Stabilized Mixed Finite Element Formulations for Materially Nonlinear Partially Saturated Media
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The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...
To enforce the conservation of mass principle, a pressure Poisson equation arises in the numerical solution of incompressible fluid flow using the pressure-based segregated algorithms such as projection methods. For unsteady flows, the pressure Poisson equ ...
A macroscopic condition to simulate the interaction between an incompressible fluid flow and a permeable micro-structured rigid surface (i.e. a thin membrane) has been developed using multiscale homogenization and matching asymptotic expansions between the ...
Weak solutions arise naturally in the study of the Navier-Stokes and Euler equations both from an abstract regularity/blow-up perspective and from physical theories of turbulence. This thesis studies the structure and size of singular set of such weak solu ...
Given any solutionuof the Euler equations which is assumed to have some regularity in space-in terms of Besov norms, natural in this context-we show by interpolation methods that it enjoys a corresponding regularity in time and that the associated pressure ...
This report focuses on the implementation of the finite element method for nonlinear dynamical problems arising in solid mechanics. The theory of continuum mechanics is extensively covered in the literature and it is assumed the reader is already familiar ...
We give an answer to a question posed in Amorim et al. (ESAIM Math Model Numer Anal 49(1):19–37, 2015), which can loosely speaking, be formulated as follows: consider a family of continuity equations where the velocity depends on the solution via the convo ...
We investigate viscoplastic fluids (described using a Herschel–Bulkley model) striking a body of water: a fixed volume of a viscoplastic material (a polymeric gel called Carbopol ultrez 10) initially contained in a box is released on a slope and flows down ...
Unsteady radiative heat transfer is analyzed numerically in a directly irradiated plane-parallel medium containing a suspension of ceria particles undergoing nonstoichiometric thermal reduction. The micrometer-sized ceria particles are assumed homogenous, ...
This work is devoted to the study of the main models which describe the motion of incompressible fluids, namely the Navier-Stokes, together with their hypodissipative version, and the Euler equations. We will mainly focus on the analysis of non-smooth weak ...