Accumulator Theory: Velocity Reinitialization
The Accumulator (for Velocity Reinitialization) feature transfers information from particles to the domain they occupy. Each Accumulator defines a variable, called the accumulated variable, on the domains in the selection of the parent Velocity Reinitialization node. The accumulated variable is discretized using constant shape functions, so its value is uniform over every mesh element and may be discontinuous between adjacent mesh elements.
The name of the accumulated variable is specified in the Accumulated variable name text field in the Accumulator Settings section of the settings window. The default variable name is rpv.
The options in the Accumulator type list are Density and Count. If Count is selected, then whenever the parent feature’s velocity reinitialization condition is satisfied, the accumulated variable in the element occupied by the particle is incremented by the value of the source term,
If instead Density is selected, the source term is first divided by the volume (in 3D) or area (in 2D) of the mesh element the particle is in,
It is not necessary for the particle velocity to change for the accumulation to occur; the reinitialization condition merely needs to be satisfied. For example, accumulation can occur even if None is selected from the Effect on primary particle list in the parent Velocity Reinitialization node.
A simple demonstration of the Accumulator subnode for the Velocity Reinitialization node is illustrated in Figure 3-9 below. A single particle is released into a square domain with initial velocity (1,0.5) m/s. From left to right, the particle trajectory is shown at solution times t = 0.25 s, t = 0.50 s, t = 0.75 s, and t = 1.00 s. The accumulated variable is shown as a surface plot and the mesh element boundaries are also shown. The reinitialization criterion is qx>0.6&&pt.vx>0. It is clear that the accumulation is applied uniformly over the mesh element the particle occupies at the time step when the reinitialization condition is met, at about t = 0.60 s.
Figure 3-9: Velocity reinitialization of a single particle with an accumulator.