EAPSI: Establishing New Mathematical Methods for Analyzing Simulated Models of Fuel Combustion

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A form of internal combustion called homogeneous-charge compression ignition (HCCI) results in relatively low emissions and high efficiency. The fuel and oxidizer are mixed and then compressed to the point of auto-ignition, though it is currently unknown how to control the exact timing of the ignition, an aspect that requires a precise understanding in order to be implemented commercially. Dr. Takashi Ishihara of Nagoya University has hypothesized that introducing stirring, or movement, in the fuel flow field will control the timing of the onset of ignition, and initial studies on simulated data support this idea. In this project, the EAPSI fellow will study 3D combustion simulations to understand how introducing a flow in the fuel chamber controls the timing of the onset of ignition. This investigation will require the development of new mathematical tools, which in turn will have further implications in problems of fluid analysis, e.g. weather simulations and the study of ocean currents.Numerical simulations of time-varying 3D fluid models tracking temperature, velocity, and chemical species, will be studied using a mathematical tool in topological data analysis called persistent homology. With this method, each time point in the simulation will generate a collection of mathematical objects called persistence diagrams, which encode the relationships of the critical points of the simulated data (e.g. local minima, maxima, and saddle points). This data will then be mined using established statistical techniques to uncover correlations with existing measurements of interest to physicists and gain insight into the mechanisms by which the dynamics of the fluid control the timing of the onset of ignition. This award under the East Asia and Pacific Summer Institutes program supports summer research by a U.S. graduate student and is jointly funded by NSF and the Japan Society for the Promotion of Science.