Parallel algorithms applied to problems in two dimensional detonation shock dynamics

This design and applications project consists in the development of a parallel extension for a two-dimensional Detonation Shock Dynamics code, and to demonstrate how it can be applied for solving engineering problems in detonation physics. Detonation Shock Dynamics (DSD) is an asymptotic theory that describes the evolution of a multidimensional curve detonation shock in terms of an intrinsic evolution equation for the shock surface. Full-LS-DSD2D is a full level set Detonation Shock Dynamics code in Fortran 77 written by Dr. John Bdzil specifically for this project. A level set function numerical algorithm which embeds the two-dimensional detonation front in a three-dimensional filed function, phi(x,y,t), is used to solve for the location of the detonation front, which is given by phi(x,y,t) = 0. The code solves a modified Level Set PDE which maintains phi(x,y,t) as a distance function and uses a fully explicit. A parallel extension of the code was designed, IPC-DSD2D (Illinois Parallel Cluster DSD2D), as a Message Passing model using an MPI interface. IPC-DSD2D was benchmarked for scalability, accuracy and overall performance. Benchmarking was performed on a vertical rate stick problem that had ideal load balancing properties. The test problem was run on three different computer architectures: the Turing Cluster at the University of Illinois Urbana-Champaign, an eight core Macintosh Mac Pro, and NCSA???s SGI Altix (Cobalt).The benchmarking of the code showed very good performance metrics; the speedup and efficiency where high, and behaved in a stable and predictable pattern. After the code was verified and tested for performance and efficiency, it was used in a shape optimization study. A multicomponent nonlinear optimization system was built to generate optimal, shaped charge geometries using Detonation Shock Dynamics. The idea was to use IPC-DSD2D to estimate the shock pressure along a shaped charge liner and the normal shock velocity at the apex of the liner. These flow variables were then to be used as inputs for a Lagrangian finite element code to determine the shape of the jet that is formed by the detonation shock pressure crushing the liner. Through a set of constrained objective functions, a nonlinear optimizer, a shape can be found that has optimal jet properties. By running a DSD simulation of a simplified shaped charge, it was successfully shown how DSD could be used in the design of shaped charges. This thesis only describes the optimization system, and did not simulate the design loop. This thesis is divided into ten chapters. Chapters 1 and 2 briefly describe the theory of DSD and some necessary concepts in parallel computing design. Chapters 3 through 5 talk about the mathematical and numerical model used in DSD2D, and the parallel implementation of the code. Chapter 6 shows numerical results using IPC-DSD2D and Chapter 7 shows the parallel benchmarking of the code using the three computer architectures mentioned earlier. Chapter 8 describes the optimization system using DSD to find optimal shape charge geometries. Chapter 9 shows how to extend IPC-DSD2D for a three-dimensional DSD code [5]. Chapter 10 has the conclusions and final thoughts about the parallel implementation of Full-LS-DSD2D and the optimization system for designing shape charges using DSD