Journal Article
Proceedings of the National Academy of Sciences, vol. 118, iss. 37, 2021
Authors
Jacob Price, Brek Meuris, Madelyn Shapiro, Panos Stinis
Abstract
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.
