Coordinate Systems

COMSOL Multiphysics uses a global Cartesian coordinate system by default to specify material properties, loads, and constraints in all physics interfaces and on all geometric entity levels (points, edges, boundaries, and domains). In boundary conditions and fluid domains, the global system is generally interpreted as having fixed axis directions in space; that is, it is a spatial frame system. When specifying properties of solid materials, the global system axes are instead fixed in the material. In other words, it is a material frame system in that context.

Not only the global coordinate system, but also coordinate systems defined as a rotation relative to the global system, are context dependent in this way. Such systems are collectively referred to as relative coordinate systems, to distinguish them from absolute coordinate systems.

The spatial Cartesian coordinate system coordinates default to the following names in 2D and 3D (in 2D axisymmetric geometries, COMSOL Multiphysics uses cylindrical coordinates):

Geometry	Default Name of Spatial coordinates
2D	x y
3D	x y z
Axial symmetry 2D	r φ z

Geometry

Default Name of Spatial coordinates

x y

x y z

Axial symmetry 2D

r φ z

In 3D, an image displays in the lower-left corner of the window

to indicate the orientation of the global coordinate system.

User-defined coordinate systems can be used on all geometric entity levels to simplify the modeling process. In the physics interfaces, you can use these coordinate systems to define orthotropic and anisotropic material properties that are not aligned with the global Cartesian coordinate system. To choose a coordinate system, select it from the list in the section. The list contains the (the default) and any other coordinate systems that you have added, for example see Figure 5-4.

See Table 5-18 for an overview of the available coordinate systems. Note in particular that some coordinate systems specify absolute directions in space, while others specify a rotation relative to the default global system, as indicated by the Type column in the table.

To add a Coordinate System to any Component:

•

In the toolbar, select coordinate system features from the menu, or

•

Right-click the (

) node and choose an option from the submenu.

Table 5-18: Coordinate System Descriptions.
Name and Link	icon	Type	Description
Base Vector System		Relative	1D, 2D, and 3D. Define this using a set of base vectors to form a coordinate system.
Boundary System		Absolute	2D and 3D. A local base vector system on 2D boundaries (t, n) and on 3D boundaries (t1, t2, n). Use it to apply loads that apply in a normal or tangential direction on a boundary that is not aligned with the global Cartesian coordinate system. This coordinate system is always available. You can add Reverse Normal and Domain Normal subnodes to reverse the normal for some boundaries and switch the normal direction on the exterior of some domains, respectively.
Combined System			1D, 2D, and 3D. Use a combined system when you need to use different coordinate systems in different domains to represent some material property, for example. You can add applicable coordinate systems as subnodes, each with a geometric entity selection.
Composite System		Same as base system	1D, 2D, and 3D. Create a composite coordinate system from a base system and a system defining axes relative to the base system.
Cylindrical System		Absolute	2D and 3D. Use a cylindrical system when rotational symmetry about the axis is required. Not available in geometries with 2D axial symmetry, where a cylindrical coordinate system is the default coordinate system.
Mapped System		Absolute	1D, 2D, and 3D. The mapped system can deal with translated and rotated coordinate systems. Use this to create a system that defines a mapping from the frame coordinate system.
Rotated System		Relative	2D and 3D. Use a rotated system to define rotation about the out-of-plane direction or Euler angles in 2D and Euler angles in 3D.
Scaling System		Absolute	For physics that support infinite elements or perfectly matched layers only. Use this coordinate system, which is similar to a mapped coordinate system, to arbitrarily deform the domain.
Spherical System		Absolute	3D only. Use a spherical system when a field or property using spherical coordinates is to be specified.
System from Geometry		Absolute	3D only. Use a coordinate system from a work plane in a 2D geometry or a 3D geometry part.

Table 5-18: Coordinate System Descriptions.