AdjustTimeStep Custom Task

A custom task to dynamically adjust the MPM time step.

Introduction

For convergence of explicit, dynamic calculations, like NairnMPM, the time step must be less then the time it takes a stress wave or a particle at its current velocity to pass across the smallest element size. For safety, the time step is usually calculated to be some fraction of this time as specified by the input Courant–Friedrichs–Lewy factor (C). But, for some material types, the wave speed might change during the calculations thereby necessitating an adjustment in the time step to retain convergence. This tasks allows you to periodically adjust the time step.

When activated, this task looks at each particle and finds the current wave speed, c_s, and particle speed

      [math]\displaystyle{ c_p = \sqrt{v_x^2+v_y^2+v_z^2} }[/math]

The time step is then set to minimum time (over all particles, p) for the particle to cross minimum cell size (Δx) at the two speeds (c_s and c_p):

      [math]\displaystyle{ \Delta t = \min_p \left({C \Delta x\over c_s}, {C_{vel} \Delta x\over c_p}\right) }[/math]

where [math]\displaystyle{ C_{vel} }[/math] is an optional different time factor for particle velocities. The time step may go up or down, depending on the states of the particles.

Task Scheduling

In scripted files, a AdjustTimeStep custom task is scheduled using

CustomTask AdjustTimeStep
Parameter adjustTime,(time)
Parameter verbose,(verbose)
Parameter velocityCFL,(Cvel)
Parameter maxIncrease,(maxInc)

In XML files, this task is scheduled using a <Schedule> element, which must be within the single <CustomTasks> block:

<Schedule name='AdjustTimeStep'>
   <Parameter name='adjustTime'>(time)</Parameter>
   <Parameter name='verbose'>(verbose)</Parameter>
   <Parameter name='velocityCFL'>(Cvel)</Parameter>
   <Parameter name='maxIncrease'>(maxInc)</Parameter>
</Schedule>

where the two parameters are:

• (time) - Enter the time interval for checking the time step and adjusting it if needed (in alt time units). This parameter is optional; if it is omitted, the time step adjustment is done each time particle data are archived. To check on every time step enter zero (or any number less than the shortest possible time step).
• (verbose) - If value is greater than 0.99, it will print the new time step whenever it changes by a factor equal to value of (verbose). For backward compatibility, if entered value is 1, the report factor will set to 2 fold change in time step. If value is less than 0.99, the new time step is silently changed. The default it 0.
• (Cvel) - Enter a different Courant–Friedrichs–Lewy factor to use for particle velocities. This parameter is optional. The default is for (Cvel) to be the same as the input Courant–Friedrichs–Lewy (C).
• (maxInc) - This option limits any increases in time step to be (1+(maxInc))*Δt where Δt is the current time step. It is most-commonly needed when using the time-step restarting option because otherwise this task would immediately return the time step to its previous value. If not entered, no limits are placed on time step increases.

Material Support

This custom task can be used with any material and respond to material point velocities. But, it should also look at current wave speed in materials, especially when compressed. This task only accounts for pressure dependent properties if some particles are using material classes for which the wave speed changes with particle state and for which the material class coding responds to CurrentWaveSpeed() to provide that state-dependent wave speed. The material classes that current provide this support are:

• ClampedNeohookean
• HEIsotropic
• HEMGEOSMaterial
• IdealGas
• Mooney
• MooneyMembrane
• Neohookean
• PhaseTransition
• ReactionPhase
• TaitLiquid
• Viscoelastic

All other materials have wave speed that is independent of particle state (or no calculations are implement to evaluate particle-state effects). These materials will still adjust time step, however, if particles approach the wave speed of the material. These adjustments can help highly-dynamic simulations.