Fluid-structure interaction simulations with a LES filtering approach in solids4Foam

Abstract The goal of this paper is to test solids4Foam, the fluid-structure interaction (FSI) toolbox developed for foam-extend (a branch of OpenFOAM), and assess its flexibility in handling more complex flows. For this purpose, we consider the interaction of an incompressible fluid described by a Leray model with a hyperelastic structure modeled as a Saint Venant-Kirchho material. We focus on a strongly coupled, partitioned fluid-structure interaction (FSI) solver in a finite volume environment, combined with an arbitrary Lagrangian-Eulerian approach to deal with the motion of the fluid domain. For the implementation of the Leray model, which features a nonlinear differential low-pass filter, we adopt a three-step algorithm called Evolve-Filter-Relax. We validate our approach against numerical data available in the literature for the 3D cross flow past a cantilever beam at Reynolds number 100 and 400.

[1]  I. Demirdzic,et al.  Space conservation law in finite volume calculations of fluid flow , 1988 .

[2]  Shanhong Ji,et al.  Finite element analysis of fluid flows fully coupled with structural interactions , 1999 .

[3]  V. M. Tikhomirov,et al.  Dissipation of Energy in Isotropic Turbulence , 1991 .

[4]  Annalisa Quaini,et al.  A Finite Volume approximation of the Navier-Stokes equations with nonlinear filtering stabilization , 2019, Computers & Fluids.

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

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

[7]  Jan Vierendeels,et al.  Multi-solver algorithms for the partitioned simulation of fluid–structure interaction , 2011 .

[8]  Thomas Richter,et al.  Goal-oriented error estimation for fluid–structure interaction problems , 2012 .

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

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

[11]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .

[12]  Shiaofen Fang,et al.  An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application , 2011, Comput. Math. Appl..

[13]  Mitul Luhar,et al.  Flow‐induced reconfiguration of buoyant and flexible aquatic vegetation , 2011 .

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

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

[16]  P. Cardiff,et al.  OpenFOAM Finite Volume Solver for Fluid-Solid Interaction , 2018, Transactions of FAMENA.

[17]  高等学校計算数学学報編輯委員会編 高等学校計算数学学報 = Numerical mathematics , 1979 .

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

[19]  Leo G. Rebholz,et al.  Modular Nonlinear Filter Stabilization of Methods for Higher Reynolds Numbers Flow , 2012 .

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

[21]  Hu Dai,et al.  Fluid-structure interaction involving large deformations: 3D simulations and applications to biological systems , 2014, J. Comput. Phys..

[22]  Oubay Hassan,et al.  Partitioned block-Gauss-Seidel coupling for dynamic fluid-structure interaction , 2010 .

[23]  P. Cardiff,et al.  An open-source finite volume toolbox for solid mechanics and fluid-solid interaction simulations , 2018, 1808.10736.

[24]  H. Jasak,et al.  A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow , 2012 .

[25]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

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

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

[28]  Annalisa Quaini,et al.  Deconvolution‐based nonlinear filtering for incompressible flows at moderately large Reynolds numbers , 2016 .

[29]  Traian Iliescu,et al.  A Bounded Artificial Viscosity Large Eddy Simulation Model , 2008, SIAM J. Numer. Anal..

[30]  Roland Wüchner,et al.  Fluid–structure interaction using a partitioned semi-implicit predictor–corrector coupling scheme for the application of large-eddy simulation , 2012 .

[31]  H. Peerhossaini,et al.  Partitioned solver for strongly coupled fluid–structure interaction , 2013 .

[32]  Bjørn H. Hjertager,et al.  Application of foam-extend on turbulent fluid-structure interaction , 2017 .

[33]  Serge Piperno,et al.  Explicit/implicit fluid/structure staggered procedures with a structural predictor and fluid subcycling for 2D inviscid aeroelastic simulations , 1997 .

[34]  Kevin Hughes,et al.  From aerospace to offshore: Bridging the numerical simulation gaps–Simulation advancements for fluid structure interaction problems , 2013 .

[35]  Hans-Joachim Bungartz,et al.  Fluid-structure interaction : modelling, simulation, optimisation , 2006 .

[36]  Gianluigi Rozza,et al.  Non-intrusive PODI-ROM for patient-specific aortic blood flow in presence of a LVAD device , 2020, Medical engineering & physics.

[37]  M. Comisso,et al.  A non-intrusive data-driven ROM framework for hemodynamics problems , 2020, ArXiv.

[38]  J. Revstedt Interaction between an incompressible flow and elastic cantilevers of circular cross-section , 2013 .

[39]  P. Moin,et al.  Eddies, streams, and convergence zones in turbulent flows , 1988 .

[40]  Leo G. Rebholz,et al.  Improved accuracy in regularization models of incompressible flow via adaptive nonlinear filtering , 2012 .

[41]  H. Jasak,et al.  Automatic mesh motion for the unstructured finite volume method , 2007 .

[42]  A. Quarteroni,et al.  Fluid–structure algorithms based on Steklov–Poincaré operators , 2006 .

[43]  Mark Cross,et al.  A finite volume unstructured mesh approach to dynamic fluid–structure interaction: an assessment of the challenge of predicting the onset of flutter , 2004 .

[44]  Wing Kam Liu,et al.  Lagrangian-Eulerian finite element formulation for incompressible viscous flows☆ , 1981 .

[45]  A. W. Vreman An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications , 2004 .

[46]  Charbel Farhat,et al.  Partitioned procedures for the transient solution of coupled aeroelastic problems , 2001 .

[47]  Erik Burman,et al.  Stabilized explicit coupling for fluid-structure interaction using Nitsche s method , 2007 .

[48]  Annalisa Quaini,et al.  A POD-Galerkin reduced order model for a LES filtering approach , 2020, J. Comput. Phys..

[49]  M. Heil An efficient solver for the fully-coupled solution of large-displacement fluid-structure interaction problems , 2004 .

[50]  J. P. V. Doormaal,et al.  ENHANCEMENTS OF THE SIMPLE METHOD FOR PREDICTING INCOMPRESSIBLE FLUID FLOWS , 1984 .

[51]  J. Vierendeels,et al.  Performance of partitioned procedures in fluid-structure interaction , 2010 .

[52]  C. Farhat,et al.  Partitioned procedures for the transient solution of coupled aroelastic problems Part I: Model problem, theory and two-dimensional application , 1995 .

[53]  A. Kolmogorov The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[54]  Ivan Kostić,et al.  Three-dimensional fluid–structure interaction simulation with a hybrid RANS–LES turbulence model for applications in transonic flow domain , 2016 .

[55]  P. Thomas,et al.  Geometric Conservation Law and Its Application to Flow Computations on Moving Grids , 1979 .

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