Journal ArticleDOI
Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes I. Abstract framework, a volume distribution of holes
TLDR
In this paper, the convergence of the homogenization of the Stokes or Navier-Stokes equations to a Dirichlet boundary condition was studied in a domain containing many tiny solid obstacles, periodically distributed in each direction of the axes.Citations
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Proceedings of the International Congress of Mathematicians
TL;DR: The main topics of eohomologieal investigation in Algebraic Geometry, as they appear at present, can be found in this article, with the main focus on the Weil cohomology.
Journal ArticleDOI
On the Domain of Validity of Brinkman's Equation
TL;DR: In this article, it was shown that Brinkman's 3D flow equation cannot describe the flow of a Newtonian fluid through a swarm of fixed particles or fibrous media at low concentration under very precise conditions.
Journal ArticleDOI
Boundary Conditions at Fluid-Permeable Interfaces in Porous Media: a Variational Approach
TL;DR: In this paper, a general set of boundary conditions at fluid-permeable interfaces between dissimilar fluid-filled porous matrices is established starting from an extended Hamilton-Rayleigh principle.
Journal ArticleDOI
Topology optimization of flow domains using the lattice Boltzmann method
TL;DR: The variation of the porosity can be used in conjunction with the lattice Boltzmann method for the optimal design of fluid domains, making the LBM an interesting alternative to NS solvers for topology optimization problems.
Journal ArticleDOI
Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models
Pablo J. Blanco,Pablo J. Blanco,Pablo J. Sánchez,Eduardo A. de Souza Neto,Raúl A. Feijóo,Raúl A. Feijóo +5 more
TL;DR: In this paper, a unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element (RVE), which allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities.
References
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Journal ArticleDOI
Asymptotic Analysis of Periodic Structures
Book
Asymptotic analysis for periodic structures
TL;DR: In this article, the authors give a systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate.
Book
Non-Homogeneous Media and Vibration Theory
TL;DR: In this article, a spectral perturbation of spectral families and applications to self-adjoint eigenvalue problems are discussed, as well as the Trotter-Kato theorem and related topics.
Journal ArticleDOI
A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles
TL;DR: In this paper, the viscous force exerted by a flowing fluid on a dense swarm of particles is described by a modification of Darcy's equation, which was necessary in order to obtain consistent boundary conditions.