Center for the Mathematics of Biosystems

Permanent URI for this community

https://hdl.handle.net/10919/123756
The Center for the Mathematics of Biosystems was created in 2024 and incorporates the former Interdisciplinary Center for Applied Mathematics (ICAM).

Browse

Browsing Center for the Mathematics of Biosystems by Author "Akhtar, Imran"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Computing Functional Gains for Designing More Energy-Efficient Buildings Using a Model Reduction Framework
    Akhtar, Imran; Borggaard, Jeffrey T.; Burns, John A. (MDPI, 2018-11-23)
    We discuss developing efficient reduced-order models (ROM) for designing energy-efficient buildings using computational fluid dynamics (CFD) simulations. This is often the first step in the reduce-then-control technique employed for flow control in various industrial and engineering problems. This approach computes the proper orthogonal decomposition (POD) eigenfunctions from high-fidelity simulations data and then forms a ROM by projecting the Navier-Stokes equations onto these basic functions. In this study, we develop a linear quadratic regulator (LQR) control based on the ROM of flow in a room. We demonstrate these approaches on a one-room model, serving as a basic unit in a building. Furthermore, the ROM is used to compute feedback functional gains. These gains are in fact the spatial representation of the feedback control. Insight of these functional gains can be used for effective placement of sensors in the room. This research can further lead to developing mathematical tools for efficient design, optimization, and control in building management systems.
  • Thumbnail Image
    Shape Sensitivity Analysis in Flow Models Using a Finite-Difference Approach
    Akhtar, Imran; Borggaard, Jeffrey T.; Hay, Alexander (Hindawi Publishing Corporation, 2010)
    Reduced-order models have a number of practical engineering applications for unsteady flows that require either low-dimensional approximations for analysis and control or repeated simulation over a range of parameter values. The standard method for building reduced-order models uses the proper orthogonal decomposition (POD) and Galerkin projection. However, this standard method may be inaccurate when used "off-design" (at parameter values not used to generate the POD). This phenomena is exaggerated when parameter values describe the shape of the flow domain since slight changes in shape can have a significant influence on the flow field. In this paper, we investigate the use of POD sensitivity vectors to improve the accuracy and dynamical system properties of the reduced-order models to problems with shape parameters. To carry out this study, we consider flows past an elliptic cylinder with varying thickness ratios. Shape sensitivities (derivatives of flow variables with respect to thickness ratio) computed by finite difference approximations are used to compute the POD sensitivity vectors. Numerical studies test the accuracy of the new bases to represent flow solutions over a range of parameter values.