Fixed Mean Value - Boundary Condition

Fixed Mean Value is a boundary condition that enforces an average (mean) value for a specified quantity. Rather than prescribing individual point values at the boundary, it ensures that the integral of the field across the patch matches a user-defined mean. This means value can be set as a constant or allowed to vary over time.

Although Fixed Mean Value is conceptually similar to Fixed Value, it introduces significantly less flow distortion near the boundary. This is because Fixed Mean Value uses values from neighboring cells to extrapolate the field onto the patch, adjusting the distribution so that the overall average meets the specified target. As a result, the variable distribution near the boundary is more realistic and physically representative.

The advantage of Fixed Mean Value is easily illustrated using pipe flow as an example. When a Fixed Value condition is applied at the inlet, the velocity is enforced to be the same across the entire boundary, from the pipe’s center line to its walls. In reality, however, the flow’s core (near the pipe axis) should have a higher velocity than the regions closer to the wall.

The Fixed Mean Value boundary condition enforces that the average value of a field (e.g., pressure or velocity) across a boundary patch remains constant at a specified mean. While individual values along the patch can vary, their integral average is constrained. This is useful when one wants to control the overall magnitude of a quantity at a boundary without prescribing its exact distribution.

This can represent conditions where the integral (or net) effect is known—such as total mass flow, total heat flux, or average pressure—without having detailed knowledge (or a constraint) on the precise local pattern. Instead, the numerical solution determines the local variations, consistent with the overall boundary value imposed and the rest of the flow field.

The definition of boundary conditions in SimFlow is both simple and intuitive. To specify the Fixed Mean Value boundary condition, the user must navigate to the Boundary Conditions panel, select the appropriate boundary, and choose the correct option from the drop-down menu.

Fixed Mean Value can be defined as a constant value where a specified filed (scalar or vector) is not changing in time - Figure 2.

Alternatively, the User can switch to table, where time-dependent value can be defined - Figure 3.

In this section, we propose boundary conditions that are alternative to Fixed Mean Value. While they may fulfill similar purposes, they might be better suited for a specific application and provide a better approximation of physical world conditions.