A Thermomechanical Hybrid Incompressible Material Point Method

TL;DR

This work tackles the challenge of visually plausible solid combustion within physics-based simulation by integrating a sparse-grid material-point method (MPM) for solids with a hybrid Eulerian/FLIP incompressible flow solver for the gas phase. Key contributions include temperature-dependent elastoplastic models for burning solids, a novel smoke-particle sampling strategy near high-temperature regions, and an ignition mechanism that provides directable flame-front propagation. The framework supports 3D scenarios such as burning matches, incense, and logs, including mesh-based fracture to depict surface damage, while maintaining computational efficiency on modern hardware. Overall, the method offers artist-directed control over flame speed and combustion progression, enabling scalable, physically grounded fire effects in complex scenes.

Abstract

We present a novel hybrid incompressible flow/material point method solver for simulating the combustion of flammable solids. Our approach utilizes a sparse grid representation of solid materials in the material point method portion of the solver and a hybrid Eulerian/FLIP solver for the incompressible portion. We utilize these components to simulate the motion of heated air and particulate matter as they interact with flammable solids, causing combustion-related damage. We include a novel particle sampling strategy to increase Eulerian flow accuracy near regions of high temperature. We also support control of the flame front propagation speed and the rate of solid combustion in an artistically directable manner. Solid combustion is modeled with temperature-dependent elastoplastic constitutive modeling. We demonstrate the efficacy of our method on various real-world three-dimensional problems, including a burning match, incense sticks, and a wood log in a fireplace.

Figures (7)

• Figure 1: After transferring mass and momentum from the MPM object (green) to the MPM grid, we identify grid nodes on the MPM grid (black) that have positive mass. We mark solid pressure cells at pressure grid nodes (orange) that correspond to the MPM grid nodes with mass, and use a Neumann velocity boundary condition for the incompressible grid (blue) by dividing the grid momentum by grid mass at those grid nodes. The components of this velocity are then set as the face velocities of the solid pressure cell.
• Figure 2: After transferring the temperature from the MPM object (green) to the MPM grid, we overwrite the temperature grid nodes (pink), located at the cell centers of the incompressible grid (blue), with the MPM grid temperature from the MPM grid nodes that have positive mass (black). After updating the temperature on the temperature grid, we transfer the updated temperatures back to the MPM grid nodes with MPM mass, which we then transfer to the MPM particles. We then extrapolate the fluid temperature to the nodes on the temperature grid corresponding to the MPM grid nodes with positive mass (white/hollow pink).
• Figure 3: Squares are ignited at the center of the bottom edge of the domain. From the burning particles (red), we determine their neighboring particles on the surface that are hot enough and mark their status as about to burn (orange) after the time to ignite (determined by $c_\text{flame}$) is satisfied. At each step, we update a particle's fuel level according to the fuel coefficient $\gamma$, and once this fuel level has fallen below a fuel threshold, we mark the particle as burnt (gray). The burning status of particles from frames 100 and 600 are shown above and below, respectively.
• Figure 4: Views of the log example focusing on the shrinking and fracturing of the log. Yellow indicates internal faces of the log mesh that become exposed due to mesh-based fracture as the log shrinks and deforms.
• Figure 5: A log undergoes anisotropic shrinking and cracks as it burns. The mesh deforms, which we model with a post-process fracturing method. Frames 0, 300, 500, and 600 are shown.