# Time Step Scale Factor

The theoretical stable time step for both elements and nodes is an approximation and may change during the following time increment.

To maintain simulation stability and prevent divergence, the calculated theoretical
stable time step is multiplied by a time step scale factor $\text{\Delta}{T}_{sca}$
. If no time step control options are being used, then the minimum nodal or
element time step of a model that is printed in the Starter output is multiplied by
the time step scale factor with the result shown as `TIME-STEP`

in
the Engine output file.

```
SOLID ELEMENTS TIME STEP
------------------------
TIME STEP ELEMENT NUMBER
2.6322377948203E-04 11021
```

```
/DT
0.9 0
```

`TIME-STEP = 0.9 * 2.6322377948203E-04 = 0.2369E-03`

```
CYCLE TIME TIME-STEP ELEMENT
0 0.000 0.2369E-03 SOLID
```

When using any of the time step control methods, such as /DT/NODA/CST or /DT/BRICK/CST, the time step control is activated when the minimum time step of the mesh multiplied by the time the time step scale factor is less than the entered minimum time step, $\text{\Delta}{T}_{sca}*\mathrm{min}(\text{\Delta}{t}_{\mathrm{m}esh})\le \text{\Delta}{T}_{\mathrm{min}}$ .

```
NODAL TIME STEP (estimation)
---------------
TIME STEP NODE NUMBER
6.9475433E-07 10009
```

```
/DT/NODA/CST
0.9 7.0E-07
```

The initial Engine time step is:

Since this initial time step is less than $\text{\Delta}{T}_{\mathrm{min}}=7.0E-7$ , mass is added to increase the theoretical minimum time step of the mesh. Enough mass must be added to increase the minimum mesh time step so that $\text{\Delta}{T}_{sca}*\mathrm{min}(\text{\Delta}{t}_{\mathrm{m}esh})\le \text{\Delta}{T}_{\mathrm{min}}$ , which means:

`MAS.ERR`

), due to mass added to increase the time
step.```
CYCLE TIME TIME-STEP ELEMENT … MAS.ERR
0 0.000 0.7000E-06 NODE 10009 0.2887E-01
1 0.7000E-06 0.7000E-06 NODE 10009 0.2887E-01
2 0.1400E-06 0.7000E-06 NODE 10009 0.2887E-01
```

If $\text{\Delta}{T}_{sca}=0.67$ , then more mass must be added to make the theoretical time step of the mesh is higher.

- Models that use advanced mass scaling, /DT/AMS to increase the time step: $\text{\Delta}{T}_{sca}=\text{0.67}$
- Models with foam materials: $\text{\Delta}{T}_{sca}=\text{0.66}$
- Model with one element: $\text{\Delta}{T}_{sca}=\text{0.1}$
- Model with two finite elements: $\text{\Delta}{T}_{sca}=\text{0.2}$
- Model with more than three finite elements: $\text{\Delta}{T}_{sca}=\text{0.9}$
- Never use a scale factor greater than 1.0