Brinkman's law as Γ-limit of compressible low Mach Navier-Stokes equations and application to randomly perforated domains

2025/05/16 by Peter Bella, Friederike Lemming, Bella, Peter +5
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Stability and Controllability of Differential Equations #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2505.11213

Abstract

We consider the time-dependent compressible Navier-Stokes equations in the low Mach number regime inside a family of domains (Ω_ε)_{ε > 0} in ℝ³. Assuming that lim_{ε → 0} Ω_ε = Ω⊂ ℝ³ in a suitable sense, we show that in the limit the fluid flow inside Ω is governed by the incompressible Navier-Stokes-Brinkman equations, provided the latter one admits a strong solution. The abstract convergence result is complemented with a stochastic homogenization result for randomly perforated domains in the critical regime.

Citations

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Related

• Γ-convergence for nearly incompressible fluids
• Homogenization of the Navier-Stokes equations in perforated domains in the inviscid limit
• Inverse of divergence and homogenization of compressible Navier-Stokes equations in randomly perforated domains
• Convergence of the pressure in the homogenization of the Stokes equations in randomly perforated domains
• Darcy's law as low Mach and homogenization limit of a compressible fluid\n in perforated domains