Using The Polynomial Particle-In-Cell Method For Liquid-Fabric Interaction

TL;DR

The paper tackles numerical damping in PIC-based liquid-fabric simulations. It replaces APIC transfers with PolyPIC transfers on MAC grids and adopts higher-order polynomial modes with count $N_r$, enabling closer to lossless energy transfer and better preservation of rotational motion. The PolyPIC formulation is integrated into the mixed-fluid/solid framework of Fei et al., including absorption of fluid mass by solids in the transfer computations. Across four scenarios, PolyPIC yields more dynamic splashes and finer vortical structures, but at increased computational cost and with the need for smaller timesteps to maintain stability.

Abstract

Liquid-fabric interaction simulations using particle-in-cell (PIC) based models have been used to simulate a wide variety of phenomena and yield impressive visual results. However, these models suffer from numerical damping due to the data interpolation between the particles and grid. Our paper addresses this by using the polynomial PIC (PolyPIC) model instead of the affine PIC (APIC) model that is used in current state-of-the-art wet cloth models. The affine transfers of the APIC model are replaced by the higher order polynomials of PolyPIC, thus reducing numerical dissipation and improving resolution of vorticial details. This improved energy preservation enables more dynamic simulations to be generated although this is at an increased computational cost.

Figures (9)

• Figure 1: Fluid splashing onto a square of yarn fabric using PolyPIC transfers.
• Figure 2: The difference between the APIC and PolyPIC algorithms is the method of transferring data between the particles and the grid. PolyPIC uses generalized higher order polynomials whereas APIC uses affine transformation matrices. (Based on Figure 7 in jiang_affine_2015.)
• Figure 3: The data stored by particles and grid node faces in PIC methods. White background boxes are consistent between all PIC variants. Velocity derivatives (yellow background) are introduced for APIC and scalar coefficients (blue boxes) are introduced in PolyPIC. (Based on a diagram in fu_polynomial_2017.)
• Figure 4: A small dam break scenario using APIC (top) and PolyPIC (bottom) transfers. Particle colours indicate velocity (dark blue = low, red = high). PolyPIC shows improved resolution of vorticial details.
• Figure 5: Fluid splash onto a small piece of cloth using APIC (top) and PolyPIC (bottom) transfers. Particle colours indicate velocity (dark blue = low, red = high). The reduced damping means that more fluid splashes off the piece of cloth rather than being absorbed. The fluid that is absorbed exhibits more thin strand behaviour as it drips from the cloth in PolyPIC than APIC (see frame 4).