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

Grant number: 18/11410-9
Support type:Scholarships in Brazil - Master
Effective date (Start): September 01, 2018
Effective date (End): August 31, 2020
Field of knowledge:Engineering - Aerospace Engineering
Cooperation agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
Principal Investigator:William Roberto Wolf
Grantee:Victor Zucatti da Silva
Home 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


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)