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Modeling complex transport-dominated phenomena and reactive flows

Many phenomena of scientific and engineering interest involve mechanical, thermal, and chemical process co-evolving on multiple time and length scales.  As process models are refined to achieve predictive power, dynamical systems of massive scale and complexity may be produced, motivating approaches that can systematically produce compactly-represented high-fidelity reduced models. . These reduced models may then serve as efficient surrogates for the original systems, enabling efficient refinement and optimization of system designs; permitting detailed exploration of the parameter tradespace; and allowing quantification of response uncertainty arising from partially specified system properties.  Ideally, reduced models should also preserve key structural features (e.g., mass conservation of passivity) to ensure that they behave as “physically plausible’” surrogates.

The objective of this project is the development of rigorous mathematical and computational frameworks for structure-preserving model reduction, focused especially on systems having port-Hamiltonian structure and systems having neutral or retarded delay structure.  Port-Hamiltionian modeling provides a framework that is especially well-suited to complex nonlinear multiphysics settings.  Delay systems present distinct challenges tied to their fundamentally infinite-order character.  Both categories are important in modeling complex transport-dominated phenomena and reactive flows.  Key goals will be to provide accessible, scalable computational tools for model reduction that give immediate practical utility to scientists and engineers, and to derive diagnostic a priori/a posteriori estimates of response error produced by these reduced models.  Aside from these technical goals, this project will further serve to connect the vibrant research environment of Berlin with a research team in Virginia having deep complementary experience in dynamical systems, computational linear algebra, control theory, inverse problems, and a variety of application areas.

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