Standard Geometry Configurations
Automatic scaling systems are available in COMSOL Multiphysics for three distinct geometrical configurations: Cartesian, Cylindrical, and Spherical. Which ones you can use depends on the space dimension of the Component. For these configurations, COMSOL Multiphysics can analyze the geometry to automatically find the right stretching directions and layer thicknesses.
The choice of a Cartesian, cylindrical, or spherical configuration depends on the shape of your corresponding 3D geometry outline (box, cylinder, or sphere). It has no formal connection to what base coordinate system your geometry is using (but Cartesian configurations will never apply in 2D axisymmetry, and spherical configurations will never apply in planar 2D for obvious reasons).
The geometry analysis tries to match the topology of the geometry and the selected domains to the selected geometry type under the assumption that the scaling system is applied as a layer on the outside of the physical geometry. If the geometry analysis fails, for example because there are geometric objects on both sides of the scaling system domain, an error message will be displayed when solving. In this case it is possible to manually define distance functions and layer thicknesses.
If Equation View nodes have been enabled in the Show More Options dialog, the result of the geometry analysis can be inspected. If the analysis is successful, variables such as the layer thickness, inner boundary position, and center points and axes for curved domains will be available in the Equation View. If the analysis fails, only a few basic input variables will be present.
Plane 2D Models
The available scaling types in plane 2D models are Cartesian and Cylindrical. Cartesian domains are stretched in one or two directions depending on whether they are attached to an edge or to a corner of the physical region of interest.
It is important that separate, normally quadratic, domains are drawn at the corners.
Figure 5-8: Typical Cartesian scaling configuration. Note the distinction between edge and corner domains.
Figure 5-9: Example of cylindrical scaling configuration in plane 2D.
Axisymmetric 2D Models
The available scaling types in 2D axisymmetric models are Cylindrical and Spherical. The axisymmetric cylindrical configuration, from the practical point of view, behaves identically to the plane 2D Cartesian option. Similarly, the axisymmetric spherical scaling is similar to plane 2D cylindrical scaling, except that it is always centered at a point on the axis.
Figure 5-10: Axisymmetric cylindrical scaling uses domains of three distinct types: with radial stretching, with axial stretching, and with both radial and axial stretching. The latter are the corner zones, which must be drawn as distinct domains.
Figure 5-11: Axisymmetric spherical scaling assumes radial stretching in an annulus centered at a point on the axis.
3D Models
The available scaling types in 3D are Cartesian, Cylindrical, and Spherical. The Cartesian scaling domains are of three different types. Depending on whether they are attached to a surface, an edge, or a point in the physical domain, they are stretched in one, two, or three directions, respectively. Cylindrical scaling domains are also of three different types: radially stretched, axially stretched, and stretched both radially and axially. Spherically scaled domains are always stretched only in the spherical domain’s radial direction.
Figure 5-12: There are three different types of Cartesian scaling domain, attached to faces, edges, and corners, respectively. They differ in the number of scaled directions. Note that the edge and corner zones must be drawn as distinct domains in the geometry.
Figure 5-13: The three different types of cylindrical scaling domain are attached to the sides, top and bottom, and edges of the cylindrical physical domain. The scaling system domains are stretched in the radial direction, away from the axis, in the axial direction, and in both radial and axial direction, respectively.
Figure 5-14: A spherical scaling domain stretches the coordinate system only in the radial direction.