AN ADAPTIVE SAMPLING APPROACH TO INCOMPRESSIBLE PARTICLE-BASED FLUID
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I propose a particle-based technique for simulating incompressible uid that includes adaptive re nement of particle sampling. Each particle represents a mass of uid in its local region. Particles are split into several particles for ner sampling in regions of complex ow. In regions of smooth ow, neghboring particles can be merged. Depth below the surface and Reynolds number are exploited as our criteria for determining whether splitting or merging should take place. For the uid dynamics calculations, I use the hybrid FLIP method, which is computationally simple and e cient. Since the uid is incompressible, each particle has a volume proportional to its mass. A kernel function, whose e ective range is based on this volume, is used for transferring and updating the particle's physical properties such as mass and velocity. In addition, the particle sampling technique is extended to a fully adaptive approach, supporting adaptive splitting and merging of uid particles and adaptive spatial sampling for the reconstruction of the velocity and pressure elds. Particle splitting allows a detailed sampling of uid momentum in regions of complex ow. Particle merging, in regions of smooth ow, reduces memory and computational overhead. An octree structure is used to compute inter-particle interactions and to compute the pressure eld. The octree supporting eld-based calculations is adapted to provide a ne spatial reconstruction where particles are small and a coarse reconstruction where particles are large. This scheme places computational resources where they are most needed, to handle both ow and surface complexity. Thus, incompressibility can be enforced even in very small, but highly turbulent areas. Simultaneously, the level of detail is very high in these areas, allowing the direct support of tiny splashes and small-scale surface tension e ects. This produces a nely detailed and realistic representation of surface motion.