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A Robust Compressible APIC/FLIP Particle Grid Method with Conservative Resampling and Adaptive APIC/PIC Blending

Jiansheng Yao, Yingkui Zhao

TL;DR

This work identifies a long time RTI failure mode: particle depletion at spike heads degrades quadrature and particle grid coupling, producing nonphysical, void-like dents, and adds two sampling-aware controls: conservative split resampling that replenishes depleted cells while exactly conserving mass, momentum, and internal energy.

Abstract

Modeling inviscid compressible flows with shocks and vortex dominated dynamics remains challenging for particle grid methods due to moving discontinuities, cell crossing noise, and quadrature degradation under strong deformation. Building on a FLIP/APIC framework with vorticity aware tensor artificial viscosity, we identify a long time RTI failure mode: particle depletion at spike heads degrades quadrature and particle grid coupling, producing nonphysical, void-like dents. Standard mitigations (CPDI lite and subcell-jittered seeding) reduce but do not eliminate this artifact. We therefore add two sampling-aware controls: (i) conservative split resampling that replenishes depleted cells while exactly conserving mass, momentum, and internal energy; and (ii) a soft-switch that attenuates only the APIC affine term when local support is insufficient. Tests on the Sod shock tube and single/multi mode RTI show that the method removes spike head voids in long-time RTI while preserving vortex roll up, and matches reference Euler growth metrics

A Robust Compressible APIC/FLIP Particle Grid Method with Conservative Resampling and Adaptive APIC/PIC Blending

TL;DR

This work identifies a long time RTI failure mode: particle depletion at spike heads degrades quadrature and particle grid coupling, producing nonphysical, void-like dents, and adds two sampling-aware controls: conservative split resampling that replenishes depleted cells while exactly conserving mass, momentum, and internal energy.

Abstract

Modeling inviscid compressible flows with shocks and vortex dominated dynamics remains challenging for particle grid methods due to moving discontinuities, cell crossing noise, and quadrature degradation under strong deformation. Building on a FLIP/APIC framework with vorticity aware tensor artificial viscosity, we identify a long time RTI failure mode: particle depletion at spike heads degrades quadrature and particle grid coupling, producing nonphysical, void-like dents. Standard mitigations (CPDI lite and subcell-jittered seeding) reduce but do not eliminate this artifact. We therefore add two sampling-aware controls: (i) conservative split resampling that replenishes depleted cells while exactly conserving mass, momentum, and internal energy; and (ii) a soft-switch that attenuates only the APIC affine term when local support is insufficient. Tests on the Sod shock tube and single/multi mode RTI show that the method removes spike head voids in long-time RTI while preserving vortex roll up, and matches reference Euler growth metrics
Paper Structure (30 sections, 35 equations, 10 figures, 1 algorithm)

This paper contains 30 sections, 35 equations, 10 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Basic equations
  3. Governing equations
  4. Material point method basic equations
  5. Particle-to-grid (mass and momentum).
  6. Grid momentum equation and internal force.
  7. Grid-to-particle (velocity update) and advection.
  8. Thermodynamics and volume update.
  9. BASELINE RECAP AND FAILURE MODES
  10. Baseline performance on Richtmyer–Meshkov instability
  11. Nonphysical spike-head dent in long-time RTI evolution
  12. Method
  13. Particle–grid transfers (PIC/FLIP/APIC)
  14. CPDI-lite transfer for reduced quadrature bias
  15. Particle-to-grid (P2G) mass and momentum
  16. ...and 15 more sections

Figures (10)

  • Figure 1: Richtmyer–Meshkov instability in the FLIP–APIC + vorticity-aware tensor-AV baseline. Particles are colored by material (red/blue), illustrating post-shock interfsace roll-up at different time.
  • Figure 2: Single-mode RTI in the FLIP–APIC + tensor-AV baseline: a nonphysical spike-head dent/void-like depression develops in long-time evolution (highlighted region).
  • Figure 3: Single-mode RTI at $t=0.58$ with varying particles per cell (PPC, denoted $N_{pc}$). Increasing PPC alleviates the late-time spike-head "dent", indicating a sampling-driven origin.
  • Figure 4: Single-mode RTI at $t=0.58$ with $N_{pc}=36$: (a) 98% FLIP + 2% APIC; (b) 98% FLIP + 2% PIC. Replacing the APIC affine transfer by PIC removes the dent but noticeably damps fine-scale roll-up.
  • Figure 5: Ablation variants for single-mode RTI (representative late-time snapshot): (a) baseline: FLIP--APIC + tensor AV; (b) baseline + CPDI-lite (c) baseline + conservative split resampling; (d) baseline + CPDI-lite + affine soft-switch; (e) full method (baseline + CPDI-lite + split + soft-switch).
  • ...and 5 more figures