Level set methods applied to modeling detonation shock dynamics

We give an extension of the level set formulation of Osher and Sethian, which describes the dynamics of surfaces that propagate under the influence of their own curvature. We consider an extension of their original algorithms for finite domains that includes boundary conditions. We discuss this extension in the context of a specific application that comes from the theory of detonation shock dynamics (DSD). We give an outline of the theory of DSD which includes the formulation of the boundary conditions that comprise the engineering model. We give the formulation of the level set method, as applied to our application with finite boundary conditions. We develop a numerical method to implement arbitrarily complex 2D boundary conditions and give a few representative calculations. We also discuss the dynamics of level curve motion and point out restrictions that arise when applying boundary conditions. (C) 1996 Academic Press, Inc.