Presentation
Wavelet Fluids
DescriptionThis paper presents a novel wavelet-based framework for simulating single-phase (e.g., smoke) and two-phase (e.g., bubbly water) flows, featuring unified boundary condition handling for free surfaces and solid obstacles.
In liquid simulations, conventional pressure projection methods solve a simplified pressure Poisson equation by enforcing zero-pressure Dirichlet conditions at free surfaces. However, these methods ignore air-phase incompressibility, resulting in artificial bubble collapse. Stream function approaches address this limitation by solving a density-variable vector potential Poisson equation, ensuring incompressibility in both simulated and unsimulated regions while maintaining divergence-free liquid phases independent of solver accuracy. Yet, they triple the linear system’s dimensionality and suffer from poor convergence with solid boundaries.
The core limitation of both methods lies in their governing equations: singularities arise as density approaches extreme values. The pressure Poisson equation becomes ill-conditioned when density nears zero (air phase), compromising air-phase incompressibility, while the vector potential equation deteriorates as density approaches infinity (solid phase), hindering solid-boundary convergence.
To resolve these singularities, we first introduce a novel decomposition where zero and infinite densities are well-defined. We then reformulate this decomposition as a fixed-point iteration using density-agnostic curl-free and divergence-free projections, eliminating the need for linear system solves. Finally, we develop an iterative algorithm that alternately applies curl-free and divergence-free wavelet projections to efficiently solve the fixed-point problem.
Our method concurrently computes pressure and stream functions, retaining the incompressibility advantages of stream function approaches while overcoming their computational inefficiencies and solid-boundary convergence challenges. By leveraging the inherent parallelism of wavelet transforms, our framework enables efficient GPU implementation, achieving substantial performance gains.
In liquid simulations, conventional pressure projection methods solve a simplified pressure Poisson equation by enforcing zero-pressure Dirichlet conditions at free surfaces. However, these methods ignore air-phase incompressibility, resulting in artificial bubble collapse. Stream function approaches address this limitation by solving a density-variable vector potential Poisson equation, ensuring incompressibility in both simulated and unsimulated regions while maintaining divergence-free liquid phases independent of solver accuracy. Yet, they triple the linear system’s dimensionality and suffer from poor convergence with solid boundaries.
The core limitation of both methods lies in their governing equations: singularities arise as density approaches extreme values. The pressure Poisson equation becomes ill-conditioned when density nears zero (air phase), compromising air-phase incompressibility, while the vector potential equation deteriorates as density approaches infinity (solid phase), hindering solid-boundary convergence.
To resolve these singularities, we first introduce a novel decomposition where zero and infinite densities are well-defined. We then reformulate this decomposition as a fixed-point iteration using density-agnostic curl-free and divergence-free projections, eliminating the need for linear system solves. Finally, we develop an iterative algorithm that alternately applies curl-free and divergence-free wavelet projections to efficiently solve the fixed-point problem.
Our method concurrently computes pressure and stream functions, retaining the incompressibility advantages of stream function approaches while overcoming their computational inefficiencies and solid-boundary convergence challenges. By leveraging the inherent parallelism of wavelet transforms, our framework enables efficient GPU implementation, achieving substantial performance gains.
Event Type
Technical Papers
TimeThursday, 18 December 20259:54am - 10:05am HKT
LocationMeeting Room S221, Level 2