Periodic Condition
The Periodic Condition node adds a periodic boundary condition that can be used to reduce the model size by using symmetries and periodicities in the geometry and physics interfaces being modeled. This feature works well for cases like opposing parallel boundaries. In other cases, use the Destination Selection section to control the destination. By default, it contains the source and destination selection that COMSOL Multiphysics identifies. The periodic condition automatically defines a mapping between the source xs and the destination xd points on the boundaries.
Boundary Selection
The software usually automatically identifies the boundaries as either source boundaries or destination boundaries, as indicated in the selection list. This works fine for cases like opposing parallel boundaries. In other cases, right-click Periodic Condition and select Manual Destination Selection to control the destination. By default it contains the selection that COMSOL Multiphysics identifies.
Destination Selection
This section is available for specifying the destination boundaries, if needed, when the Manual Destination Selection option is selected in the context menu for the Periodic Condition node. You can only select destination boundaries from the union of all source and destination boundaries.
Periodicity Settings
Select a Type of periodicity: Continuity (the default), Antiperiodicity, Floquet periodicity (Bloch periodicity), Cyclic symmetry, or User Defined.
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For Continuity the values of the field variables at destination are set equal to the source: p(xd) = p(xs), u(xd) = u(xs), and T(xd) = T(xs). If the source and destination boundaries are rotated with respect to each other, a transformation is automatically performed, so that corresponding velocity components are connected.
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For Antiperiodicity the values of the field variables on the destination are set equal to the values on the source with the sign reversed: p(xd) = −p(xs), u(xd) = −u(xs), and T(xd) = −T(xs). If the source and destination boundaries are rotated with respect to each other, a transformation is automatically performed, so that corresponding velocity components are connected.
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For Floquet periodicity, also known as Bloch periodicity, enter a k-vector for Floquet periodicity kF (SI unit: rad/m) for the x, y, and z coordinates (3D components), the r and z coordinates (2D axisymmetric components), or x and y coordinates (2D components). This is the wave number of the excitation.
This condition is used to model infinite periodic structures with nonnormal incident pressure fields or excitations. Use it to model, for example, a large perforated plate with an oblique incident wave with wave vector k (and set kF = k) by only analyzing one hole or one subset of holes that is periodic.
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For Cyclic symmetry select a Sector angle: Automatic (the default) or User defined. For User defined enter a value for θS (SI unit: rad). Enter an Azimuthal mode number m (dimensionless).
This condition is used to model any geometry that has a cyclic periodic structure such as a microphone or a loudspeaker driver. Setting the azimuthal mode number determines what mode is analyzed. The response of the full system to an external excitation is in general a linear combination of many different modes.
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For User defined select the check box for any of the field variables as needed. Then for each selection, choose the Type of periodicity — Continuity or Antiperiodicity. If the source and destination boundaries are rotated with respect to each other, a transformation is automatically performed, so that corresponding velocity components are connected.
In the time domain, both the Cyclic symmetry and the Floquet periodicity boundary conditions reduce to the continuity condition.
To get correct behavior of the Periodic Condition, in particular the Floquet periodicity and the Cyclic symmetry conditions, it is recommended that the source and destination meshes are identical. This can be achieved using the Identical Mesh mesh feature. When the Periodic Condition stretches across regions with a mix of default material models, PMLs, background pressure fields, or background acoustic fields, it is recommended to add one Periodic Condition for each set of such boundaries.
Constraint Settings
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box. For information about the Constraint Settings section, see Constraint Settings in the COMSOL Multiphysics Reference Manual.
Excluded Edges/Points
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box. See Suppressing Constraints on Lower Dimensions for details.
Orientation of Source
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box. For information about the Orientation of Source section, see Orientation of Source and Destination in the COMSOL Multiphysics Reference Manual.
Orientation of Destination
This section appears if the setting for Transform to intermediate map in the Orientation of Source section is changed from the default value, Automatic, and Advanced Physics Options is selected in the Show More Options dialog box. For information about the Orientation of Destination section, see Orientation of Source and Destination in the COMSOL Multiphysics Reference Manual.
Mapping Between Source and Destination
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box. For information about the Mapping Between Source and Destination section, see Mapping Between Source and Destination in the COMSOL Multiphysics Reference Manual.