2022/03/03 by Maxim A. Olshanskii, Olshanskii, Maxim A., Arnold Reusken +3 · 2 citations
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2203.01521
openalex publication_date 2022/03/03 · openalex created_date 2022/04/03 · openalex updated_date 2026/08/01
The paper considers a system of equations that models a lateral flow of a Boussinesq--Scriven fluid on a passively evolving surface embedded in ℝ3. For the resulting Navier-Stokes type system, posed on a smooth closed time-dependent surface, we introduce a weak formulation in terms of functional spaces on a space-time manifold defined by the surface evolution. The weak formulation is shown to be well-posed for any finite final time and without smallness conditions on data. We further extend an unfitted finite element method, known as TraceFEM, to compute solutions to the fluid system. Convergence of the method is demonstrated numerically. In another series of experiments we visualize lateral flows induced by smooth deformations of a material surface.