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

Jiansheng Yao, Yingkui Zhao|arXiv (Cornell University)|Mar 4, 2026

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TL;DR

The paper extends FLIP–APIC with tensor artificial viscosity by adding conservative resampling and a soft-switching APIC/PIC blend to fix long-time RTI spike-head voids while preserving vortical dynamics.

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

Motivation & Objective

• Address sampling-induced failure modes in compressible particle–grid solvers during long-time RTI and shock-dominated flows.
• Develop sampling-aware controls to restore local quadrature quality and stabilize affine APIC components.
• Retain the robustness of tensor artificial viscosity while preserving vortex-rich advection in well-sampled regions.
• Demonstrate effectiveness on Sod shock tube and single-/multi-mode RTI benchmarks.

Proposed method

• Adopt CPDI-lite transfers to reduce quadrature bias under imperfect particle distributions.
• Introduce conservative split resampling to replenish depleted cells with exact conservation of mass, momentum, and internal energy.
• Implement a cell-wise soft-switch that attenuates the APIC affine term toward PIC-like behavior when local particle support is insufficient.
• Use a bi-indicator gating for APIC affine contributions based on local support and flow features.
• Combine FLIP–APIC transfers with vorticity-aware tensor artificial viscosity to stabilize shocks while preserving vortical structures.
• Leak the APIC affine term only in under-sampled regions to prevent spurious energy injection.

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.

Experimental results

Research questions

• RQ1 Can sampling-induced under-sampling near spike heads in long-time RTI cause nonphysical denting or voids in compressible particle–grid simulations?
• RQ2 Do conservative resampling and adaptive APIC/PIC blending mitigate spike-head voids without sacrificing vortex roll-up fidelity?
• RQ3 How do CPDI-lite transfers and subcell jittering interact with the proposed controls to improve long-time stability?
• RQ4 Does the augmented method preserve benchmark Euler growth metrics and shock-capturing performance?

Key findings

• Conservative split resampling replenishes depleted cells while exactly conserving mass, momentum, and internal energy, restoring local quadrature quality.
• Soft-switching the APIC affine term toward PIC-like transfers prevents affine-instability in depleted regions while retaining APIC benefits in well-sampled zones.
• CPDI-lite transfers plus subcell jittering reduce grid imprinting and quadrature bias, mitigating spike-head artifacts.
• The full method removes spike-head dents in long-time RTI while preserving vortex roll-up and aligns with reference Euler growth metrics.
• Baseline RM/RTI tests show robust shock capturing and improved shear-layer fidelity compared to the unmodified APIC/FLIP framework.

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).