This is a grant under the Scientific Computing Research Equipment for the Mathematical Sciences program of the Division of Mathematical Sciences of the National Sciences Foundation. This program supports the purchase of special purpose computing equipment dedicated to the conduct of research in the mathematical sciences. This equipment is required for several research projects and would be difficult to justify for one project alone. Support from the National Science Foundation is coupled with discounts and contributions from manufacturers and with substantial cost-sharing from the institutions submitting the proposal. This program is an example of academic, corporate, and government cooperation in the support of the basic research in the mathematical sciences. This equipment will be used to support four projects in the Aerospace Engineering Department of University of Michigan, Ann Arbor: multidimensional schemes for the Euler equations, Ken Powell, Phil Roe, and Bram van Leer participating faculty; fundamentals of vortical flows, Ken Powell participating faculty; improving the efficiency of explicit Euler codes, Ken Powell and Bram van Leer participating faculty; adaptive grid refinement methods, Ken Powell and Phil Roe participating faculty.