The timestep is one of the main factors that determine the amount of time required for the completion of a simulation in Rocky. The simulation timestep should be large enough to ensure reasonable completion time, but small enough to guarantee the accuracy and stability of the simulation.
It is a customary practice in DEM to set the timestep size as a fraction of the
oscillation period of a equivalent mass-spring system, 
, where 
and 
are critical values of mass and stiffness, respectively. That period of time
will approximate the duration of the shortest possible collision among all possible
combinations of particles and boundaries. The timestep value is chosen in a way that even that
shortest collision may be solved numerically with a reasonable resolution.
In Rocky, the timestep value is calculated automatically at the beginning of a simulation, using the expressions listed below for each normal contact model. If necessary, however, users can override that value and set a new one determined by their own means. In order to do so, the Fixed Timestep option must be turned on from the Advanced sub-tab of the Solver panel. Enabling this option allows the subsequent Timestep value to be defined. Users must be aware, however, that the timestep value is a critical parameter in Rocky, so its manual modification is not recommended in general, because it may lead to either instability of the solution process or excessively long simulation times.
In the hysteretic linear spring model, the loading and the unloading stages of the
contact occur with two different values of stiffness, 
and 
, respectively. Therefore, the calculation of the timestep takes into
account those two stages independently. That calculation can be summarized into the
following expression:
 | (5–1) |
where:
is the effective mass, defined in Equation 2–10. 
is the minimum number of timesteps per loading cycle, which is a user
input parameter listed as Loading N-steps in the Rocky UI.
For using Equation 5–1, all particle-particle and
particle-boundary possible combinations are examined, searching for the critical values of 
and 
. That equation guarantees that, during any collision, the loading portion
will be discretized with at least 
timesteps, while the unloading will comprehend at least 4 timesteps.
In the linear spring-dashpot model, the contact stiffness for the loading and the unloading have the same value. Hence, it is enough to analyze the loading for determining the timestep when that model is used. The expression considered for that is simply:
 | (5–2) |
where all parameters have the same definition as in Equation 5–1. All particle-particle and
particle-boundary possible contacts are examined for finding the minimum value of 
.
The Hertzian spring-dashpot model is a nonlinear model, so the contact stiffness
depends on the normal overlap 
. The expression for the contact stiffness on this model is:
 | (5–3) |
When the Hertzian spring-dashpot model is used, the timestep is determined by means of:
 | (5–4) |
in which 
is estimated considering that the magnitude of the maximum overlap is 10%
of the effective radius 
. Again, all particle-particle and particle-boundary possible combinations
are examined for finding the minimum value of 
.
As previously mentioned, the size of the timestep is one of the main factors that determine how much processing time a simulation will demand. It would be desirable to increase the timestep as much as possible, without compromising stability or accuracy, in order to speed up a simulation.
As described in previous sections, the timestep is always inversely proportional to the square root of a critical stiffness. Because of this, one of the techniques most frequently used in order to speed up a DEM simulation is the reduction of the stiffness. Rocky allows the users to use this technique through a global reduction factor that multiplies all stiffness values computed in the different models. This parameter is listed in the Rocky UI as Numerical Softening Factor, which is located on the Momentum tab of the Physics panel.
As an example, reducing the value of the numerical softening factor from 1 to 0.01 will increase the timestep approximately 10 times. This change may speed up the simulation in that proportion also. However, users must be very careful when specifying values for the numerical softening factor. Values that are too low can lead to very large overlaps, and therefore, serious stability and accuracy issues in a simulation.