2018/09/12 by Arianna Giunti, Giunti, Arianna, Richard M. Höfer +1 · 1 citation
Computer Science · Engineering · Mathematics · #35B27 #35J15 #35J57 #60F15 #60G55 #76D07 #76M50 #76S05 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1809.04491
openalex publication_date 2018/09/12 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
We prove the homogenization to the Brinkman equations for the incompressible\nStokes equations in a bounded domain which is perforated by a random collection\nof small spherical holes. The fluid satisfies a no-slip boundary condition at\nthe holes. The balls generating the holes have centres distributed according to\na Poisson point process and i.i.d. unbounded radii satisfying a suitable moment\ncondition. We stress that our assumption on the distribution of the radii does\nnot exclude that, with overwhelming probability, the holes contain clusters\nmade by many overlapping balls. We show that the formation of these clusters\nhas no effect on the limit Brinkman equations. Due to the incompressiblility\ncondition and the lack of a maximum principle for the Stokes equations, our\nproof requires a very careful study of the geometry of the random holes\ngenerated by the class of probability measures considered.\n