Wave tracking in complex geometries

An extension of the standard level-set method is developed to track the motion of moving fronts, with applications to detonation shock dynamics (DSD) and other moving-boundary problems. For DSD, the shock surface angle boundary condition is included in the formulation.; To carry out front (wave) tracking in complex geometries, we use the level-set method in two reciprocal procedures—a front parameterization procedure G: $F\to C$ and a field construction procedure G−1 : $C\to F$, to represent the fronts as level sets embedded in narrow surrounding bands. High-order interpolating polynomials are extensively used to ensure the accuracy of normal derivatives, front curvatures, and attachment angles.; For the dynamically changing, banded computational set associated with the embedded surface, we have devised three data structures, ADDRESSMATRIX, BAND-SET, and SURFACE, and an algorithm we call the stack sweep algorithm, to construct and manage these data structures efficiently. The field construction algorithm uses the fast marching method for the surface velocity extension in both two and three dimensions.; An integrated software framework has been developed specifically for the explosive's engineering application, as a part of the thesis. This framework allows the user to develop quickly the DSD-based motion rule and related quantities for the explosive shock front and obtain all the related boundary conditions, given a geometric design.; A new equation of state (EOS) for a reactive, non-ideal explosive was developed to be used in the explosive applications. The new EOS was based on the earlier work of W. C. Davis, who developed equations of state for the reactants and products separately. The new EOS presents a plausible way to generate a tractable one that fits experimental data and that can be used for DSD theory. It can also be used as an input to the integrated software framework.