Optimal renormalization of multiscale systems

Price, Jacob; Meuris, Brek; Shapiro, Madelyn; Stinis, Panos

doi:10.1073/pnas.2102266118

Optimal renormalization of multiscale systems

Journal Article · Wed Sep 08 00:00:00 EDT 2021 · Proceedings of the National Academy of Sciences of the United States of America

DOI:https://doi.org/10.1073/pnas.2102266118· OSTI ID:1819994

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Department of Mathematics and Computer Science, University of Puget Sound, Tacoma, WA 98416,
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195,
Department of Mathematics and Computer Science, University of Puget Sound, Tacoma, WA 98416,, Computing &, Analytics Division, Pacific Northwest National Laboratory, Richland, WA 99354,
Department of Applied Mathematics, University of Washington, Seattle, WA 98195,, Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, Richland, WA 99354

Significance

Many systems involve more variables than can be reasonably simulated. Even when only some of these variables are of interest, they usually depend strongly on the other variables. Reduced order models of the relevant variables, which behave as those variables would in a full simulation, are of great interest. Many such models involve a “memory” term that is difficult to compute and can lead to instability if not properly approximated. We have developed a time-dependent renormalization approach to stabilize such models. We validate the approach on the inviscid Burgers equation. We use it to obtain a perturbative renormalization of the three-dimensional Euler equations of incompressible fluid flow including all the complex effects present in the dynamics.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 1819994

Alternate ID(s):: OSTI ID: 1827275

Journal Information:: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 37 Vol. 118; ISSN 0027-8424

Publisher:: Proceedings of the National Academy of SciencesCopyright Statement

Country of Publication:: United States

Language:: English

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