In this case you view a cross section in the xy-plane of the actual 3D geometry. The geometry is mathematically extended to infinity in both directions along the z-axis, assuming no variation along that axis. All the total flows in and out of boundaries are per unit length along the z-axis. A simplified way of looking at this is to assume that the geometry is extruded one unit length from the cross section along the z-axis. The total flow out of each boundary is then from the face created by the extruded boundary (a boundary in 2D is a line).

In some applications there are special 2D assumptions, such as the plane strain and plane stress conditions for 2D stress analysis in solid mechanics.

The spatial coordinates are called r and z, where r is the radius. The flow at the boundaries is given per unit length along the third dimension. Because this dimension is a revolution, you have to multiply all flows with αr, where α is the revolution angle (for example, 2π for a full turn). COMSOL Multiphysics provides this as an option during postprocessing.

Given that the necessary approximations are small, the solution is more accurate in 2D because a much denser mesh can be used. See 2D Models if this is applicable.

COMSOL Multiphysics uses a global Cartesian or cylindrical (axisymmetric) coordinate system as the basic coordinate system for the geometry. You select the geometry dimension and coordinate system when creating a new model. The default variable names for the spatial coordinates are x, y, and z for Cartesian coordinates and r, φ, and z for cylindrical coordinates. These coordinate variables (together with the variable t for the time in time-dependent models) make up the independent variables in COMSOL Multiphysics models.

For axisymmetric cases the geometry model must fall in the positive half plane (r ≥ 0).