Ignis Divinus

Final Report - CS 184 Summer 2025

Abstract

Technical Approach

Core Simulation Architecture

Our fire simulation system is built on a 3D grid-based fluid solver implementing the incompressible Navier-Stokes equations. We chose a Semi-Lagrangian advection scheme for its unconditional stability, allowing larger time steps without numerical explosion. The simulation operates on a staggered MAC (Marker-And-Cell) grid where velocity components are stored at cell faces and scalar quantities (density, temperature) at cell centers. The core solver performs these steps each frame:

• Advection: Semi-Lagrangian backward particle trace for stability
• Buoyancy: Temperature-driven forces using α(ρ - ρ₀) + β(T - T₀)
• Pressure Projection: 40 Jacobi iterations to enforce incompressibility
• Dissipation: Per-second rates for velocity (20/s), density (1/s), temperature (1/s)

Rendering Pipeline

We implemented a ray marching-based volume renderer that directly integrates emission and absorption along view rays. The renderer uses physically-based blackbody radiation to map temperature values to colors. Key innovations include:

• 256-step adaptive ray marching with early termination when opacity > 0.95
• Blackbody radiation lookup table for temperatures 800K-3000K
• Emission-absorption model: L = L₀e^(-κρt) + ε(1 - e^(-κρt))
• Screen-space heat refraction using temperature gradient displacement

Comparison with Reference Approaches

Challenges and Solutions

Problem 1: Numerical Instability. Initial implementation suffered from velocity field explosion at high temperatures. We solved this by implementing Semi-Lagrangian advection with CFL-based adaptive time stepping (dt = min(0.066, 0.5 * dx/|v|_max)) and added numerical dissipation.

Problem 2: Unrealistic Flame Motion. Flames appeared too laminar. We added vorticity confinement (ε = 6.0) to restore small-scale rotational motion lost to numerical dissipation, and introduced stochastic fuel injection for natural flickering.

Problem 3: Performance Bottlenecks. Initial ray marcher achieved only 5-10 FPS. We implemented adaptive step sizes, early termination, and moved all computation to GPU kernels via Taichi, achieving 6x performance improvement.

Lessons Learned

• Stability vs Accuracy Trade-off: Semi-Lagrangian methods sacrifice some accuracy for unconditional stability, but this is acceptable for visual applications where stability is paramount.
• Importance of Physical Models: Using blackbody radiation for color mapping made a dramatic difference in realism compared to ad-hoc color gradients.
• GPU Memory Patterns Matter: Coalesced memory access patterns in Taichi kernels provided 2-3x speedup over naive implementations.
• Post-processing Impact: Simple effects like bloom and heat refraction contribute disproportionately to perceived quality with minimal performance cost.

Results

Our system achieves real-time performance across multiple quality presets. At high quality (96³ grid, 256 ray steps), we maintain 30+ FPS while producing visually compelling fire effects. The frame time breakdown shows: Fluid Simulation (40%), Volume Rendering (50%), Post-processing (7%), Other (3%).

Team Contributions

References