A Fast Iterated Orthogonal Projection Framework for Smoke Simulation.

Area of Science:

• Computer Graphics
• Computational Physics
• Numerical Analysis

Background:

• Smoke simulation is computationally intensive, often limited by the speed of Poisson solvers.
• Existing Iterated Orthogonal Projection (IOP) methods can suffer from slow convergence.
• Efficient solvers are crucial for real-time or high-fidelity simulations.

Purpose of the Study:

• To present a significantly accelerated Iterated Orthogonal Projection (IOP) framework for fluid simulations.
• To improve the convergence rate and reduce computational cost of smoke simulations.
• To introduce a novel divergence redistributor and Multigrid-based Poisson solver.

Main Methods:

• Modified the IOP framework with a divergence redistributor component.
• Integrated Jacobi, Gauss-Seidel (GS), and Successive Over-Relaxation (SOR) as divergence redistributors.
• Employed a Multigrid scheme to construct an efficient Poisson solver.
• Tested performance against the Incomplete Cholesky Preconditioned Conjugate Gradient (ICPCG) solver.

Main Results:

• The new framework requires only 2-3 iterations for 1e-5 and 5-7 iterations for 1e-10 convergence.
• Achieved 7- to 30-fold speedup compared to ICPCG on grids from 128^3 to 256^3.
• Demonstrated independence of iteration count from problem size, enabling greater acceleration on larger grids.
• Presented a method to support free surfaces for both IOP and the fast IOP.

Conclusions:

• The proposed fast IOP framework with a Multigrid Poisson solver dramatically enhances smoke simulation efficiency.
• The divergence redistributor effectively overcomes convergence limitations of standard IOP.
• This method offers a substantial performance improvement for large-scale fluid simulations.