This IMA Volume in Mathematics and its Applications COMPUTATIONAL FLUID DYNAMICS AND REACTING GAS FLOWS is in part the proceedings of a workshop which was an integral part of the 1986-87 IMA program on SCIENTIFIC COMPUTATION. We are grateful to the Scientific Committee: Bjorn Engquist (Chairman), Roland Glowinski, Mitchell Luskin and Andrew Majda for planning and implementing an exciting and stimulating year-long program. We especially thank the Workshop Organizers, Bjorn Engquist, Mitchell Luskin and Andrew Majda, for organizing a workshop which brought together many of the leading researchers in the area of computational fluid dynamics. George R. Sell Hans Weinberger PREFACE Computational fluid dynamics has always been of central importance in scientific computing. It is also a field which clearly displays the essential theme of interaction between mathematics, physics, and computer science. Therefore, it was natural for the first workshop of the 1986- 87 program on scientific computing at the Institute for Mathematics and Its Applications to concentrate on computational fluid dynamics. In the workshop, more traditional fields were mixed with fields of emerging importance such as reacting gas flows and non-Newtonian flows. The workshop was marked by a high level of interaction and discussion among researchers representing varied "schools of thought" and countries.

This IMA Volume in Mathematics and its Applications COMPUTATIONAL WAVE PROPAGATION is based on the workshop with the same title and was an integral part of the 1994-1995 IMA program on "Waves and Scattering." We would like to thank Bjorn Engquist and Gregory A. Kriegsmann for their hard work in organizing this meeting and in editing the proceedings. We also take this opportunity to thank the National Science Foundation, the Army Research Office, and the Office of Naval Research, whose financial support made this workshop possible. A vner Friedman Robert Gulliver v PREFACE Although the field of wave propagation and scattering has its classical roots in the last century, it has enjoyed a rich and vibrant life over the past 50 odd years. Scientists, engineers, and mathematicians have devel oped sophisticated asymptotic and numerical tools to solve problems of ever increasing complexity. Their work has been spurred on by emerging and maturing technologies, primarily concerned with the propagation and reception of information, and the efficient transmission of energy. The vitality of this scientific field is not waning. Increased demands to precisely quantify, measure, and control the propagation and scattering of waves in increasingly complex settings pose challenging scientific and mathematical problems. These push the envelope of analysis and comput ing, just as their forerunners did 50 years ago. These modern technological problems range from using underwater sound to monitor and predict global warming, to periodically embedding phase-sensitive amplifiers in optical fibers to insure long range digital communication."

The first book to approach high oscillation as a subject of its own, Highly Oscillatory Problems begins a new dialogue and lays the groundwork for future research. It ensues from the six-month programme held at the Newton Institute of Mathematical Sciences, which was the first time that different specialists in highly oscillatory research, from diverse areas of mathematics and applications, had been brought together for a single intellectual agenda. This ground-breaking volume consists of eight review papers by leading experts in subject areas of active research, with an emphasis on computation: numerical Hamiltonian problems, highly oscillatory quadrature, rapid approximation of functions, high frequency wave propagation, numerical homogenization, discretization of the wave equation, high frequency scattering and the solution of elliptic boundary value problems.