggd  structure.

We will follow the terminology of the GGD manual. The IMAS data dictionary is a hierarchical tree-like structure consisting of substructures. The following terms will be used:

• A  node  is any element of the tree.
• A  simple node  is a regular single node.
• An  array of structures node (AOS)  is a 1D array of structures under the same node label.
• A  leaf  is and endpoint of the tree. It holds data in specified format.
• The  parent  of a node is the element one level above this node.
• A  child  of a node is an element one level below this node.
• A  sibling  of a node is a node having the same parent.

First of all,  grid_ggd  is AOS whose elements correspond to different time slices of the IDS. If the grid does not depend on time, this array can contain only one element.

Each element of  grid_ggd  has (inter alia) two children AOS’s: spaces and grid subsets.

The spaces are used to contain the description of geometric objects constituting the grid, including their location in space. Let us consider a rectangular grid in 2D space as an example. To describe it, we can introduce one 2D space, provide the coordinates of all nodes and then describe the other grid elements (edges and cells) in terms of the nodes they consist of. However, it may be easier to choose another way. We can organize two 1D spaces, put the nodes along each coordinate and (if required) describe edges connecting these nodes.

It seems that for EIRENE in 3D geometry, it will be worthwhile to introduce 2 spaces: a 2D space in the poloidal plane and a 1D space in the toroidal direction. At present, only the poloidal 2D space is implemented.

The main child of each element of the  space  AOS is the  objects_per_dimension   AOS, each element of this AOS having only one child – the  object  AOS.

The element  objects_per_dimension(1)  contains information about the 0D objects of the space – the grid nodes. In each element of the  object   AOS, only one child – the  geometry(:)  real array containing the spatial coordinates of the node – is actually filled.

The 2^nd  and 3^rd  elements of  objects_per_dimension   hold information about 1D and 2D objects, respectively. For each 1D object (edge), we store the indices of the 2 nodes that the edge connects. They are stored in the  nodes(:)  child of each object. For a 2D object (triangle), we fill its children nodes(:) (with 3 elements) and boundary.  In the AOS  boundary, we fill the  index   child leaf (the index of the bounding edge) and one element of the  neighbours  child AOS (the index of the neighbouring triangle).

Each grid subset is an arbitrary set of grid elements of the same dimensionality. For examples, all grid nodes, all grid edges, all grid cells, all boundary grid edges, all cells situated in SOL can be examples of subsets. Each subset provided in the  grid_ggd  branch can be used in the  ggd  branch of the IDS in order to save a distribution of some physical quantity on this subset. For example, if we have organized the subset of all boundary edges in 2D, we can save in  ggd  the flux of particles through these edges as a 1D array. By giving a reference to this grid subset, we establish relation between the flux values and the edges.

To describe a subset, we can refer to objects from several spaces. Let us consider again the example of a 2D rectangular grid represented via two 1D grid spaces. The subset of all grid nodes can be organized as follows. The  grid_subset  AOS has a child element, holding information about all subset elements. In our case, the elements are the grid nodes. Each node can be described as a combination of one node of the x-grid and one node of the y-grid. So, each element in the  element  AOS has the only child – the  object  AOS. Each element of the  object  AOS has three leaves:  space   (the index of the space from which it is taken),  dimension   (its dimensionality index), and  index  (its index in the list of objects of this dimensionality). In our case, the elements are grid nodes. Each node (element) can be described as a combination of one node of the x-grid (0-dimensional object of the x-space) and one node of the y-grid (0-dimensional object of the x-space).

The subsets can be distinguished by their identifiers. The  identifier  node has three leaves:

1. name  contains the name given to the subset.
2. index  contains the integer identifier given to the subset (the list of standard integer identifiers can be found in the GGD manual).
3. description  contains a verbose description.

For the triangular EIRENE grid, the following subsets are created (this list can be extended if required or shortened if some subsets are not needed):

1. Subset of all nodes in the poloidal plane (the subset name is  'pol1', the integer identifier is 1).
2. Subset of all edges in the poloidal plane (the subset name is  'pol2', the integer identifier is 2).
3. Subset of all 2D cells (triangles) in the poloidal plane (the subset name is  'pol3').
4. Several subsets of edges with a certain MP in the poloidal plane (the subset names are  'MPnnnn', where nnnn is the material property value).
5. Special subset with no objects for storing averages in  ggd_fast  (the subset name is 'average').
6. Subset of all nodes in 3D space. 
7. Subset of all 3D cells (trigonal prisms).

At present, only items 1-4 of this lists are implemented.

4.3. Module triangular_grid_module

The module contains a data type for storing the information about all elements of a triangular grid and a library of methods (subroutines and functions). The methods solve the following tasks:

1. Reading and writing files in the EIRENE format
2. Checking the grid description for sanity
3. Building the missing parts of the information from available parts

The last item is important because the information set in the EIRENE files and the information set in GGD are different. In particular, the EIRENE files do not contain information about edges.

The module depends on the IMAS module  ids_types   (uses the constant  IDS_real  – the kind of real variables in IMAS).

4.3.1. Data types provided

The following data types are provided:

type triangular_grid
    type(coordinates_2d), allocatable, dimension(:) :: vertex
    type(triangle_structure), allocatable, dimension(:) :: triangle
    type(edge_structure), allocatable, dimension(:) :: edge
end type triangular_grid

The type  triangular_grid  is intended for storing the description of a triangular grid, its components keeping information about the grid vertices, the grid cells (triangles), and the grid edges, respectively.

type coordinates_2d
    real(IDS_real) :: x, y
end type coordinates_2d

The type  coordinates_2d  is intended for storing the grid point coordinates in the poloidal plane.

type triangle_structure
    integer :: vertex(3)
    integer :: neighbor(3) = (/0,0,0/)
    integer :: neighbors_side(3) = (/0,0,0/)
    integer :: side(3)
    integer :: material_property(3)=(/0,0,0/)
    integer :: ixtri=0, iytri=0              
end type triangle_structure

The type  triangle_structure  is intended for storing information about a grid triangle, including the information about neighbouring triangles available in the EIRENE files. The integer child array vertex holds indices of the triangle vertices in  triangular_grid%vertex. The child arrays  side  and  material_property  hold indices of the sides in  triangular_grid%edges   and their MPs, respectively (side 1 connects vertices 1 and 2; side 2, vertices 2 and 3; side 3, vertices 3 and 1). The child arrays  neighbor   and  neighbors_side   hold indices of the corresponding neighbouring triangles N_i  in  triangular_grid%triangle   and the indices of the separating edge in N_i. The child leaves  ixtri   and  iytri  will be used later (maybe).

type edge_structure
    integer :: vertex(2)           
    integer :: material_property=0 
    integer :: adjacent(2)=(/0,0/) 
end type edge_structure

The type  edge_structure  is intended for information about an edge. The integer child array  vertex   holds indices of the edge vertices in  triangular_grid%vertex  . The leaf  material_property   holds the MP of the edge. The child array  adjacent   holds the indices of the neighbouring triangles in  triangular_grid%triangle .

4.3.2. Methods provided

The module member routines are as follows:

• function read_eirene_grid 
  Read information about a triangular grid from EIRENE-format files and generate a list of grid edges;
• subroutine write_eirene_grid 
  Write information about a triangular grid into EIRENE-format files;
• subroutine provide_grid_object_lists 
  Provide lists of objects (nodes, edges and cells); nodes are characterized by their coordinates; edges and cells, by indices of nodes they consist of;
• subroutine arrange_neighbors 
  Build information about neighboring cells necessary the EIRENE file format; 
• integer, allocatable, dimension(:) function give_edges_with_mat_property 
  Provide list of all MP values available in the grid;
• subroutine deallocate_grid 
  Deallocate the structure child arrays.

Service routines:

• subroutine read_vertices 
• subroutine read_triangles 
• subroutine read_neighbors 
• subroutine write_vertices 
• subroutine write_triangles 
• subroutine write_neighbors 
• subroutine find_neighboring_triangles 
• integer function find_side 
• subroutine write_edges 
• subroutine check_edges 
• subroutine check_vertices 
• subroutine grid_statistics 
• integer function neighboring_triangle_index 
• integer function edge_index 

Detailed description of the methods:

function read_eirene_grid (coord_file, triangles_file, neighbors_file, do_tests, io_unit) result (grid)

Read information about a triangular grid from EIRENE-format files and generate a list of grid edges (using the method  build_edges).

subroutine write_eirene_grid (grid, coord_file, triangles_file, neighbors_file, do_tests, io_unit)

Write information about a triangular grid into EIRENE-format files;

subroutine provide_grid_object_lists (grid, coordinates, edge_connect, cell_connect)

Given a grid stucture, the subroutine provides three arrays:

• coordinates  , real 2D array containing  the coordinates for all grid nodes;
• edge_connect  , integer 2D array containing indices of vertices for all edges;
• cell_connect  , integer 2D array containing indices of vertices for all cells (triangles).

This subroutine is no longer used in the module  triangular_grid_ids_io.f90 .

subroutine arrange_neighbors (grid)

Process a grid structure taken from IMAS, filling up the missing components of  grid%triangle  (information about neighbouring edges and triangles).

subroutine build_edges (grid)

Process a grid structure, building the missing substructure  grid % edge . The order of the edges in the substructure is as follows: side 1 of triange 1, side 2 of triange 1, side 3 of triange 1, side 1 of triangle 2 (if not accounted for earlier), side 2 of triangle 2 (if not accounted for earlier), and so on.

function give_edges_with_mat_property (grid, mat_property)

Return a list of edges with a given value of MP.

subroutine deallocate_grid (grid)

Deallocate all grid components.

For description of service routines (some of them are no longer used), see comments in the module file.

4.4. Module  triangular_grid_ids_io

The module contains routines that support writing a grid having the  type(triangular_grid)  form to IMAS IDS and, vice versa, reading a grid from IMAS and putting it into the  type(triangular_grid)  form. It depends on the module  triangular_grid_module   and the IMAS modules  ids_schemas   and  ids_routines .

The module contains the following routines:

• get_triangular_grid_from_ids 
  Read a triangular grid contained in a given space of a GGD grid and transform it into a  type(triangular_grid)-structure.
• put_eirene_grids_to_ids 
  Save a triangular grid given as a  type(triangular_grid)-structure in  grid_ggd, invoking other routines of this module (arrange_triangular_grid_space,  arrange_standard_2d_subset, and  arrange_mat_property_subset).
• arrange_triangular_grid_space 
  Put a triangular grid given as a  type(triangular_grid)-structure to a desired  grid_ggd  space.
• arrange_standard_2d_subset 
  Arrange a "standard" subset in the poloidal space (subset of all nodes, all edges, or all triangular cells).
• arrange_mat_property_subset 
  Arrange a subset of edges with a certain value of MP.

Detailed description of the methods:

function get_triangular_grid_from_ids (grid_ggd, space_index) result (eirene_grid)

Read data about a triangular grid from a given space of GGD grid, put it into a  type(triangular_grid)-structure and call the function  arrange_neighbors   (from  triangular_grid_module) to build the missing parts of the structure.

subroutine put_eirene_grids_to_ids (eirene_grid, coord_type, grid_ggd, nSpaces, eirene_space_index, grid_name, grid_description, eirene_space_name, eirene_space_description)

Allocate the space AOS in a given  grid_ggd   element with a given number of grid spaces, put a triangular grid given as a  type(triangular_grid)-structure into a desired element of the  space  AOS, and organize necessary grid subsets.

subroutine arrange_triangular_grid_space (space, grid, space_name, space_description)

Put a triangular grid into a given element of the  space  AOS. The grid information is taken from a  type(triangular_grid)-structure.

subroutine  arrange_standard_2d_subset(subset, space, space_index, dimensionality, subset_id)

Arrange a "standard" subset in the poloidal space – a subset of all nodes, edges, or triangular cells (depending on the dimensionality, 1, 2, or 3, respectively). The subset gets the name 'poln', where n is the dimensionality.

subroutine  arrange_mat_property_subset (subset, space, space_index, grid, mat_property, subset_id)

Arrange a subset for edges with a certain value of MP. The subset gets the name 'MPnnnn', where nnnn is the MP value.

4.5. Template files  save_grid.f90   and  recover_grid.f90 

The program contained in the file  save_grid.f90  performs the following actions:

• Initializes an instance of the  edge_profiles   IDS in the code memory (with writing some mandatory fields), using the subroutine  setIDSFundamentals  (module ids_utility).
• Writes some labels to the IDS.
• Allocates the  grid_ggd  AOS with only one element.
• Reads information about the grid from files and establishes grid edges, using the  read_eirene_grid  function (module  triangular_grid_module).
• Puts the grid information into the IDS, using the  put_triangular_grid_to_ids  subroutine (module  triangular_grid_ids_io).
• Creates the corresponding IDS in an IMAS database, using the  createIDS  subroutine (module  ids_utility).
• Writes the IDS prepared in the code memory to the IMAS database and closes the database, using the subroutine  putIDS  (module  ids_utility).

The program contained in the file  recover_grid.f90  performs the following actions:

• Opens the IMAS database by calling the subroutine  imas_open_env  .
• Reads the IMAS IDS  edge_profiles, using the subroutine  ids_get .
• Extracts the information about the grid from the IDS and puts it into a  type(triangular_grid)-structure, using the subroutine  get_triangular_grid_from_ids  (module  triangular_grid_ids_io).
• Writes the grid to EIRENE-format files (subroutine  write_eirene_grid, module  triangular_grid_module).
• Closes the IMAS database.

5. Storing EIRENE input

6. Things to be done

• Add some simple methods for reading and writing physical data.
• Organize a 1D toroidal space and a couple of subsets in the 3D space.
• Add standard integer identifiers where appropriate.
• Try to adjust the processing of exceptions to GSL practices.
• Understand how the triangular grid can be united with the rectangular grid.