2020/07/17 by Richard M. Höfer, Höfer, Richard M., Karina Kowalczyk +3 · 1 citation
Computer Science · Engineering · #35B27 #35J57 #76M50 #76N06 #76S05 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2007.09031
openalex publication_date 2020/07/17 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We consider the homogenization limit of the compressible barotropic\nNavier-Stokes equations in a three-dimensional domain perforated by\nperiodically distributed identical particles. We study the regime of particle\nsizes and distances such that the volume fraction of particles tends to zero\nbut their resistance density tends to infinity. Assuming that the Mach number\nis increasing with a certain rate, the rescaled velocity and pressure of the\nmicroscopic system converges to the solution of an effective equation which is\ngiven by Darcy's law. The range of sizes of particles we consider are exactly\nthe same which lead to Darcy's law in the homogenization limit of\nincompressible fluids. Unlike previous results for the Darcy regime we estimate\nthe deficit related to the pressure approximation via the Bogovski u i\noperator This allows for more flexible estimates of the pressure in Lebesgue\nand Sobolev spaces and allows to proof convergence results for all barotropic\nexponents \γ> frac32.\n