An Eulerian approach to fluid flow provides an efficient, stable paradigm for realistic fluid simulation. However, its traditional reliance on a fixed-resolution grid is not ideal for simulations that simultaneously exhibit both large and small-scale fluid phenomena. Octree-based fluid simulation approaches have provided the needed adaptivity, but the inherent weakness of a pointer-based tree structure has limited their effectiveness. We present a linear octree structure that provides a significant runtime speedup using these octree-based simulation algorithms. As memory prices continue to decline, we leverage additional memory when compared to traditional octree structures to provide this improvement. In addition to reducing the level of indirection in the data, because our linear octree is stored contiguously in memory as a simple C array rather than a recursive set of pointers, we provide a more cache-friendly data layout than a traditional octree. In our testing, our approach yielded run-times that were 1.5 to nearly 5 times faster than the same simulations running on a traditional octree implementation.

The investigation of the dynamics of chemical reactions, both from the theoretical and experimental side, has drawn an increasing interest since Ahmed H. Zewail was awarded the 1999 Nobel Prize in Chemistry for his work on femtochemistry. On the experimental side, new techniques such as femtosecond lasers and attosecond lasers enable laser control of chemical reactions. Numerical simulations serve as a valuable complement to experimental techniques, not only for validation of experimental results, but also for simulation of processes that cannot be investigated through experiments. With increasing computer capacity, more and more physical phenomena fall within the range of what is possible to simulate. Also, the development of new, efficient numerical methods further increases the possibilities. The focus of this thesis is twofold; numerical methods for chemical reactions including dissociative states and methods that can deal with coexistence of spatial regions with very different physical properties. Dissociative chemical reactions are reactions where molecules break up into smaller components. The dissociation can occur spontaneously, e.g. by radioactive decay, or be induced by adding energy to the system, e.g. in terms of a laser field. Quantities of interest can for instance be the reaction probabilities of possible chemical reactions. This thesis discusses a boundary treatment model based on the perfectly matched layer (PML) approach to accurately describe dynamics of chemical reactions including dissociative states. The limitations of the method are investigated and errors introduced by the PML are quantified. The ability of a numerical method to adapt to different scales is important in the study of more complex chemical systems. One application of interest is long-range molecules, where the atoms are affected by chemical attractive forces that lead to fast movement in the region where they are close to each other and exhibits a relative motion of the atoms that is very slow in the long-range region. A numerical method that allows for spatial adaptivity is presented, based on the summation-by-parts-simultaneous approximation term (SBP-SAT) methodology. The accuracy and the robustness of the numerical method are investigated. / eSSENCE

As the fidelity of computer generated imagery has increased, the need to digitally create convincing natural phenomena like fluids has become fundamental to the entertainment production industry. Because fluids are complex, the underlying physics must be computationally simulated. However, because a strictly physics-based approach is both computationally expensive and difficult to control, it does not lend itself well to the way artists and directors like to work. Directors require control to achieve their specific artistic vision. Furthermore, artistic workflows rely on quick iteration and the ability to apply changes late in the production process. In this dissertation we present novel techniques in adaptive simulation and fluid post-processing to improve artistic workflows for fluid simulation. Our methods reduce fluid simulation iteration time and provide a new way for artists to intelligently resize a wide range of volumetric data including fluid simulations. To reduce iteration time, we present a more cache-friendly linear octree structure for adaptive fluid simulation that reduces the overhead of previous octree-based methods. To increase the viability of reusable effects libraries, and to give artists intuitive control over simulations late in the production process we present a ``fluid carving" technique. Fluid carving uses seam carving methods to allow intelligent resizing on a variety of fluid phenomena without the need for costly re-simulation. We present methods that improve upon traditional seam carving approaches to address issues with scalability, non-rectangular boundaries, and that generalize to a variety of different visual effects data like particles, polygonal meshes, liquids, smoke, and fire. We achieve these improvements by guiding seams along user-defined lattices that can enclose regions of interest defined as OpenVDB grids with a wide range of shapes. These techniques significantly improve artist workflows for fluid simulation and allow visual entertainment to be produced in a more intuitive, cost-effective manner.