Stability analysis of Gauss-Seidel iterations in a partitioned simulation of fluid-structure interaction

A stability analysis of Gauss-Seidel coupling iterations for partitioned simulation of fluid-structure interaction is performed for the flow in a flexible tube. In a previous study, the inertia of the structure and the interaction between the segments of the structure were not taken into account. It is now demonstrated that especially the structural inertia has a significant effect on the stability of Gauss-Seidel iterations for a certain range of the time step's size.

[1]  C. Michler,et al.  Efficient Numerical Methods for Fluid-Structure Interaction , 2005 .

[2]  Klaus-Jürgen Bathe,et al.  The inf–sup condition and its evaluation for mixed finite element methods , 2001 .

[3]  K. Bathe,et al.  On a composite implicit time integration procedure for nonlinear dynamics , 2005 .

[4]  Miguel Angel Fernández,et al.  A Newton method using exact jacobians for solving fluid-structure coupling , 2005 .

[5]  Charbel Farhat,et al.  Higher-Order Subiteration-Free Staggered Algorithm for Nonlinear Transient Aeroelastic Problems , 1998 .

[6]  K. Bathe,et al.  Performance of a new partitioned procedure versus a monolithic procedure in fluid-structure interaction , 2009 .

[7]  W. Wall,et al.  Fixed-point fluid–structure interaction solvers with dynamic relaxation , 2008 .

[8]  Randolph E. Bank,et al.  Transient simulation of silicon devices and circuits , 1985, IEEE Transactions on Electron Devices.

[9]  Jan Vierendeels,et al.  Stability of a coupling technique for partitioned solvers in FSI applications , 2008 .

[10]  K. Bathe Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme , 2007 .

[11]  Alfio Quarteroni,et al.  Computational vascular fluid dynamics: problems, models and methods , 2000 .

[12]  Jan Vierendeels,et al.  A multigrid semi-implicit line-method for viscous incompressible and low-mach-number flows on high aspect ratio grids , 1999 .

[13]  Jan Vierendeels,et al.  Implicit coupling of partitioned fluid-structure interaction problems with reduced order models , 2007 .

[14]  Fabio Nobile,et al.  Added-mass effect in the design of partitioned algorithms for fluid-structure problems , 2005 .

[15]  Nathan M. Newmark,et al.  A Method of Computation for Structural Dynamics , 1959 .

[16]  E. Ramm,et al.  Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows , 2007 .