On the application of principal component analysis for the construction of reduced order models

• Grant number: 18/11410-9
• Support Opportunities: Scholarships in Brazil - Master
• Start date: September 01, 2018
• End date: April 30, 2021
• Field of knowledge: Engineering - Aerospace Engineering - Aerodynamics
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: William Roberto Wolf
• Grantee: Victor Zucatti da Silva
• Host Institution: Faculdade de Engenharia Mecânica (FEM). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID
• Associated scholarship(s): 19/18809-7 - Reduced order modeling strategies for simulation of unsteady flows, BE.EP.MS

Abstract

The present work will focus on the study of numerical methods for reduced order modeling of problems in fluid mechanics. The performance of computers today is greater than that of computers used two or three decades ago but, for many engineering problems, the computational cost is still not feasible. It is in this reality that rests the interest in models of reduced order. The combination of projection and sparse regression techniques coupled with the principal component analysis (PCA) method is very promising today. There are several articles and other documents that bear witness to the great potential of these methods. On the other hand, knowledge and comprehension of the intrinsic limitations are necessary when dealing with a problem with this tool. In this work, we will investigate reduced order modeling techniques along with the POD method. We will develop these methods for the solution of linear and nonlinear partial differential equations representing problems of fluid mechanics. Subsequently, we will apply the methods to computational fluid dynamics simulations. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ZUCATTI, VICTOR; LUI, HUGO F. S.; PITZ, DIOGO B.; WOLF, WILLIAM R.. Assessment of reduced-order modeling strategies for convective heat transfer. NUMERICAL HEAT TRANSFER PART A-APPLICATIONS, v. 77, n. 7, p. 702-729, APR 2 2020. (18/11410-9, 13/07375-0, 13/08293-7, 19/18809-7)

ZUCATTI, VICTOR; WOLF, WILLIAM. Data-driven closure of projection-based reduced order models for unsteady compressible flows. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, v. 386, DEC 1 2021. (19/18809-7, 18/11410-9, 13/08293-7)

ZUCATTI, VICTOR; WOLF, WILLIAM; BERGMANN, MICHEL. Calibration of projection-based reduced-order models for unsteady compressible flows. Journal of Computational Physics, v. 433, MAY 15 2021. (19/18809-7, 13/08293-7, 18/11410-9)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SILVA, Victor Zucatti da. Hyper-reduction and calibration techniques for projection-based reduced order models of unsteady flows. 2021. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Mecânica Campinas, SP.