Abstract : Thin fluid sheets are visually important elements in particle-based fluid simulation; however, they are extremely difficult to represent due to numerical diffusion, particle sparsity, and topological instability. Existing particle-based thin fluid sheet preservation methods primarily rely on geometric criteria to insert particles into sparse regions, which often leads to non-physical hole filling, artificial mass increase, and instability caused by repeated split-collapse operations. In this paper, we propose a physically consistent framework for thin fluid sheet preservation using constraint-based particle insertion and temporal hysteresis. Unlike conventional approaches, the proposed method introduces physically motivated criteria such as local density, relative velocity, and a pairwise strain-rate proxy to clearly distinguish between sheet preservation and natural rupture. This allows the method to prevent unnecessary particle insertion in regions where the fluid should physically separate, resulting in more realistic topological evolution. In addition, we employ a constraint-based candidate generation strategy based on original fluid particles to prevent recursive particle proliferation, and we consider mass and momentum conservation during particle insertion and removal to minimize non-physical behavior. Furthermore, temporal hysteresis is applied to the collapse process so that particles are removed only when the collapse condition persists over a certain period, effectively reducing flickering caused by repeated split-collapse operations. Experimental results show that the proposed method maintains thin fluid sheet structures more stably and in a physically plausible manner compared to existing particle-based approaches, while suppressing unnecessary particle growth and improving temporal consistency. In particular, these improvements are achieved with only a modest computational overhead, since the additional operations are restricted to local thin-sheet analysis, rupture-aware candidate filtering, and lightweight hysteresis tracking, while unnecessary particle growth is suppressed.

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