Spatiotemporal FLIP for Fast Free-Surface and Two-Phase Simulation With Very Large Time Steps

ACM Transactions on Graphics, vol. 45, pp. 1–20

Abstract

We present ST-FLIP, a spatiotemporal extension of the Fluid-Implicit Particle (FLIP) method for incompressible free-surface and two-phase liquid simulation. ST-FLIP enables time steps up to an order of magnitude larger than those typically used in CFL-constrained solvers, while preserving detailed flow structures and visual fidelity. It addresses a common failure mode of large time steps in hybrid particle-grid liquid solvers: temporal under-sampling of particle motion produces aliasing-driven free-surface artifacts after projection. Our key idea is to interpret particles as samples in four-dimensional space-time: in addition to standard spatial jittering, we randomize particle positions along the time axis as well and perform particle-to-grid deposition using a separable 4D kernel. This yields a Monte Carlo estimator of perstep time-slab-integrated particle quantities. Although particles are treated as samples in 4D space-time, our approach works as a lightweight plugin by collapsing to slab-integrated 3D grid fields for projection. Building on recent particle-based phase-field work, we reuse the particle-to-grid weight accumulators as a conceptual space-time phase field, providing variable-coefficient projection weights and eliminating the need for per-step surface reconstruction. The method can be easily integrated into existing FLIP/PIC or APIC solvers with negligible additional computational cost per time step. The effectiveness of our approach is demonstrated through a series of comparisons with state-of-the-art solvers, yielding several-fold speedups for multi-billion-particle simulations at high effective 3D resolutions on a single workstation.

Authors 4

1. Bernhard Braun

   Technical University of Munich

   Affiliation as printed

   Technical University Munich, Rauenberg, Germany

2. Rene Winchenbach

   Technical University of Munich

   Affiliation as printed

   Technical University Munich, Munich, Germany

3. Jan Bender Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

4. Nils Thuerey

   Technical University of Munich

   Affiliation as printed

   Technical University Munich, Munich, Germany