We propose a datadriven correction reduced order model (DDCROM) framework for the numerical simulation of fluid flows, which can be formally written as DDCROM = GalerkinROM + Correction. The new DDCROM is constructed by using ROM spatial filtering and datadriven ROM closure modeling (for the Correction term). Furthermore, we propose a physicallyconstrained DDCROM (CDDCROM), which aims at improving the physical accuracy of the DDCROM. The new physical constraints require that the CDDCROM operators satisfy the same type of physical laws (i.e., the Correction term's linear component should be dissipative and the Correction term's nonlinear component should conserve energy) as those satisfied by the fluid flow equations. To implement these physical constraints, in the datadriven modeling step, we replace the unconstrained least squares problem with a constrained least squares problem. We perform a numerical investigation of the new CDDCROM and standard DDCROM for a 2D channel flow past a circular cylinder at Reynolds numbers $Re=100, Re=500$, and $Re=1000$. To this end, we consider a reproductive regime as well as a predictive (i.e., crossvalidation) regime in which we use as little as 50% of the original training dWe propose a datadriven correction reduced order model (DDCROM) framework for the numerical simulation of fluid flows, which can be formally written as DDCROM = GalerkinROM + Correction. The new DDCROM is constructed by using ROM spatial filtering and datadriven ROM closure modeling (for the Correction term). Furthermore, we propose a physicallyconstrained DDCROM (CDDCROM), which aims at improving the physical accuracy of the DDCROM. The new physical constraints require that the CDDCROM operators satisfy the same type of physical laws (i.e., the Correction term's linear component should be dissipative and the Correction term's nonlinear component should conserve energy) as those satisfied by the fluid flow equations. To implement these physical constraints, in the datadriven modeling step, we replace the unconstrained least squares problem with a constrained least squares problem. We perform a numerical investigation of the new CDDCROM and standard DDCROM for a 2D channel flow past a circular cylinder at Reynolds numbers Re=100, Re=500$, and Re=1000. To this end, we consider a reproductive regime as well as a predictive (i.e., crossvalidation) regime in which we use as little as 50% of the original training data. The numerical investigation clearly shows that the new CDDCROM is significantly more accurate than the DDCROM in both regimes.ata. The numerical investigation clearly shows that the new CDDCROM is significantly more accurate than the DDCROM in both regimes.
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PhysicallyConstrained DataDriven Correction for Reduced Order Modeling of Fluid Flows
Research Group:
Traian Iliescu
Institution:
Virginia Tech
Location:
A133
Schedule:
Tuesday, July 3, 2018  11:30
Abstract:
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