An adaptive sampling approach to incompressible particle-based fluid

I propose a particle-based technique for simulating incompressible fluid that includes adaptive refinement of particle sampling. Each particle represents a mass of fluid in its local region. Particles are split into several particles for finer sampling in regions of complex flow. In regions of smooth flow, 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 fluid dynamics calculations, I use the hybrid FLIP method, which is computationally simple and efficient. Since the fluid is incompressible, each particle has a volume proportional to its mass. A kernel function, whose effective 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 fluid particles and adaptive spatial sampling for the reconstruction of the velocity and pressure fields. Particle splitting allows a detailed sampling of fluid momentum in regions of complex flow. Particle merging, in regions of smooth flow, reduces memory and computational overhead. An octree structure is used to compute inter-particle interactions and to compute the pressure field. The octree supporting field-based calculations is adapted to provide a fine 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 flow 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 effects. This produces a finely detailed and realistic representation of surface motion.