Actively deforming porous media in an incompressible fluid: a variational approach
DOI10.1016/j.physd.2021.132984OpenAlexW3181997786MaRDI QIDQ2077575
Tagir Farkhutdinov, François Gay-Balmaz, Vakhtang Putkaradze
Publication date: 21 February 2022
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2107.03661
incompressible fluidvariational principleporous mediaequations of motionLagrangian formulationnumerical schemepotential energybiological applications
PDEs in connection with fluid mechanics (35Q35) Nonlinear elasticity (74B20) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Flows in porous media; filtration; seepage (76S05) Variational methods applied to PDEs (35A15) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Biomechanics (92C10) Biomechanical solid mechanics (74L15) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) PDEs in connection with mechanics of deformable solids (35Q74)
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Cites Work
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- The vanishing viscosity limit in the presence of a porous medium
- General quantitative analysis of stress partitioning and boundary conditions in undrained biphasic porous media via a purely macroscopic and purely variational approach
- Analysis of nonlinear poro-elastic and poro-visco-elastic models
- A Lagrangian variational formulation for nonequilibrium thermodynamics. I: Discrete systems.
- A Lagrangian variational formulation for nonequilibrium thermodynamics. II: Continuum systems.
- Formulation of a finite deformation model for the dynamic response of open cell biphasic media
- General coupling of porous flows and hyperelastic formulations -- from thermodynamics principles to energy balance and compatible time schemes
- On flexible tubes conveying fluid: geometric nonlinear theory, stability and dynamics
- On noisy extensions of nonholonomic constraints
- Reduced variational formulations in free boundary continuum mechanics
- Geometric variational approach to the dynamics of porous medium, filled with incompressible fluid
- Boundary conditions at fluid-permeable interfaces in porous media: a variational approach
- Variational formulation of pre-stressed solid-fluid mixture theory, with an application to wave phenomena
- Geometric framework for modeling nonlinear flows in porous media, and its applications in engineering
- A variational theory of porous media
- A micro-structured continuum modelling compacting fluid-saturated grounds: The effects of pore-size scale parameter
- The role of porous media in modeling flow and heat transfer in biological tissues.
- A variational approach for the deformation of a saturated porous solid: A second-gradient theory extending Terzaghi's effective stress principle
- Diffusion in poro-elastic media
- Geometric analysis of noisy perturbations to nonholonomic constraints
- Vibration and instability analysis of closed-cell poroelastic pipes conveying fluid
- Mechanical integrators derived from a discrete variational principle
- Nonlinear quasi-static poroelasticity
- Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media
- Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. I: Abstract framework, a volume distribution of holes
- Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. II: Non-critical sizes of the holes for a volume distribution and a surface distribution of holes
- Multi-component multiphase flow through a poroelastic medium
- Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
- Macroscopic Lagrangian formulation of poroelasticity with porosity dynamics
- Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids
- The Darcy-Forchheimer law for modelling fluid flow in biological tissues
- Theory of Elasticity and Consolidation for a Porous Anisotropic Solid
- Mechanics of Deformation and Acoustic Propagation in Porous Media
- Variational Methods for Fluid-Structure Interactions
- Discrete mechanics and variational integrators
- Variational discretization of the nonequilibrium thermodynamics of simple systems
- Penalization model for Navier–Stokes–Darcy equations with application to porosity-oriented topology optimization
- A variational derivation of the thermodynamics of a moist atmosphere with rain process and its pseudoincompressible approximation
- ON A HIERARCHY OF APPROXIMATE MODELS FOR FLOWS OF INCOMPRESSIBLE FLUIDS THROUGH POROUS SOLIDS
- Analysis of the consolidation problem of compressible porous media by a macroscopic variational continuum approach
- A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles
- From variational to bracket formulations in nonequilibrium thermodynamics of simple systems
- Variational continuum multiphase poroelasticity. Theory and applications
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