PeriodicXPIC Custom Task

A custom task to use XPIC(k) and FMPM(k) methods on all or selected time steps

Introduction

The XPIC(k) and FMPM(k) methods are advanced methods that filters out unwanted noise (in the null space) without damping out useful information. Their drawback is that they adds calculation time as order k increases. In many simulations, it is best to use XPIC(k) or FMPM(k) methods on every time step. This custom tasks lets create such simulations or you can covert them use XPIC(k) or FMPM(k) periodically instead of on every time step. Note that FMPM(k) is currently only available in OSParticulas.

Using FMPM(k) For Particle Velocities

The first step is to select default update method. Normally, the default method would be a standard FLIP method selected by using Damping commands and setting (fractionPIC) to 1. Next, you schedule this task and use it to select an XPIC order (the m in XPIC(m)) and frequency to run the XPIC(m) calculations. In scripted files, a PeriodicXPIC custom task is scheduled with

CustomTask PeriodicXPIC
Parameter XPICOrder,(order)
(... or Parameter FMPMOrder,(order))
Parameter periodicSteps,(stepInterval)
Parameter periodicTime,(timeInterval)
Parameter periodicCFL,(CFLfactor)
Parameter verbose,{verbose}
Parameter GridBCOption,(BCoption)

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

<Schedule name='PeriodicXPIC'>
   <Parameter name='XPICOrder'>(order)</Parameter>
   <Parameter name='periodicSteps'>(stepInterval)</Parameter>
   <Parameter name='periodicTime'>(timeInterval)</Parameter>
   <Parameter name='periodicCFL'>(CFLfactor)</Parameter>
   <Parameter name='verbose'>(verbose)</Parameter>
   <Parameter name='GridBCOption'>(BCoption)</Parameter>
</Schedule>

where the parameters are:

• (XPICOrder) - Enter XPIC order (the m in XPIC(m)) to use when doing periodic XPIC(m) calculations. See Damping Options for details on this setting..
• (FMPMOrder) - Using this parameter instead of XPICOrder switched to a new mode in development called FMPM.
• (stepInterval), (timeInterval), and (CFLfactor) - sets the frequency for running periodic XPIC(m) calculations for mechanics. The (stepInterval) option sets number of time steps between each XPIC(m) calculation, (timeInterval) sets frequency in alt time units, and (CFLfactor) sets frequency relative to the basic time step for the momentum equation. If (stepInterval) is used, it is used and the other two are ignored. If (stepInterval) is not used, the time step is found from the (CFLfactor) (if provided) or from (timeInterval). One of these three parameters is required to enable periodic XPIC calculations.
• (verbose) - If a non-zero integer, a comment line is printed in the output file every time XPIC(m) calculations are done. The default is 0.
• (BCOption) - Use "lumped" to use lumped mass matrix methods for boundary conditions, "velocity" to all impose grid velocity conditions in the velocity field, or "combined" to do both. The default is "combined." Note that XPIC cannot use "velocity" option (that setting will be changed to "lumped" is used. This option only affects calculations when (XPICOrder) or (FMPMOrder) is greater than 1.

Using XPIC(m) For Transport Properties

You can also use XPIC(m) for temperature (when doing conduction calculations) or for concentration (when doing diffusion calculations). XPIC(m) seems to provide significant improvement of transport modeling and can eliminate oscillations sometimes seen for temperature or concentration for particles within one cell.

To use XPIC(m) for transport equations, select order and fraction PIC (using parameters in previous section) and then select periodicity of XPIC(m) for conduction and/or diffusion with following task parameters:

Parameter periodicStepsConduction,(stepInterval)
Parameter periodicTimeConduction,(timeInterval)
Parameter periodicCFLConduction,(CFLfactor)
Parameter periodicStepsDiffusion,(stepInterval)
Parameter periodicTimeDiffusion,(timeInterval)
Parameter periodicCFLDiffusion,(CFLfactor)

In XML files, this new parameter options within the <CustomTasks> block are

<Parameter name='periodicStepsConduction'>(stepInterval)</Parameter>
<Parameter name='periodicTimeConduction'>(timeInterval)</Parameter>
<Parameter name='periodicCFLConduction'>(CFLfactor)</Parameter>
<Parameter name='periodicStepsDiffusion'>(stepInterval)</Parameter>
<Parameter name='periodicTimeDiffusion'>(timeInterval)</Parameter>
<Parameter name='periodicCFLDiffusion'>(CFLfactor)</Parameter>

The meanings of values (stepInterval), (timeInterval) and (CFLfactor) are given in the previous section except that CFL factor is applied to transport time step and not the simulation time step.

When using XPIC(m) for transport equations, you should never pick m=1 because it causes too much numerical diffusion. Any higher order works, unless it XPIC(m) filtering is done too frequently. Because transport time step is usually much longer then mechanics time step, it is usually best to pick transport XPIC(m) frequency using the CFL parameter options and the chosen CFL factor should be 0.5 or higher to avoid any numerical diffusion.