COMP_DropletphaseWithDisturbance

Default: COMP_DropletphaseWithDisturbance = 0 By default the update of the positions of DROPLETPHASE points is: \( \mathbf{x}_i^{n+1}\) is the current and \( \mathbf{x}_i^n\) is the previous position. \( \Delta t_i\) is the current time step size and \( \mathbf{v}_i^{n+1}\) is the current velocity. If the disturbance is switched on by COMP_DropletphaseWithDisturbance = 1, the default update is disturbed by the following procedure.

2. Rotate the default update position \( \mathbf{x}_{\text{default}}\) by a small, smoothing length dependent angle (based on a random number) with respect to a random, normalized axis through the previous position:
   • random number \( r\) determines the sign (-1, 0, 1) of angle \( \alpha\) (rotation only for non-zero sign)
   • random vector \( \mathbf{d}\) determines the rotation axis as \( \mathbf{a} = \frac{\mathbf{x}_i^n - \mathbf{d}}{\lVert \mathbf{x}_i^n - \mathbf{d}\rVert_2}\)
   • rotation of default update position by \( \mathbf{x}_i^{n+1} = (\mathbf{a} \cdot \mathbf{x}_{\text{default}}) \mathbf{a} + \cos(\alpha)(\mathbf{a} \times \mathbf{x}_{\text{default}}) \times \mathbf{a} + \sin(\alpha)(\mathbf{a} \cdot \mathbf{x}_{\text{default}})\)
3. Adapt the current velocity.

Note: This procedure guarantees that the distance between previous and current position is not changed compared to the default behavior.