We propose a novel formulation of the projection method for Smoothed Particle Hydrodynamics (SPH). We combine a symmetric SPH pressure force and an SPH discretization of the continuity equation to obtain a discretized form of the pressure Poisson equation (PPE). In contrast to previous projection schemes, our system does consider the actual computation of the pressure force. This incorporation improves the convergence rate of the solver. Furthermore, we propose to compute the density deviation based on velocities instead of positions as this formulation improves the robustness of the time-integration scheme. We show that our novel formulation outperforms previous projection schemes and state-of-the-art SPH methods. Large time steps and small density deviations of down to 0.01 percent can be handled in typical scenarios. The practical relevance of the approach is illustrated by scenarios with up to 40 million SPH particles.

The simulation of believable, photorealistic fire is difficult because fire is highly detailed, fast-moving, and turbulent. Traditional gridbased simulation models require large grids and long simulation times to capture even the coarsest levels of detail. In this paper, we propose a novel combination of coarse particle grid simulation with very fine, view-oriented refinement simulations performed on a GPU. We also propose a simple, GPU-based volume rendering scheme. The resulting images of fire produced by the proposed techniques are extremely detailed and can be integrated seamlessly into film-resolution images. Our refinement technique takes advantage of perceptive limitations and likely viewing behavior to split the refinement stage into separable, parallel tasks. Multiple independent GPUs are employed to rapidly refine final simulations for rendering, allowing for rapid artist turnaround time and very high resolutions. Directability is achieved by allowing virtually any user-defined particle behavior as an input to the initial coarse simulation. The physical criteria enforced by the coarse stage are minimal and could be easily implemented using any of the wide variety of commercially available fluid simulation tools. The GPU techniques utilized by our refinement stage are simple and widely available on even consumer-grade GPUs, lowering the overall implementation cost of the proposed system.