RIGIDBODY

The geometry with MOVE-flag $MOVE_index$ moves due to the acting forces of the flow as well as additional outer forces and momentum. Note:

• The physical constants/variables have to be initialized in the MOVE statement (see below).
• To speed up the calculation, activate %MOVE_InvokeDataCaching%. Ensure that you follow the correct order: It must be the first of the optional arguments.

In particular, we solve the ODE of movement of rigid rotating bodies: \begin{align} \frac{d }{dt} \left( \mathbf{x}_{COG} \right) = \mathbf{v}_{COG}\end{align} \begin{align} \frac{d }{dt} \left( m \cdot \mathbf{v}_{COG} \right) = F_{fluid} + F_{gravity} + F_{outer} + \left( F_{contact} + F_{friction} \right)\end{align} \begin{align} \frac{d}{dt} \left( \mathbf{I} \cdot \mathbf{\omega}_{COG} \right) = M_{fluid} + M_{outer} + \left( M_{contact} + M_{friction} \right)\end{align} The variables are

• \( t\): time
• \( m\): mass of the body,
• \( \mathbf{x}_{COG}\): position of the center of gravity of the body; this can be extracted by the function xCOG(),
• \( \mathbf{v}_{COG}\): velocity of the center of gravity; this can be extracted by the function vCOG(),
• \( F_{fluid}\): forces acting from the fluid onto the body (automatically measured and applied!); this can be extracted by the function FCOG(), Note: The pointwise pressure field is averaged using the values from the current and previous timestep. No averaging is done for the stress tensor, esp. PCindices, %ind_Sn(1)%, %ind_Sn(2)%, %ind_Sn(3)% . To skip averaging, please refer to RIGIDBODY_ForceToApplyOnBody_PC .
• \( F_{gravity}\): the gravity forces deduced from the definition of gravity of the appropriate material,
• \( F_{outer}\): additional / outer forces other than fluid or gravity/body forces,
• \( \mathbf{I}\): tensor of rotational inertia,
• \( \mathbf{\omega}_{COG}\): rotational speed about the center of gravity of the body; this can be extracted by the function omCOG(),
• \( M_{fluid}\): moment about the center of gravity (automatically measured and applied!); this can be extracted by the function MCOG(),
• \( M_{outer}\): outer moments other than the moment applied by the fluid,
• \( F_{contact}, M_{contact}\): if RIGIDBODY_UseCollisionModel > 0, then MESHFREE detects the body-body and body-boundary intersections and automatically applies contact forces and moments \( M_{contact} = \left( \mathbf{x}_{contact} - \mathbf{x}_{COG} \right) \times F_{contact}\).

Entry	Description
(xCenterInit, yCenterInit, zCenterInit)	initial center of gravity \( \mathbf{x}_{COG}\)
Mass	mass of RIGIDBODY \( m\)
(xxInertia, xyInertia, xzInertia, yxInertia, yyInertia, yzInertia, zxInertia, zyInertia, zzInertia)	initial tensor of inertia \( \mathbf{I}\)
(xVelocityInit, yVelocityInit, zVelocityInit)	initial velocity \( \mathbf{v}_{COG}\)
(xOmegaInit, yOmegaInit, zOmegaInit)	inital rotational state \( \mathbf{\omega}_{COG}\)
(xForce, yForce, zForce)	outer forces \( F_{outer}\)
(xMomentum, yMomentum, zMomentum)	outer momentum \( M_{outer}\)
%MOVE_InvokeDataCaching%	activate data caching (must be the first optional argument)
%RIGIDBODY_FixVelocity%, v_x, v_y, v_z,	fix a velocity vector (that is fix a velocity in a given direction)
	The direction of fixation is given by the normalized velocity. So, it becomes clear, that 0 velocity cannot be fixed. In this case a tiny value has to be given.
	Be aware that you can provide up to three %RIGIDBODY_FixVelocity% statements.
%RIGIDBODY_FixOmega%, omega_x, omega_y, omega_z	fix a rotational speed vector (that is fix the speed around a given axis)
	The direction of the axis is given by the normalized rotational speed vector. So, it becomes clear, that 0 rotational speed cannot be fixed. In this case a tiny value has to be given.
	Be aware that you can provide up to three %RIGIDBODY_FixOmega% statements.