In the collision model of O’Rourke, [65] spray particles are allowed to collide only if they reside in the same computational cell. In a cylindrical mesh, the cell size around the spray axis can be very small, preventing collisions from occurring.

The Radius-of-Influence (ROI) collision model [58] is used in Ansys Forte to remove both mesh-size dependency and time-step dependency for the droplet collision process. In the ROI method, one particle is allowed to collide with another only if this particle resides within in the radius of influence of the other. Collision partners of a certain parcel are searched for within a "sphere of influence" centered at the parcel's location. All parcels within this sphere are possible collision partners for collide with the centered parcel. This approach removes the dependency on the CFD mesh size (as seen in O'Rourke's model [65] ), and the dependency on collision mesh size if a separate collision mesh is used [87] .

The issue of time-step dependency was also investigated in Munnannur 2007 [59] in light of the observation that the time step must be properly chosen such that the average distance traveled by a particle within the time step is a fraction of the average cell length. Using the ROI approach, the " mean collision time" (MCT) for each cell is estimated as:

(6–74)

in which is the maximum droplet velocity magnitude in the cell, is the Radius of Influence, is the number of parcels in the cell, and is a constant. The global MCT is then the minimum of the cell MCTs. In Ansys Forte, the MCT is calculated for each parcel based on the ROI concept:

(6–75)

in which is the average droplet velocity magnitude, and is number of parcels in the sphere of influence. The global MCT is taken as the minimum of all parcels' MCTs. The time step is dynamically controlled, such that if is smaller than the computational time step, is chosen as the computational time step; if is greater than the time step, collisions occur only when the accumulated time of is reached.

To avoid imposing a small collision time step on the entire engine simulation, the collision calculations are sub-cycled within the CFD time step if < . After each sub-cycle, all the droplet properties except their spatial locations are updated to reflect the collision outcomes, and these updated properties are used to predict the collision process in the next sub-cycle.

In the ROI model, the radius-of-influence is an input parameter in Ansys Forte that assumes the suggested value of Munnannur 2007 [59] by default.