The variables that characterize geometric properties and the mesh are listed in Table 5-10, with detailed descriptions for some of the variables following the table.

For example, replace u with the names of the dependent variables in the model, and replace x, y, and z with the first, second, and third spatial coordinate variable, respectively. xi represents the ith spatial coordinate variable. If the model contains a deformed mesh or the displacements control the spatial frame (in solid mechanics, for example), you can replace the symbols x, y, and z with either the spatial coordinates (x, y, and z by default) or the material (reference) coordinates (X, Y, and Z by default).

The variables curv, dvol, h, qual, reldetjac, and reldetjacmin are based on the mesh viewed in the material (reference) frame. If you have a moving mesh, the corresponding variables for the mesh viewed in the spatial frame have a suffix _spatial (that is, curv_spatial, dvol_spatial, and so on). If you use a deformed geometry, the corresponding variables for the original, undeformed geometry have a suffix _geometry (for example dvol_geometry). After automatic remeshing, variables referring to the current mesh have a suffix _mesh (for example, h_mesh).

The arc length parameters edgparal and edgparnal are available on edges in 2D and 3D. The parameter edgparnal is the normalized arc length, that is edgparal divided by the edge length, and goes from 0 to 1.

Use a line plot to visualize the range of the parameter. The direction is the same as the edge direction, indicated by the arrows shown on the edges when in the boundary or edge selection mode and if you have selected the Show edge direction arrows checkbox in the Settings window for View ().

The curve parameter s (or s1) is available in 2D. Use a line plot to see if the relationship between x and y (the spatial coordinates) and s is nonlinear, and to see if the curve parameterization is aligned with the direction of the corresponding boundary. In most cases it runs from 0 to 1 in the edge’s direction.

The surface parameters s1 and s2 in 3D are available on boundaries (faces). They can be difficult to use because the relationship between x, y, and z (the spatial coordinates) and s1 and s2 is nonlinear. Often it is more convenient to use expressions with x, y, and z for specifying distributed boundary conditions. To see the values of s1 and s2, plot them using a surface plot.

If a deformed mesh is used, the tangent variables are available both for the deformed configuration and for the undeformed configuration. In the first case, replace x, y, and z with the spatial coordinate names (x, y, and z by default). In the second case, replace x, y, and z with the material/reference coordinate names (X, Y, and Z by default).

The variables components nx, ny, and nz make up a vector that normally points from the downside toward the upside of a boundary. Boundaries between meshed and unmeshed domains constitute an exception where the normal vector instead points from the meshed domain toward the unmeshed domain. On interior boundaries, which side is up and which side is down is arbitrary, but the void surrounding a geometry is always on the upside, so on boundaries exterior to the geometry, the normal points away from the geometry.

For frame coordinates x, y, and z which are identical to the mesh frame coordinates, the normal is evaluated based on the geometry (if a geometry is available). Otherwise, the components are evaluated based on the mesh element shapes, and are identical to the corresponding nxmesh, nymesh, and nzmesh variables. See Normal Vector Variables Representing Element Surface Normals. This, for example, happens for the spatial frame normal vector when there are Moving Mesh features or a Solid Mechanics interface in the model

If a deformed mesh is used, the normal variables are available both for the deformed configuration and for the undeformed configuration. In the first case, replace x, y, and z with the spatial coordinate names (x, y, and z by default). In the second case, replace x, y, and z with the material/reference coordinate names (X, Y, and Z by default).

A similar set of variables — nxmesh, unxmesh, and dnxmesh, where x is the name of a spatial coordinate — use the element shape function and are normal to the actual element surfaces rather than to the geometry surfaces. These normal vectors always have unit length, but they are typically not continuous at interelement boundaries.

In some situations, it can be necessary to use a normal vector that is based on the mesh element shape functions but is still continuous. Such normal vector components are defined with names similar to those for the standard normal vector variables, except that they have a c appended at the end: For example, nxc, nyc, and nzc in a 3D model or nrc and nzc in a 2D axisymmetric model. If you have a material frame and a spatial frame in a 3D model, the normal vector continuous variables are nxc, nyc, and nzc for the spatial frame and nXc, nYc, and nZc for the material frame.

These variables are continuous within each boundary (but typically discontinuous where boundaries meet), but they do not necessarily have unit length. It is possible to compute their tangential derivatives with the dtang operator as, for example, dtang(nxc,x). Computing tangential derivatives in this way works only when the normal variable and the coordinate in the second argument of dtang belong to the same frame; dtang(nxc,x) and dtang(nXc,X) both work, but dtang(nXc,x) and dtang(nxc,X) are both 0.

In 2D, the curvature is denoted curv. Positive curvature is toward the normal (nx,  ny).

In 2D axisymmetry, the curvature variables refer to the curvature of the 2D geometry and use the same naming as in 2D. The second curvature, which is induced by the axisymmetry, is -nr/r (using the default radial space variable name r) and has no predefined variable.

In 3D, there are two principal curvatures named curv1 and curv2, where curv1 is less than curv2 and seen as real numbers. These correspond to the minimal and maximal values for the curvature of a curve you get by intersecting the boundary with a plane in which the normal lies. Positive curvature is toward the normal (nx, ny, nz).

The components of the normalized tangential directions for the corresponding curvatures are called tcurvx, tcurvy in 2D and tcurv1x, tcurv1y, tcurv1z, tcurv2x, tcurv2y, and tcurv2z in 3D. The tangents (tcurv1x,tcurv1y,tcurv1z) and (tcurv2x,tcurv2y,tcurv2z) are orthogonal.

Curvature variables are defined for all separate frames in a model. The names of the curvature variables in the spatial, mesh, and geometry frame are formed by appending the suffix _spatial, _mesh, and _geometry, respectively, to the name curv (in 2D and 2D axisymmetry) or curv1 and curv2 (in 3D). The variables without suffix always refer to the curvature in the material frame. Note that the variables with suffix are defined only if the spatial, mesh, or geometry frame actually is different from the material frame. For more information about frames and deformed mesh configurations, see Deformed Mesh Fundamentals.

In the normalized tangent variable names, replace x, y, and z with the coordinate names in another frame to get the tangents in that frame.

The following predefined variables are created by the spatial frame and can be of interest, for example, to monitor the quality of the mesh and define a stop criterion for remeshing (see Adding a Stop Condition):