Homogenization of the Stokes System in a Domain with an Oscillating Boundary
T. Muthukumar, K. Sankar · Multiscale Modeling and Simulation · 2022
Abstract. This article examines the homogenization issue for the Stokes system in a domain with an oscillating boundary portion. On the oscillating boundary, we impose inhomogeneous oscillating Dirichlet boundary data. The proposed method is an attempt to develop the homogenization technique for the nonstationary Stokes system on noncylindrical domains. To resolve the uniform bound of solutions with respect to heterogeneous parameters, we transform the system into a reference domain and demonstrate its existence and uniqueness in the reference domain. In order to homogenize the velocity and pressure in the reference domain, two-scale convergence is employed. In contrast to all other available homogenization techniques, the one presented in this work is easily adaptable to evolving domains. We also establish error estimates for the homogenized system approximation by transforming the system into its initial configuration.