Issues with passive scalars at the flow reversal with turbulent outflow BC

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Chinthaka Jacob

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Feb 10, 2026, 4:07:36 PM (10 days ago) Feb 10

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Dear Nek Community,

I am simulating reciprocating pipe flow driven by a time-varying velocity profile at one end, with the opposite end treated using the turbulent outflow boundary condition ('O ' with turb_outflow). The velocity field remains stable, although the outflow treatment introduces a small region of artificial divergence near the boundary, which can be excluded from analysis.

The issue arises when passive scalars are included. During the second half of the reciprocation cycle, the flow reverses direction and enters the domain through the boundary previously designated as outflow. Physically, scalars should then be advected into the domain from that boundary. However, the artificial divergence imposed by the turbulent outflow condition enforces outward flux regardless of flow direction, preventing scalar inflow.

I would appreciate advice on how to handle flow-reversing boundaries while ensuring physically consistent scalar transport.

As a related but separate point, I have been reading about the so-called directional do-nothing boundary condition. The motivation is that the natural ('O ') boundary condition becomes unstable when a boundary switches to inflow, since the bilinear form of the linearised problem is no longer coercive. In contrast, Robin boundary conditions are stable for inflow but unstable for outflow.

The directional do-nothing approach therefore switches between natural and Robin conditions depending on whether the local velocity points out of or into the domain. This is commonly achieved by introducing a coefficient

\alpha = \alpha* ( || \u\cdot\n || - u\cdot\n )

which activates the Robin term only when the flow is inward.

In a finite-element setting, the homogeneous natural condition corresponds to “doing nothing” on the boundary, while the Robin condition adds a boundary integral of the form

\int_{out} \alpha* ( || \u\cdot\n || - u\cdot\n ) \u \cdot v

where v is the test function. Since Nek5000 does not explicitly expose the test-function space at the user level, I would appreciate any advice on how such a directional switching mechanism could be implemented within Nek5000.