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DTSTART:19911015T033000
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DTSTAMP:20251218T030655Z
LOCATION:Meeting Room S221\, Level 2
DTSTART;TZID=Asia/Hong_Kong:20251218T095400
DTEND;TZID=Asia/Hong_Kong:20251218T100500
UID:siggraphasia_SIGGRAPH Asia 2025_sess149_papers_2284@linklings.com
SUMMARY:Wavelet Fluids
DESCRIPTION:Luan Lyu (Guangdong University of Technology); Xiaohua Ren (We
 Chat Vision, Tencent Inc.); Wei Cao (Qingdao University); Jian Zhu (Guangd
 ong University of Technology); Ziyang Ma (WeChat Vision, Tencent Inc.); an
 d Enhua Wu (Key Laboratory of System Software (Chinese Academy of Sciences
 ) and SKLCS, Institute of Software, Chinese Academy of Sciences, China; Un
 iversity of Macau)\n\nThis paper presents a novel wavelet-based framework 
 for simulating single-phase (e.g., smoke) and two-phase (e.g., bubbly wate
 r) flows, featuring unified boundary condition handling for free surfaces 
 and solid obstacles.\nIn liquid simulations, conventional pressure project
 ion methods solve a simplified pressure Poisson equation by enforcing zero
 -pressure Dirichlet conditions at free surfaces. However, these methods ig
 nore air-phase incompressibility, resulting in artificial bubble collapse.
  Stream function approaches address this limitation by solving a density-v
 ariable vector potential Poisson equation, ensuring incompressibility in b
 oth simulated and unsimulated regions while maintaining divergence-free li
 quid phases independent of solver accuracy. Yet, they triple the linear sy
 stem’s dimensionality and suffer from poor convergence with solid boundari
 es.\nThe core limitation of both methods lies in their governing equations
 : singularities arise as density approaches extreme values. The pressure P
 oisson equation becomes ill-conditioned when density nears zero (air phase
 ), compromising air-phase incompressibility, while the vector potential eq
 uation deteriorates as density approaches infinity (solid phase), hinderin
 g solid-boundary convergence.\nTo resolve these singularities, we first in
 troduce a novel decomposition where zero and infinite densities are well-d
 efined. We then reformulate this decomposition as a fixed-point iteration 
 using density-agnostic curl-free and divergence-free projections, eliminat
 ing the need for linear system solves. Finally, we develop an iterative al
 gorithm that alternately applies curl-free and divergence-free wavelet pro
 jections to efficiently solve the fixed-point problem.\nOur method concurr
 ently computes pressure and stream functions, retaining the incompressibil
 ity advantages of stream function approaches while overcoming their comput
 ational inefficiencies and solid-boundary convergence challenges. By lever
 aging the inherent parallelism of wavelet transforms, our framework enable
 s efficient GPU implementation, achieving substantial performance gains.\n
 \nRegistration Category: Full Access, Full Access Supporter\n\nSession Cha
 ir: Bo Ren (TMCC, College of Computer Science, Nankai University)\n\n
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