Coupling schemes for the FSI forward prediction challenge: Comparative study and validation

This paper presents a numerical study in which several partitioned solution procedures for incompressible fluid-structure interaction are compared and validated against the results of an experimental fluid-structure interaction benchmark. The numerical methods discussed cover the three main families of coupling schemes: strongly coupled, semi-implicit, and loosely coupled. Very good agreement is observed between the numerical and experimental results. The comparisons confirm that strong coupling can be efficiently avoided, via semi-implicit and loosely coupled schemes, without compromising stability and accuracy. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  William Gropp,et al.  Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries , 1997, SciTools.

[2]  Miguel Angel Fernández,et al.  Coupling schemes for incompressible fluid-structure interaction: implicit, semi-implicit and explicit , 2011 .

[3]  Cornel Marius Murea,et al.  A stable time advancing scheme for solving fluid-structure interaction problem at small structural displacements , 2008 .

[4]  A. Quarteroni,et al.  A SEMI-IMPLICIT APPROACH FOR FLUID-STRUCTURE INTERACTION BASED ON AN ALGEBRAIC FRACTIONAL STEP METHOD , 2007 .

[5]  J-F Gerbeau,et al.  External tissue support and fluid–structure simulation in blood flows , 2012, Biomechanics and modeling in mechanobiology.

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

[7]  Rajeev K. Jaiman,et al.  A stable second-order scheme for fluid-structure interaction with strong added-mass effects , 2014, J. Comput. Phys..

[8]  V. Brummelen.  Added Mass Effects of Compressible and Incompressible Flows in Fluid-Structure Interaction , 2009 .

[9]  Tayfun E. Tezduyar,et al.  Computational Methods for Parachute Fluid–Structure Interactions , 2012 .

[10]  Miguel Angel Fernández,et al.  Incremental displacement-correction schemes for the explicit coupling of a thin structure with an incompressible fluid , 2011 .

[11]  K. Bathe,et al.  A continuum mechanics based four‐node shell element for general non‐linear analysis , 1984 .

[12]  Dominique Chapelle,et al.  The Finite Element Analysis of Shells - Fundamentals - Second Edition , 2011 .

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

[14]  Rainald Löhner,et al.  Extending the Range and Applicability of the Loose Coupling Approach for FSI Simulations , 2006 .

[15]  P. Tallec,et al.  Fluid structure interaction with large structural displacements , 2001 .

[16]  Michael Schäfer,et al.  Experimental and numerical study on a laminar fluid-structure interaction reference test case , 2011 .

[17]  Trond Kvamsdal,et al.  Goal oriented error estimators for Stokes equations based on variationally consistent postprocessing , 2003 .

[18]  Miguel A. Fernández,et al.  Fully decoupled time-marching schemes for incompressible fluid/thin-walled structure interaction , 2015, J. Comput. Phys..

[19]  Erik Burman,et al.  Explicit strategies for incompressible fluid‐structure interaction problems: Nitsche type mortaring versus Robin–Robin coupling , 2014 .

[20]  Roland Glowinski,et al.  Stable loosely-coupled-type algorithm for fluid-structure interaction in blood flow , 2009, J. Comput. Phys..

[21]  Fabio Nobile,et al.  Robin-Robin preconditioned Krylov methods for fluid-structure interaction problems , 2009 .

[22]  Erik Burman,et al.  Stabilization of explicit coupling in fluid-structure interaction involving fluid incompressibility , 2009 .

[23]  C. A. Figueroa,et al.  Sequential identification of boundary support parameters in a fluid-structure vascular model using patient image data , 2012, Biomechanics and Modeling in Mechanobiology.

[24]  Paolo Crosetto,et al.  Parallel Algorithms for Fluid-Structure Interaction Problems in Haemodynamics , 2011, SIAM J. Sci. Comput..

[25]  Annalisa Quaini,et al.  Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect , 2008 .

[26]  T. Wick,et al.  Finite elements for fluid–structure interaction in ALE and fully Eulerian coordinates , 2010 .

[27]  G. Hou,et al.  Numerical Methods for Fluid-Structure Interaction — A Review , 2012 .

[28]  Annalisa Quaini,et al.  Fluid-structure interaction in blood flow capturing non-zero longitudinal structure displacement , 2012, J. Comput. Phys..

[29]  Dominique Chapelle,et al.  MODELING OF THE INCLUSION OF A REINFORCING SHEET WITHIN A 3D MEDIUM , 2003 .

[30]  Joris Degroote,et al.  Partitioned Simulation of Fluid-Structure Interaction , 2013 .

[31]  Philippe Moireau,et al.  Identification of artery wall stiffness: in vitro validation and in vivo results of a data assimilation procedure applied to a 3D fluid-structure interaction model. , 2014, Journal of biomechanics.

[32]  George E. Karniadakis,et al.  A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping , 2012, J. Comput. Phys..

[33]  T. Richter.  A monolithic geometric multigrid solver for fluid‐structure interactions in ALE formulation , 2015 .

[34]  Padmanabhan Seshaiyer,et al.  A nonconforming finite element method for fluid–structure interaction problems , 2005 .

[35]  Marina Vidrascu,et al.  Generalized Robin–Neumann explicit coupling schemes for incompressible fluid‐structure interaction: Stability analysis and numerics , 2015 .

[36]  Jean-Frédéric Gerbeau,et al.  A Quasi-Newton Algorithm Based on a Reduced Model for Fluid-Structure Interaction Problems in Blood Flows , 2003 .

[37]  Jeffrey W. Banks,et al.  An analysis of a new stable partitioned algorithm for FSI problems. Part II: Incompressible flow and structural shells , 2014, J. Comput. Phys..

[38]  Thomas J. R. Hughes,et al.  Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device , 2009 .

[39]  Miguel A. Fernández,et al.  A projection semi‐implicit scheme for the coupling of an elastic structure with an incompressible fluid , 2007 .

[40]  Annalisa Quaini,et al.  A modular, operator‐splitting scheme for fluid–structure interaction problems with thick structures , 2013, 1311.3324.

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

[42]  Sorin Mitran,et al.  A numerical model of cellular blebbing: a volume-conserving, fluid-structure interaction model of the entire cell. , 2010, Journal of biomechanics.

[43]  Matteo Astorino,et al.  Fluid-structure interaction and multi-body contact. Application to aortic valves , 2009 .

[44]  Gianluigi Rozza,et al.  Numerical Simulation of Sailing Boats: Dynamics, FSI, and Shape Optimization , 2012 .

[45]  Fabio Nobile,et al.  Fluid-structure partitioned procedures based on Robin transmission conditions , 2008, J. Comput. Phys..

[46]  Annalisa Quaini,et al.  Splitting Methods Based on Algebraic Factorization for Fluid-Structure Interaction , 2008, SIAM J. Sci. Comput..

[47]  Damodar Maity,et al.  Effect of baffles on a partially filled cubic tank: Numerical simulation and experimental validation , 2009 .

[48]  W. Wall,et al.  Truly monolithic algebraic multigrid for fluid–structure interaction , 2011 .

[49]  Fabio Nobile,et al.  Inexact accurate partitioned algorithms for fluid-structure interaction problems with finite elasticity in haemodynamics , 2014, J. Comput. Phys..

[50]  Matthias Heil,et al.  An efficient preconditioner for monolithically-coupled large-displacement fluid-structure interaction problems with pseudo-solid mesh updates , 2012, J. Comput. Phys..

[51]  Miguel A. Fernández,et al.  Robin Based Semi-Implicit Coupling in Fluid-Structure Interaction: Stability Analysis and Numerics , 2009, SIAM J. Sci. Comput..

[52]  Marina Vidrascu,et al.  Explicit Robin–Neumann schemes for the coupling of incompressible fluids with thin-walled structures , 2013 .

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

[54]  Pascal Frey,et al.  Fluid-structure interaction in blood flows on geometries based on medical imaging , 2005 .

[55]  Yuri Bazilevs,et al.  An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves. , 2015, Computer methods in applied mechanics and engineering.

[56]  Mária Lukáčová-Medvid’ová,et al.  Kinematic splitting algorithm for fluid–structure interaction in hemodynamics , 2013 .

[57]  Miguel A. Fernández,et al.  Convergence and error analysis for a class of splitting schemes in incompressible fluid–structure interaction , 2016 .

[58]  T. Tezduyar,et al.  Mesh Moving Techniques for Fluid-Structure Interactions With Large Displacements , 2003 .

[59]  Fabio Nobile,et al.  Time accurate partitioned algorithms for the solution of fluid–structure interaction problems in haemodynamics , 2013 .

[60]  Miguel A. Fernández,et al.  Nitsche-XFEM for the coupling of an incompressible fluid with immersed thin-walled structures , 2016 .

[61]  Matteo Astorino,et al.  Convergence analysis of a projection semi-implicit coupling scheme for fluid–structure interaction problems , 2010, Numerische Mathematik.

[62]  Brummelen van Eh,et al.  Flux evaluation in primal and dual boundary-coupled problems , 2011 .

[63]  J. Mandel.  Balancing domain decomposition , 1993 .

[64]  A. Marsden,et al.  A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations , 2011 .

[65]  van Eh Harald Brummelen,et al.  Partitioned iterative solution methods for fluid–structure interaction , 2011 .

[66]  Miguel A. Fernández,et al.  Incremental displacement-correction schemes for incompressible fluid-structure interaction , 2012, Numerische Mathematik.