Optimal spatiotemporal reduced order modeling of the viscous Burgers equation

Authors:
A. Labryer;P. J. Attar;P. Vedula
Affiliations:
-;-;-
Venue:
Finite Elements in Analysis and Design
Year:
2014

Citing 7
Cited 0

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Abstract

The one-dimensional viscous Burgers equation with a time-periodic inflow boundary condition is investigated within the context of a newly developed optimal spatiotemporal reduced order modeling (OPSTROM) framework. Flow simulations are carried out with a conventional finite-difference scheme, and are expedited by coarsening the computational grid in space and time. The OPSTROM framework is used to maintain reliable predictions for the flow by constructing interactive subgrid-scale models to account for the effects due to unresolved spatial and temporal scales. Model construction is data-driven, and is based upon principles of mean-square error minimization, conditional expectations and stochastic estimation. The results indicate a need to model both subgrid spatial and temporal scales in order to improve the accuracy of under-resolved simulations.