Implicit Position-Based Fluids (IPBF)
The efficient simulation of incompressible fluids remains a difficult and open problem. Prior works often make various tradeoffs between incompressibility, stability, and cost. Yet, it is rare to obtain all three. In this paper, we introduce a novel incompressible Smoothed Particle Hydrodynamics (SPH) scheme which uses a second-order implicit descent scheme to optimize a variational energy specially formulated to approach incompressibility. We demonstrate that our method is superior in both incompressibility and stability with a minimal cost to computational budget. Furthermore, we demonstrate that our method is unconditionally stable even under extreme time steps, making it suitable for interactive applications.
Results
Velocity-based methods IISPH (Implicit Incompressible SPH) and DFSPH (Divergence-Free SPH) fail to maintain numerical stability. While position-based methods PBF(Position-Based Fluids), SISPH (Semi-Implicit SPH), and our IPBF (Implicit Position-Based Fluids) remain stable, PBF suffers from excessive compression and SISPH produces noisy results. Our IPBF produces stable results with minimal compression.
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