Paulo Correia | Universidade de Évora (original) (raw)
Address: Évora, Evora, Portugal
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Esta publicação resulta da evolução dos apontamentos facultados desde o ano lectivo de 2007/2008 ... more Esta publicação resulta da evolução dos apontamentos facultados desde o ano lectivo de 2007/2008 aos alunos das licenciaturas em Agronomia, Biologia e Ciência e Tecnologia Animal da Universidade de Évora. O conteúdo está adaptado ao programa da unidade curricular de Matemática incidindo, por um lado, na consolidação e desenvolvimento dos conhecimentos adquiridos no Ensino Secundário, nomeadamente nas áreas de Análise e Álgebra e, por outro, na apresentação de novos temas como cálculo integral, equações diferenciais, matrizes e determinantes. No final de cada capítulo são apresentados vários exercícios que servem de base para o estudo individual e para as aulas práticas
A pressure-correction algorithm is presented for compressible fluid flow regimes. It is well-suit... more A pressure-correction algorithm is presented for compressible fluid flow regimes. It is well-suited to simulate flows at all levels of Mach number with smooth and discontinuous flow field changes, by providing a precise representation of convective transport and acoustic propagation. The co-located finite volume space discretisation is used with the AUSM flux splitting. It is demonstrated that two ingredients are essential for obtaining good quality solutions : the presence of an inertia term in the transporting velocity expression ; a velocity difference diffusive term in the face pressure expression, with a correct Mach number scaling to recover the hydrodynamic and acoustic low Mach number limits. To meet these two requirements, a new flux scheme, named MIAU, for Momentum Interpolation with Advection Upstream splitting is proposed.
This paper is concerned with the application of finite element methods to obtain solutions for st... more This paper is concerned with the application of finite element methods to obtain solutions for steady fully developed second-grade flows in a curved pipe of circular cross-section and arbitrary curvature ratio, under a given axial pressure gradient. The qualitative and quantitative behavior of the secondary flows is analyzed with respect to inertia and viscoelasticity.
Symmetry
In this work, we present sufficient conditions in order to establish different types of Ulam stab... more In this work, we present sufficient conditions in order to establish different types of Ulam stabilities for a class of higher order integro-differential equations. In particular, we consider a new kind of stability, the σ-semi-Hyers-Ulam stability, which is in some sense between the Hyers–Ulam and the Hyers–Ulam–Rassias stabilities. These new sufficient conditions result from the application of the Banach Fixed Point Theorem, and by applying a specific generalization of the Bielecki metric.
Na verdade, A = B se e só se A ⊂ B e B ⊂ A. Estaé de facto a forma de provar que A = B.
Esta publicação resulta da evolução dos apontamentos facultados desde o ano lectivo de 2007/2008 ... more Esta publicação resulta da evolução dos apontamentos facultados desde o ano lectivo de 2007/2008 aos alunos das licenciaturas em Agronomia, Biologia e Ciência e Tecnologia Animal da Universidade de Évora. O conteúdo está adaptado ao programa da unidade curricular de Matemática incidindo, por um lado, na consolidação e desenvolvimento dos conhecimentos adquiridos no Ensino Secundário, nomeadamente nas áreas de Análise e Álgebra e, por outro, na apresentação de novos temas como cálculo integral, equações diferenciais, matrizes e determinantes. No final de cada capítulo são apresentados vários exercícios que servem de base para o estudo individual e para as aulas práticas
A pressure-correction algorithm is presented for compressible fluid flow regimes. It is well-suit... more A pressure-correction algorithm is presented for compressible fluid flow regimes. It is well-suited to simulate flows at all levels of Mach number with smooth and discontinuous flow field changes, by providing a precise representation of convective transport and acoustic propagation. The co-located finite volume space discretisation is used with the AUSM flux splitting. It is demonstrated that two ingredients are essential for obtaining good quality solutions : the presence of an inertia term in the transporting velocity expression ; a velocity difference diffusive term in the face pressure expression, with a correct Mach number scaling to recover the hydrodynamic and acoustic low Mach number limits. To meet these two requirements, a new flux scheme, named MIAU, for Momentum Interpolation with Advection Upstream splitting is proposed.
This paper is concerned with the application of finite element methods to obtain solutions for st... more This paper is concerned with the application of finite element methods to obtain solutions for steady fully developed second-grade flows in a curved pipe of circular cross-section and arbitrary curvature ratio, under a given axial pressure gradient. The qualitative and quantitative behavior of the secondary flows is analyzed with respect to inertia and viscoelasticity.
Symmetry
In this work, we present sufficient conditions in order to establish different types of Ulam stab... more In this work, we present sufficient conditions in order to establish different types of Ulam stabilities for a class of higher order integro-differential equations. In particular, we consider a new kind of stability, the σ-semi-Hyers-Ulam stability, which is in some sense between the Hyers–Ulam and the Hyers–Ulam–Rassias stabilities. These new sufficient conditions result from the application of the Banach Fixed Point Theorem, and by applying a specific generalization of the Bielecki metric.
Na verdade, A = B se e só se A ⊂ B e B ⊂ A. Estaé de facto a forma de provar que A = B.