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In many problems, one wants to track an interface propagating with complex physics through a medium. In several of these calculations, a great deal of resolution is often required. For example, to accurately compute turbulent combustion processes, the amount of resolution required is infeasible for many practical uses. Tracking the full set of kinetics and chemistry is impractical if one wants to embed this problem into more complex problems, such as in boilers, furnaces, or internal combustion engines. An attractive alternative is to use highly resolved specialized calculations to build models that can capture the correct multi−scale physics inside a far larger calculation.
My research is in developing adaptive mesh, high order level set methods, to track moving interfaces in combustion fluid flow solvers, in order to design such models. Level set methods are powerful techniques that implicitly track moving interfaces as the zero level set of a function, which is evolved by solving an initial value problem. The main advantage of using this Eulerian framework is that the interface location is precisely calculated even when sharp corners develop, which is critical when the behavior depends on its geometry.
In order to properly capture the chemistry of a system, the behavior of the interface must be carefully coupled with the flow solvers. In particular, we need to understand the mathematics of how to match chemistry inside the flame front to a macro−model across the flame front. This will require multi−scale analysis, homogenization theory, and an understanding of the interaction of the flame geometry with transport of curvature and species. While a few specialized adaptive versions have been built, my goal is to provide a complete methodology to solve a host of fluid problems, including simulation of boilers and combustion furnaces, mantle convection, and type Ia supernovae flames.
-Benedetto, J.J.; Donatelli, J.; Konstantinidis, I.; Shaw, C., A Doppler statistic for zero autocorrelation waveforms, 2006 40th Annual Conference on Information Sciences and Systems, March 2006 Page(s):1403 - 1407.
-Benedetto, John J. ; Donatelli, Jeffrey ; Konstantinidis, Joannis ; Shaw, Christopher, Zero Autocorrelation Waveforms: A Doppler Statistic and Multifunction Problems, ICASSP 2006 Proceedings. 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, 2006. May 2006, Volume: 5, On page(s): V-V.
-Benedetto, J.J.; Donatelli, J.J., Ambiguity Function and Frame-Theoretic Properties of Periodic Zero-Autocorrelation Waveforms, IEEE Journal of Selected Topics in Signal Processing, Volume 1, Issue 1, June 2007 Page(s):6 - 20.
-Benedetto, J.J.; Donatelli, J.J, Frames and a Vector Valued Ambiguity Function, Asilomar Conference on Signals, Systems, and Computers, October 2008.
-Benedetto, J.J.; Donatelli, J.J., Ambiguity functions for vector-valued periodic codes, to be submitted (2010).
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