This project had two objectives in using Lagrangian techniques and their application in flows. The first research thrust area was to develop a modeling technique that will allow for efficient computation of compressible flows which could include simulations involving both shock and turbulent behavior. Spatial averaging of the nonlinear convective term was applied to the Burgers and Euler equations. The second research thrust area was the development of Lagrangian averaging ...
We have derived, in a mathematically precise way, Lagrangian-averaged models for incompressible and compressible flow. This work has now appeared in the SIAM Journal "Multiscale Modeling and Simulation;" Bhat, Fetecan, Marsden Mohseni, and West. That work lays important foundations for our computational work on the averaged equations as a computational tool for shocks.
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