偏微分方程式セミナー: Homogenization of Stokes–Cahn–Hilliard equations with a logarithmic free energy for two-phase flow in porous media, Rong Lei 氏

Time：16：30 – 17：30

Place：理学部 3 号館 3-202 (hybrid)

Organizer：喜多 航佑、津原 駿

Speaker：Rong Lei 氏 (東北大学)

Title：Homogenization of Stokes–Cahn–Hilliard equations with a logarithmic free energy for two-phase flow in porous media

Abstract：We investigate the homogenization of a phase-field model for two-phase, immiscible, and incompressible flow in porous media, incorporating surface tension effects. The model is governed by the coupled Stokes–Cahn–Hilliard system with a logarithmic free energy, where the two fluids are separated by a diffuse interface of finite width, assumed independent of the spatial scale parameter. By applying the method of two-scale convergence, we rigorously derive the homogenized limit, which takes the form of a generalized Richards’ equation that includes an additional correction term beyond the classical model. This is joint work with Jun Masamune.