Space-time formulation of the finite element method for the analysis of FSI problems with topological changes in the flow domain

• Grant number: 24/20929-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: August 01, 2025
• End date: April 30, 2029
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: Rodolfo André Kuche Sanches
• Grantee: Thiago Rodrigues Carvalho
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 24/05554-9 - Development of alternative computational tools for advanced fluid-structure interaction problems, AP.R

Abstract

The simulation of fluid-structure interaction (FSI) problems with topological changes in the fluid domain is a very challenging task. Although there are several studies in this context, there is still no consensus on the most appropriate techniques for this.Recently, the research group in which this proposal is inserted developed a unified formulation for solids, incompressible fluids and FSI, which employs an alternative form of the Particle Finite Element Method (PFEM), based on the positions of the particles.This technique has proven to be quite efficient for such problems; however, the constant remeshing consists of an additional source of numerical errors, in addition to using only geometric criteria to obtain the free surface. Consequently, the conservation of volume, as well as the consideration of the fluid-structure contact, are dependent on a purely graphical algorithm.In this sense, the present work proposes to develop a more mathematically consistent approach, using the space-time Finite Element Method (FEM) with unstructured discretization for the analysis of FSI problems with topological changes.When applied to both space and time, an unstructured discretization of the space-time FEM allows the spatial mesh at different times to be completely different, accommodating topological changes and avoiding the need for an additional step of projecting values ¿¿from the old spatial mesh to the current one. Thus, it is possible to reduce the projection errors introduced by frequent remeshing. In this sense, it is expected to obtain a more accurate and conservative approach for the analysis of FEM problems with topological changes in the fluid domain.Therefore, the project has great potential for the development of new computational tools and for application in several fields of engineering, such as the analysis of the impact of waves on structures, the study of flows with complex free surfaces, the study of multiphase fluid dynamics, such as the analysis of Rayleigh-Taylor instability, and in fluid-structure interaction problems with topological changes, such as the problem of dam failure with deformable obstacles. (AU)