Numerical study of the erosion of a porous solid layer in a channel flow

Fluid-structure interaction (FSI) is a strongly nonlinear problem involving the interaction between the governing equations of fluid dynamics and solid mechanics. The FSI problem can be found in several scientific fields, rang- ing from civil, aeronautical, and biomedical engineering to geotechnics. FSI involves multi-physics phenomena and becomes more complex when crack ini- tialization and fracture (e.g. hydraulic fracturing) are taken into account. The solid-fluid interfaces of the immersed structure are modified by the coupling of the fluid dynamics laws with the mechanical laws of the solid involved in the process. For decades, this problem has been extensively studied and theories have been developed that can simulate the complexity of this phenomenon. One of the major difficulties was the introduction of a model that could over- come the difficulty of classical mechanics due to the increase of a singularity in partial differential equations and therefore a discontinuity in the presence of the crack. An innovative approach comes from the use of peridynamics, a theory of the solid continuous that allows to study of the interaction of the two phases involved and allows the study of the formation and propagation of cracks. This manuscript is devoted the study of the preliminary stage of the erosion of an ablative porous solid by a method based on peridynamics and the incomprehensible three-dimensional formulation of the Navier-Stokes equations, using a technique called the Immersed Boundary Method (IBM). Direct numerical simulations (DNS), based on this methodology, to simulate the crack of porous material fibers in laminar and stationary regime in a chan- nel flow; the software was developed and validated by F. Dalla Barba based on CaNS (Canonical Navier-Stokes) open-source software developed by P. Costa. The first chapter of this thesis focuses on the analysis of the interaction phe- nomenon by presenting different approaches that can be used to deepen the analysis. The methodology for studying the problem is explained in a gen- eral manner, before focusing on the theory of peridynamics and moving on to numerical methods used for simulation. In the end, the software used in the formulations is presented to provide a presentation and analysis of the results and their conclusions, and possible future developments in the engineering field. It has been noticed that the fibers of the material break due to the fluid dynamic forces generated by the fluid phase. Material damage is not an instantaneous phenomenon, but rather a continuous process that causes the solid to continuously decay and fracture.