Velocity.cl File Reference

Euler-XYZ based velocity computation. More...

#include "resources/Scripts/types/types.h"

Include dependency graph for Velocity.cl:

Functions
__kernel void	entry (const __global uint *iset, const __global int *imove, __global vec *r, __global vec *u, unsigned int N, unsigned int motion_iset, vec motion_r, vec motion_drdt, vec4 motion_a, vec4 motion_dadt)
	Compute the boundary elements velocity applying Euler-XYZ motion.

Detailed Description

Euler-XYZ based velocity computation.

Function Documentation

entry()

__kernel void entry	(	const __global uint *	iset,
		const __global int *	imove,
		__global vec *	r,
		__global vec *	u,
		unsigned int	N,
		unsigned int	motion_iset,
		vec	motion_r,
		vec	motion_drdt,
		vec4	motion_a,
		vec4	motion_dadt
	)

Compute the boundary elements velocity applying Euler-XYZ motion.

In Euler-XYZ the following transformation is applied to a particle \( a \):

\[ R_z \cdot R_y \cdot R_x \cdot \mathbf{x_a} + \mathbf{cor}, \]

where \( \mathbf{cor} \) is the position of the center of rotation (global translations), and \( \mathbf{x_a} \) is the constant position of the boundary element with respect to \( \mathbf{cor} \), and \( R_x, R_y, R_z \) are the rotation matrices:

\[ R_x = \left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \mathrm{cos}(\phi) & -\mathrm{sin}(\phi) \\ 0 & \mathrm{sin}(\phi) & \mathrm{cos}(\phi) \\ \end{matrix} \right], \]

\[ R_y = \left[ \begin{matrix} \mathrm{cos}(\theta) & 0 & \mathrm{sin}(\theta) \\ 0 & 1 & 0 \\ -\mathrm{sin}(\theta) & 0 & \mathrm{cos}(\theta) \\ \end{matrix} \right], \]

\[ R_z = \left[ \begin{matrix} \mathrm{cos}(\psi) & -\mathrm{sin}(\psi) & 0 \\ \mathrm{sin}(\psi) & \mathrm{cos}(\psi) & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right]. \]

To compute the velocity the following process can be followed:

1. The velocity due to the rotations is computed in the local coordinates: \( \omega \times \mathbf{x_a} \), with \( \omega = \left[ \dot \phi, \dot \theta, \dot \psi \rigth] \)
2. Then the vector is rotated using the rotation matrix.
3. Finally the linear velocity, \( \dot \mathbf{cor} \) is added.

Parameters

iset	Set of particles index.
imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r	Position \( \mathbf{r} \).
u	Velocity \( \mathbf{u} \).
N	Number of particles.
motion_iset	Set of particles affected.
motion_r	Center of rotation.
motion_drdt	Center of rotation velocity.
motion_a	Rotation angles \( \phi, \theta, \psi \).
motion_dadt	Angular velocities.

See also

MotionTransform.cl