XPIC Features

XPIC(m) is an improved form of MPM, which is only available in OSParticulas.. The page explains how to use XPIC(m) features.

Introduction

The PIC method can be described as applying a projection operator that modifies (and filters) particle velocities before updating them with the grid acceleration. The problem with PIC is that its projection operator filters most problems too heavily resulting in significant dissipation of energy. XPIC(m) is a new method that solves the energy dissipation problem, enhances overall stability of MPM, and reduces noise. XPIC(m) defines a series of new projection operators that can significantly reduce the over damping of PIC simulations. XPIC(m) is defined by an order m, where m=1 is PIC, m>1 is XPIC, and large m approaches an ideal FLIP method with all null-space noise removed. In other words, m from 1 to infinity provides an interpolation between PIC and optimized FLIP, but is probably a better interpolation than the simple linear combination provided by standard PIC damping.

Performance

The drawback of XPIC(m) is that each higher order of XPIC(m) requires an extra extrapolation. The extra calculations scale with m*N where N is the number of particles in the problem. XPIC is therefore less efficient than PIC or FLIP (or a PIC damping linear combination of FLIP and PIC). In many problems, m=2 already provides much improvement over PIC and reduces undesirable energy dissipation with minimal extra calculations. Larger m is often better with m=5 appearing to provide much benefit without too much extra cost. Very high values of m (e.g., m>40) are typically unstable (due to too many additional extrapolations).

Another option to use XPIC(m) efficiently, is to you XPIC(m) projects periodically rather then on every time step.

XPIC(m) Command

XPIC is activated by using the XPICOrder setting in combination with activating PIC by having β<1 in a Damping or a PDamping command. Note that XPIC can be used in combination with PIC damping where that method will now provide linear combination of fraction β FLIP and (1-β) of XPIC.