Derivation of the Stokes-Brinkman problem and extension to the Darcy regime

DOI10.1007/s41808-021-00123-yzbMath1481.76212OpenAlexW3204331999MaRDI QIDQ2061632

Matthieu Hillairet

Publication date: 16 December 2021

Published in: Journal of Elliptic and Parabolic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s41808-021-00123-y

zbMATH Keywords

weak solutionexistenceuniquenesshomogenizationStokes equationsmoving porous mediumLax-Milgram argument

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Stokes and related (Oseen, etc.) flows (76D07) Homogenization applied to problems in fluid mechanics (76M50)

Cites Work

• The mean-field limit for solid particles in a Navier-Stokes flow
• The method of reflections, homogenization and screening for Poisson and Stokes equations in perforated domains
• On the homogenization of the Stokes problem in a perforated domain
• Derivation of Darcy's law in randomly perforated domains
• Effective viscosity of a polydispersed suspension
• Analysis of the viscosity of dilute suspensions beyond Einstein's formula
• 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
• On the derivation of a Stokes-Brinkman problem from Stokes equations around a random array of moving spheres
• On the effect of polydispersity and rotation on the Brinkman force induced by a cloud of particles on a viscous incompressible flow
• Mild assumptions for the derivation of Einstein’s effective viscosity formula
• ESTIMATES FOR THE HOMOGENIZATION OF STOKES PROBLEM IN A PERFORATED DOMAIN
• A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles

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