%BND_slip%

velocity boundary conditions: slip with viscous friction

BC_v($BCindex$) = ( %BND_slip%, ... Optional: FrictionCoefficient , ... Optional: ControlThicknessMomentum , ... Optional: vPenetration , ... Optional: uBoundary, Optional: vBoundary, Optional: wBoundary )
where the default options are:
Parameter Default
FrictionCoefficient \(\alpha = 0.0\) (ideal slip)
ControlThicknessMomentum 0.0, if Eulerian or very viscous flow
0.3, else, see below.
vPenetration 0.0
{u,v,w}Boundary Movement of boundary as given by MOVE-statements for the BEs: Y%ind_v_p(1)%, Y%ind_v_p(2)%, Y%ind_v_p(3)%

FrictionCoefficient

Viscous friction in the sense

\begin{align} {\bf S} \left( {\bf v}^{n+1} \right) \cdot {\bf a} = \alpha \cdot ( {\bf v}^{n+1} - {\bf v}_0 ) \cdot {\bf a}.\end{align}

Here, \(\alpha\) is the FrictionCoefficient, \(\alpha=0\) would lead to pure slip, \(\alpha \rightarrow \infty\) would lead to pure no-slip. If the turbulence model is in action, the effective friction coefficient is given by \( \alpha_{eff}=\alpha_{turb} + \alpha\), where \( \alpha_{turb}=\alpha_{turb}(k,\epsilon)\).

Default: pure slip with \(\alpha = 0.0\)

ControlThicknessMomentum

Incorporation of the momentum balance into the boundary condition, especially important for big Re-numbers. The thickness of the momentum control cell is ControlThicknessMomentum*H (smoothing length). See section 2.2 in DOCUMATH_LIQUID_BoundaryConditions.pdf

For current scientific reasons: by putting a minus in front of ControlThicknessMomentum, a special tear-off criterion is launched. In fact, an additional component is locally added to the gradient of pressure in tangential direction, if

  • the point is marked as tear-off-point (see %ind_TearOff%).

  • the point is in a local suction regime (pressure decreases from the free surface towards the interior).

This additional pressure component might provoke tear-off, as it forces the tear-off-point to move away from the free surface.

Make sure to set the ControlThicknessMomentum to ZERO if using EULER, EULERIMPL or EULEREXPL!

Defaults:
  • If the corresponding chamber is EULER, EULERIMPL or EULEREXPL then the Default is ControlThicknessMomentum = 0.0.

  • If the Reynolds-Number is below 1, then the default is also 0.0.

  • In all other cases the Default is 0.3.

vPenetration

Force the normal component of the flow to penetrate through the wall, i.e.

\begin{align} v_\text{Penetration} = ( {\bf v}^{n+1} - {\bf v}_0 ) \cdot {\bf n}.\end{align} Default: 0.0

{u,v,w}Boundary

Usually, MESHFREE checks the appropriate wall and applies the movement of this wall as the basis wall velocity \( {\bf v}_0\). Optionally, the user is able to redefine the components of the velocity of the wall movement by {u,v,w}Boundary. Note however, that turbulence effects on \(\alpha\) due to this movement are neglected in this case.

An alternative approach for simulations with turbulence is to instead directly define the relative wall movement via an EVENT. This works essentially in the same way as %MOVE_VirtualRotation% in %MOVE_TranslationRotation%.

Example:

EVENT(1) = ( [binA("MovedWallAlias")], %EVENT_FunctionManipulation%, ... %ind_v_p(1)%, [Y%ind_v_p(1)% + &relativeWallMovementX& ], ... %ind_v_p(2)%, [Y%ind_v_p(2)% + &relativeWallMovementY& ], ... %ind_v_p(3)%, [Y%ind_v_p(3)% + &relativeWallMovementZ& ])
Default: Y%ind_v_p(1)%, Y%ind_v_p(2)%, Y%ind_v_p(3)%