ABSTRACT CTS-9521373 An Engineering description of multi-phase flows by necessity must be made on the basis of macroscopic equations in which the phase inhomogeneties are accounted for in an average sense, rather than in detail. The difficulty in formulating the models resides in the fact that any averaging procedure applied to the fundamental equations of continuum mechanics leads to models containing more unknowns than equations. The fundamental problem is then that of closing the equation set, namely of determining "constitutive relations" that express some unknown quantities in terms of others. This is the central theme of the proposed research for the case of disperse flows, such as particles in a fluid phase. The problem will be attacked by relying on a new method for deriving averaged equations and on the state-of-the-art numerical direct-simulation techniques. Both tools have been previously developed under NSF support. The new averaging procedure expresses the unknown in terms of integrals over the particles surfaces that can readily be calculated from numerical simulations of the motion. The computations will be carried out by means of a space-time finite-element method implemented on massively parallel supercomputers. The insight into the structure of the equations that, if successful, will derive from this research promises to answer long-standing questions as to the mathematical structure of the equations and their relationship to observe phenomena. The enhancement of the numerical techniques necessary to carry out this research constitutes in itself a significant advancement in the current direct numerical simulation capabilities. This research will be carried out in conjunction with Professor Andres Prosperetti of the Johns Hopkins University who has a separate from NSF. ***
