Dear All,

I've several questions about outflow boundary conditions for boundary regions and conditions specified below for a pipe flow problem:

<BOUNDARYREGIONS>
            <B ID="0"> C[2] </B>  <!-- Inlet -->
            <B ID="1"> C[3] </B>  <!-- Outlet -->
            <B ID="2"> C[1] </B>  <!-- Wall -->
        </BOUNDARYREGIONS>

        <BOUNDARYCONDITIONS>
            <REGION REF="0">
                <D VAR="u" VALUE="0" />
                <D VAR="v" VALUE="0" />
                <D VAR="w" VALUE="1" />
                <N VAR="p" USERDEFINEDTYPE="H" VALUE="0" />
            </REGION>
            <REGION REF="1">
                <N VAR="u" VALUE="0" />
                <N VAR="v" VALUE="0" />
                <N VAR="w" VALUE="0" />
                <D VAR="p" VALUE="0" />
            </REGION>
            <REGION REF="2">
                <D VAR="u" VALUE="0" />
                <D VAR="v" VALUE="0" />
                <D VAR="w" VALUE="0" />
                <N VAR="p" USERDEFINEDTYPE="H" VALUE="0" />
            </REGION>
        </BOUNDARYCONDITIONS>

1) What is the meaning of <N VAR="p" USERDEFINEDTYPE="H" VALUE="0" />  and why do we specify such a BC at the wall of the pipe? What happens if I don't specify any pressure BC at the wall of the pipe?

2) Is there any other option to specify pressure BC at the outlet other than <D VAR="p" VALUE="0" /> ? For example is it possible to apply the pressure BC at the outlet given below which is specified in a paper (Direct numerical simulation of stenotic flows. Part 1. Steady flow, SONU S. VARGHESE, STEVEN H. FRANKEL AND PAUL F. FISCHER) ?

In turbulent flows, it is possible to have vortices strong enough to yield a (locally) negative flux at the outflow boundary. Since no flow characteristics are specified on these boundaries, a negative flux condition typically leads to instabilities with catastrophic results. One way to ensure that the characteristics at the exit are always pointing outwards is to force the exit flow through a nozzle, effectively adding a mean axial component to the velocity field. In contrast, schemes based on viscous buffer zones require knowledge of the anticipated space and time scales to ensure that vortical structures are adequately damped as they pass through the buffer zone.
This nozzle effect can be imposed numerically without having to change the mesh geometry by imparting a positive divergence to the flow field near the exit (in the spirit of a supersonic nozzle). In the current study, this is done by identifying the layer of elements adjacent to the outflow and imposing a divergence function D(x) that is zero at the upstream end of the layer and ramps to a fixed positive value at the exit. Specifically, we set D(x)=C[1−(x⊥/L⊥)2], where x⊥ is the distance normal to the boundary and L⊥ is the maximum thickness of the last layer of elements. A net gain in mean velocity is obtained over the extent of the layer by integrating the expression for D from x⊥/L⊥=1 to 0. The constant C is chosen such that the gain is equal to the mean velocity prior to the correction.

Regards,
Kamil