### 12.4.3. Symmetry vs. Periodicity

In most cases, periodicity or slip conditions cannot be employed in regions that border on zones of resolved turbulence, even if the geometry and the time-averaged flow are symmetric with respect to a given plane. The reason is that unsteady turbulence does not obey symmetry instantaneously. The application of symmetry boundaries would therefore impose an unphysical constraint onto the resolved scales. It is therefore essential to either compute the full domain, or to apply periodicity at such planes if possible (for example, if there is a matching plane at the other end of the domain).

Symmetry and slip wall conditions can be used if the resolved turbulence is confined to regions not touching these boundaries.

Periodicity conditions can lead to problems for axi-symmetric situations. As the radius approaches zero, the circumferential size of the domain goes to zero, and periodicity conditions would not enable turbulence structures of finite size to exist. An example is the flow in an axi-symmetric pipe. If you were to compute that flow in a pipe segment with periodicity conditions in the circumferential direction, you would restrict the size of the resolved eddies to zero near the axis. This effect is not correct and would substantially alter the solution. Such a simulation would therefore have to be carried out in full mode. Note that the situation would be different in the case of the flow through a ring segment, where the axis is excluded from the SRS domain. Periodicity could be applied in the case of with being the outer radius, the inner radius of the segment and being a constant of the order 1 or larger.

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