2012/05/31 by Sunčica Čanić, Canic, Suncica, Boris Muha +3
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1205.6887
openalex publication_date 2012/05/31 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
It is well-known that classical Dirichlet-Neumann loosely coupled partitioned schemes for fluid-structure interaction (FSI) problems are unconditionally unstable for certain combinations of physical and geometric parameters that are relevant in hemodynamics. It was shown in \citecausin2005added on a simple test problem, that these instabilities are associated with the so called ``added-mass effect''. By considering the same test problem as in \citecausin2005added, the present work shows that a novel, partitioned, loosely coupled scheme, recently introduced in \citeMarSun, called the kinematically coupled β-scheme, does not suffer from the added mass effect for any β∈ [0,1], and is unconditionally stable for all the parameters in the problem. Numerical results showing unconditional stability are presented for a full, nonlinearly coupled benchmark FSI problem, first considered in \citeformaggia2001coupling.