For incompressible fluids, the stream function is given by

(30–1)

These equations are slightly different for the 2D axisymmetric case. Equation 30–1 does not require any material parameters to be specified, and boundary conditions are always of the Neumann type.

On parts of boundaries where a zero normal velocity has been imposed, Ansys Polyflow requires the stream function to be constant, to ensure that an isoline of will not cross the domain boundary due to approximation errors.

Equation 30–1 guarantees the uniqueness of the stream function only if the value of has been imposed at a minimum of one node. By default, Ansys Polydata sets equal to zero at the node nearest to (, ) = (0, 0). Isolines of are always parallel to the velocity vector and correspond to particle trajectories only in steady-state flows.