9. Nonorthogonal tips

This page is intended to collect the material for a page in the docs with advice on how to generate a non-orthogonal grid, since there are a lot of options to tweak. Anyone who manages to generate a good grid, please add advice here!

9.1. The settings

These settings are part of the general user-options, and can only be set when the Equilibrium and Mesh are first recreated. If they need to be changed, you need to re-create Equilibrium and Mesh. However, they have slightly different meanings and default values when creating nonorthogonal grids than when creating orthogonal ones

Set, in arbitrary normalised units, the grid spacing at the end of a region, used to create an orthogonal grid of points when the contours are first created, from which a spacing function (sfunc_orthogonal) is defined by interpolation
xpoint_poloidal_spacing_length	X-point end
target_poloidal_spacing_length	target end

The following settings can be changed, and the grid reconfigured by calling redistributePoints() (or using the ‘Regrid’ button in the GUI), rather than creating a new Mesh object (which is expensive). Note to be doubly sure of the reproducibility of the final grid, it is recommended to use redistributePoints() or the ‘Regrid’ button only for prototyping: once you have finished prototyping, save the final settings to a file and generate the production grid directly from that file.

grid spacing for perpendicular or poloidal spacing function at the ends of a region
nonorthogonal_xpoint_poloidal_spacing_length	X-point end
nonorthogonal_target_poloidal_spacing_length	wall end
ranges near the X-point over which fixed perpendicular position changes to orthogonal position
nonorthogonal_xpoint_poloidal_spacing_range	range at the separatrix side of a region, also used as the default for inner and outer sides
nonorthogonal_xpoint_poloidal_spacing_range_inner	range at an inner side
nonorthogonal_xpoint_poloidal_spacing_range_outer	range at an outer side
ranges near the wall over which fixed poloidal position changes to orthogonal position
nonorthogonal_target_poloidal_spacing_range	range at the separatrix side of a region, also used as the default for inner and outer sides
nonorthogonal_target_poloidal_spacing_range_inner	range at an inner side
nonorthogonal_target_poloidal_spacing_range_outer	range at an outer side
nonorthogonal_radial_range_power	gives p in (1-x**p)*range_sep + x**p*range_edge which is the actual poloidal range used on a contour where range_sep is the range on the separatrix, range_edge is the range on an inner or outer edge and x is proportional to the radial index of the contour, 0 on the separatrix and 1 on the edge
nonorthogonal_spacing_method	switches between different spacing methods. The default "combined" is described here, the others are mainly useful for debugging as they give access to the methods that are combined in the default one

9.2. Explanation

This sketch attempts to indicate what the ‘range’ parameters do

9.3. Comments

• To make a smooth grid line across the separatrix, make nonorthogonal_range_* for the separatrix sides of regions small so that points on contours near the separatrix are very close to the positions they would have with orthogonal spacing

• Orthogonal spacing would make the points at the inner or outer edges very close together (near X-points) or displaced from the wall (near targets), so the nonorthogonal_*_poloidal_spacing_range_* for the inner or outer edges probably needs to be larger.

• nonorthogonal_range_radial_power gives some control over the radial position of the transition in the (poloidal) ranges, use values in the range [0, 1) to make more contours close to inner or outer side spacing, or values >1 to make more contours close to the separatrix spacing

• Grid generation is more robust when nonothogonal_target_poloidal_spacing_range_* is fairly large, as this prevents the grid from being affected by regions where the orthogonal spacing function would put the grid points behind the target. The default values for these parameters have therefore been made fairly large, to ensure an initial grid can be generated most of the time. You probably want to reduce these parameters, at least nonorthogonal_target_poloidal_spacing_range which is used for the range near the separatrix; the separatrix ends on the target in the initial grid from which the orthogonal spacing function is created, so it is fine to push the final spacing close to orthogonal near the separatrix - at the outer edges you may need to keep the range larger.

• Grid generation can also be more robust when nonorthogonal_xpoint_poloidal_spacing_range_* is fairly large. It may be useful to set these parameters to fairly large (~1) values initially, especially if grid generation fails with the defaults, before refining.

• The parameters xpoint_poloidal_spacing_length and target_poloidal_spacing_length are used for nonorthogonal grid generation - they control the grid spacing in the initial orthogonal grid which is used to create sfunc_orthogonal spacing functions. They have different defaults than when an orthogonal grid is generated, but are not part of the nonorthogonal_* family of options because they cannot be changed after the Equilibrium and Mesh are first created.

• The default of setting nonorthogonal_target_poloidal_spacing_length = target_poloidal_spacing_length is probably a reasonable choice - it means that the spacing of the orthogonal-spacing and poloidal-spacing grids is the same on the targets at the separatrix, which is probably the best choice to combine them consistently.

• It is probably good to have nonorthogonal_xpoint_poloidal_spacing_length somewhat smaller than xpoint_poloidal_spacing_length (by default it is a factor 4 smaller). This is because the perpendicular-spaced grid lines have a sharp corner at the separatrix, whereas the orthogonal-spaced contours are smooth, but get much closer to the normal from the X-point as you go radially away from the separatrix. That means if the spacing on the separatrix was the same for the orthogonal and perpendicular grid lines, weighting towards the orthogonal positions would make the curve ‘overshoot’ the perpendicular-spacing grid line, resulting in a grid line which changes the sign of its curvature several times. Making the xpoint_poloidal_spacing_length larger than nonorthogonal_xpoint_poloidal_spacing_length allows for less-curved grid lines (if the range parameters are adjusted appropriately).

• The default combined spacing method uses uniform poloidal spacing near walls, and uniform perpendicular spacing (perpendicular to a line along the Grad(psi) direction through the X-point) near the X-point.