2019/04/21 by Jiajun Tong, Tong, Jiajun · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1904.09528
openalex publication_date 2019/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inspired by the numerical immersed boundary method, we introduce regularized Stokes immersed boundary problems in two dimensions to describe regularized motion of a 1-D closed elastic string in a 2-D Stokes flow, in which a regularized δ-function is used to mollify the flow field and singular forcing. We establish global well-posedness of the regularized problems, and prove that as the regularization parameter diminishes, string dynamics in the regularized problems converge to that in the Stokes immersed boundary problem with no regularization. Viewing the un-regularized problem as a benchmark, we derive error estimates under various norms for the string dynamics. Our rigorous analysis shows that the regularized problems achieve improved accuracy if the regularized δ-function is suitably chosen. This may imply potential improvement in the numerical method, which is worth further investigation.