Advancing our understanding in a wide range of scientific and engineering fields require the solution of the fluid equations over a very large range of densities and physical scales. These problems, which are not soluble on the current generation of computers, can be solved with the new generation of massively parallel high performance computers using object oriented languages and are likely to form one of the most important scientific applications of these machines. The MAE and Astrophysics departments at Princeton are at the forefront of research into the development of numerical algorithms and computer technology to utilize the next generation of machines in this effort. The engineering and scientific goals are the applications to aerodynamics (the design of airplanes, cars and ships); to turbulence research; and to structure formation in the universe. Progress in these different application areas requires a continuing research effort toward the development of algorithms amenable to parallel processing, automatic grid adaption, coloring schemes for domain decomposition of an arbitrary unstructured tetrahedral grid, and implementation of efficient message passing algorithms to reduce the communication costs on distributed memory architectures. These problems are generic, and not specific to a particular field of application. It is felt that a multi-disciplinary approach to the study of such problems would greatly benefit the training of students and enhance the effective use of high performance computing in research. The MAE and Astrophysics departments have collaborated in this effort in the past, and will continue to do so in the future. We request support for five graduate students to be trained in the design of algorithms for the numerical solution of partial differential equations using massively parallel computer platforms and the application of complex hydrocodes to engineering and physics problems ranging from turbulence research in aerodyna mics to the evolution of cosmological structure.
