Nodal Time Step Control

The nodal time step control is activated for a simulation by using the option:

/DT/NODA/Keyword3/Iflag
$Δ T_{s c a}$ $Δ T_{\min}$

With the time step of a node in the mesh defined as:(1)

Δ t_{n o d a l} = \sqrt{\frac{2 m}{k}}

Where,

$m$: Nodal mass
$k$: Equivalent nodal stiffness

Note: If the mass of a node increases or the stiffness decreases, then the time step of the simulation increases.

By default, the nodal timestep is applied to the entire model. If Iflag=1, then an additional line with a group node set ID is input after the scale factor and time step. This can be used to apply the nodal time step control to a group of nodes /GRNOD that have been defined in the Starter.

Note: No matter which Keyword3 option is used, only one /DT/NODA/Keyword3/Iflag option can be used at a time in an Engine file. If multiple ones are included, only the last one is used.

/DT/NODA/CST

/DT/NODA/CST is by far the most popular option for maintaining or increasing the time step in a simulation. Radioss will automatically add mass to nodes to maintain the entered value. If needed, the mass will be added at the beginning of the simulation to meet the entered value.

Advantages and Disadvantages

Increase the nodal mass via /DT/NODA/CST is the easiest way to increase the time step of a model or prevent a time step from dropping below a certain value during the simulation. Good engineering judgement must be used to determine how much mass is an acceptable amount to be added to a model. Adding too much mass can affect the physics by increasing the kinetic energy of a drop or impact simulation. This is because the object being simulated weighs more than the real part. Increased mass can also change the high frequency behavior of a model which can be very important in very high speed impacts such as ballistics, or explosions.

In general, it is recommended to keep the amount of mass added to less than 5%. However, larger mass increases may be acceptable in some types of simulation. For example, in quasi-static simulations the velocities are usually small, so adding mass does not greatly increase the kinetic energy. For those reasons, it is recommended to check the mass increase in the model by running a simulation without or with reduced mass scaling and comparing the results. If added mass results in added kinetic energy, the energy error calculated by Radioss will be positive.

Choose a Time Step for Mass Scaling

To determine how much mass will be added to a model, Radioss calculates a target time step for different amounts of percent mass increase. The target time step is calculated for percent mass increases from 0.5% to 10% for time step scale factors (

Δ T_{s c a}

) of 0.9 and 0.67. This information is printed in a table and a graph in the Starter output file.

Note: This estimation is valid at first cycle only. The added mass can increase during the run because of element deformation or contacts which means the added mass can become higher than the value expected from the Starter estimation.

The target time step and scale factor can then used in /DT/NODA/CST.

Check for Mass Increase

The total mass increase is listed in the Engine output file in the last column titled, MAS.ERR. Using the animation output option /ANIM/NODA/DMASS or /H3D/NODA/DMASS, the relative mass increase per node can be visualized in a post-processor as a contour plot. Both the total mass error and nodal mass error represent the change in mass divided by the original mass at the beginning of the simulation.(2)

M A S S . E R R or D M A S = (\frac{D M}{M_{0}})

With, $D M = M - M_{0}$

Where,

$M_{0}$: Initial mass at the beginning of the simulation for each Engine file
$M$: Current mass

Note: The initial mass is reset at the beginning of every Engine file simulation and the total mass increase should be added from all the Engine output files.

The global time history mass and energy curves can be plotted to understand how the increased mass effects the simulation.

Note: That part mass output using /TH/PART does not include the mass added, due to mass scaling.

/DT/NODA/SET

Reduces the equivalent nodal stiffness ( $k$ ) to maintain the entered $Δ T_{\min}$ value. This reduction in stiffness also changes the physics of a simulation and is typically only used when modeling fluids.

/DT/NODA/STOP

Stops the simulation when the simulation’s time step drops below the entered $Δ T_{\min}$ value. Many times, a reduction in time step is caused by a model's instability, so stopping the simulation can be useful to diagnose the issue.