A nonlinear PDE system for phase separation and damage
Tuesday, 13.11.12, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Modeling and simulation of fluid-structure interaction in haemodynamics
Tuesday, 4.12.12, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We consider the fluid-structure interaction problem arising in\nhaemodynamic applications where the blood interacts with the arterial\nwall. Blood dynamics is described by the Navier-Stokes equations for\nNewtonian fluids, conveniently rewritten in Arbitrary Lagrangian\nEulerian (ALE) formulation to account for the deformation of the fluid\ndomain boundary; arterial dynamics is described by non-linear\nfinite elasticity equations.\n\nWe consider partitioned algorithms based on Robin interface conditions\nto solve numerically the fluid-structure interaction problem. At each\ntime step the non-linear or linearized fluid and structure subproblems\nare solved iteratively until convergence and linear combinations of\nvelocities and normal stresses (Robin interface conditions) are\nexchanged at the common interface. In particular, we discuss suitable\nchoices of the coefficients in the Robin conditions based on reduced\nmodels and show how the optimized Robin conditions greatly reduce the\neffect of added mass on the convergence of the iterative algorithm.\n\nWe present finally some simulations of blood flow in carotid\nbifurcations reconstructed from MRI data, from patients having\natherosclerotic plaques, before and after the plaque removal.\n\nReferences\n\n[1] S. Badia, F. Nobile, and C. Vergara (2008). Fluid-structure\npartitioned procedures based on Robin transmission\nconditions. J. Comp. Phy 227, 7027–7051.\n\n[3] P. Causin, J. Gerbeau, and F. Nobile (2005). Added-mass effect in\nthe design of partitioned algorithms for fluid-structure\nproblems. Comput. Methods Appl. Mech. Engrg 194(42-44), 4506– 4527.\n\n[4] F. Nobile, M. Pozzoli, C. Vergara, Exact and inexact partitioned\nalgorithms for fluid-structure interaction problems with finite\nelasticity in haemodynamics, MOX Report 37/2012, submitted.