2015/05/17 by Boris Muha, Sunčica Čanić, Muha, Boris +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1505.04462
openalex publication_date 2015/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a nonlinear, moving boundary fluid-structure interaction problem\nbetween an incompressible, viscous Newtonian fluid, modeled by the 2D\nNavier-Stokes equations, and an elastic structure modeled by the shell or plate\nequations. The fluid and structure are coupled via the em Navier slip\nboundary condition and balance of contact forces at the fluid-structure\ninterface. The slip boundary condition is more realistic than the classical\nno-slip boundary condition in situations, e.g., when the structure is "rough",\nand in modeling dynamics near, or at a contact. Cardiovascular tissue and\ncell-seeded tissue constructs, which consist of grooves in tissue scaffolds\nthat are lined with cells, are examples of "rough" elastic interfaces\ninteracting with and incompressible, viscous fluid. The problem of heart valve\nclosure is an example of a fluid-structure interaction problem with a contact.\nWe prove the existence of a weak solution to this class of problems by\ndesigning a constructive proof based on the time discretization via operator\nsplitting. This is the first existence result for fluid-structure interaction\nproblems involving elastic structures satisfying the Navier slip boundary\ncondition\n