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 an effective particle speed

      [math]\displaystyle{ c_p = |v_x| + |v_y| + |v_z| }[/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 maximum of 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)

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>
</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 its integer value is not zero, it will print the new time step whenever it changes by more than 1%. If it is zero, the new time step is silently changed. The default it 0.
• (Cvel) - Enter an optional, different Courant–Friedrichs–Lewy factor to use for particle velocities. This parameter is option. The default is for (Cvel) to be the same as the input Courant–Friedrichs–Lewy (C).

Material Support

This custom task only has an effect 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:

• HEMGEOSMaterial
• IdealGas
• TaitLiquid
• ClampedNeohookean

Some other material classes could have wave speed that depends on particle state, but do not yet provide the needed CurrentWaveSpeed() code. These materials, which will update in the future as needed, are:

• IsoPlasticity
• HillPlastic
• WOODMATERIAL
• Mooney
• HEIsotropic
• HEAnisotropic
• Viscoelastic

All other materials have wave speed that is independent of particle state and therefore have no need for dynamic adjustment of the time step during calculations.