Eventos Anais de eventos
COBEM 2019
25th International Congress of Mechanical Engineering
An assessment of reduced order modeling techniques applied to unsteady flows
Submission Author:
Victor Zucatti da Silva , SP
Co-Authors:
Victor Zucatti da Silva, William Wolf
Presenter: William Wolf
doi://10.26678/ABCM.COBEM2019.COB2019-0224
Abstract
High fidelity modeling of complex non-linear dynamical systems is necessary for the comprehension of several processes found in engineering systems. For example, in fluid mechanics, numerical simulations aid in the design and optimization of more efficient aircraft, automobiles, engines and wind turbines. Accurate numerical simulations of unsteady flows are required to perform such analyses and they are associated with high computational costs since high resolution spatial and temporal schemes are typically employed to resolve the broad range of spatial and temporal scales. On one hand, small time steps are required to capture the fine temporal scales of the problem. On the other hand, the simulations need to be carried out for long periods to obtain meaningful statistics. Reduced order modeling is a methodology that can considerably reduce the computational costs associated with simulations of unsteady flows. In order to be useful, the reduced order model (ROM) should be able to reproduce the relevant physical mechanisms observed in the full order model (FOM). In this work, ROMs of an incompressible flow past a cylinder are studied via Galerkin-type projection techniques of the Navier-Stokes equations. Proper orthogonal decomposition (POD) is used to generate a reduced basis space from high fidelity simulations. Although the current methodology is data driven, it is linked to the physics of the problem through direct projection of the partial differential equations governing the fluid flows. Galerkin and Petrov-Galerkin methods are employed in the ROMs and results are analyzed in terms of the relative error compared to the FOM.
Keywords
Reduced Order Modeling, Proper Orthogonal Decomposition, Galerkin projection, Navier-Stokes Equations, Petrov-Galerkin projection
