Vortex methods increasingly receive attention from the computer graphics community for simple and direct modeling of complex flow phenomena such as turbulence. The coupling between free-form solids, represented by arbitrary surface meshes, and fluids simulated with vortex methods, leads to visually rich simulations. In this paper, we introduce a novel approach for simulating the interaction between solids and inviscid fluids for high-quality simulations using Lagrangian vortex particles. The key aspect of our method is simulating the creation of vorticity at a solid's surface. While previous vortex simulators only focus on modeling the solid as a boundary for the fluid, our approach allows the accurate simulation of two processes of visual interest. The first is the introduction of surface vorticity in the main flow as turbulence (vortex shedding). The second is the motion of the solid induced by fluid forces. We also introduce to computer graphics the concept of source panels to model nonturbulent flow around objects. To the best of our knowledge, this is the first work on two-way coupling of 3D solids and fluids using Lagrangian vortex methods in computer graphics.

Abstract When simulating fluids, tetrahedral methods provide flexibility and ease of adaptivity that Cartesian grids find difficult to match. However, this approach has so far been limited by two conflicting requirements. First, accurate simulation requires quality Delaunay meshes and the use of circumcentric pressures. Second, meshes must align with potentially complex moving surfaces and boundaries, necessitating continuous remeshing. Unfortunately, sacrificing mesh quality in favour of speed yields inaccurate velocities and simulation artifacts. We describe how to eliminate the boundary‐matching constraint by adapting recent embedded boundary techniques to tetrahedra, so that neither air nor solid boundaries need to align with mesh geometry. This enables the use of high quality, arbitrarily graded, non‐conforming Delaunay meshes, which are simpler and faster to generate. Temporal coherence can also be exploited by reusing meshes over adjacent timesteps to further reduce meshing costs. Lastly, our free surface boundary condition eliminates the spurious currents that previous methods exhibited for slow or static scenarios. We provide several examples demonstrating that our efficient tetrahedral embedded boundary method can substantially increase the flexibility and accuracy of adaptive Eulerian fluid simulation.

This article introduces the Hierarchical Run-Length Encoded (H-RLE) Level Set data structure. This novel data structure combines the best features of the DT-Grid (of Nielsen and Museth [2004]) and the RLE Sparse Level Set (of Houston et al. [2004]) to provide both optimal efficiency and extreme versatility. In brief, the H-RLE level set employs an RLE in a dimensionally recursive fashion. The RLE scheme allows the compact storage of sequential nonnarrowband regions while the dimensionally recursive encoding along each axis efficiently compacts nonnarrowband planes and volumes. Consequently, this new structure can store and process level sets with effective voxel resolutions exceeding 5000 × 3000 × 3000 (45 billion voxels) on commodity PCs with only 1 GB of memory. This article, besides introducing the H-RLE level set data structure and its efficient core algorithms, also describes numerous applications that have benefited from our use of this structure: our unified implicit object representation, efficient and robust mesh to level set conversion, rapid ray tracing, level set metamorphosis, collision detection, and fully sparse fluid simulation (including RLE vector and matrix representations.) Our comparisons of the popular octree level set and Peng level set structures to the H-RLE level set indicate that the latter is superior in both narrowband sequential access speed and overall memory usage.

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