A lattice Boltzmann-finite element model for two-dimensional fluid–structure interaction problems involving shallow waters

In this paper, a numerical method for the modeling of shallow waters interacting with slender elastic structures is presented. The fluid domain is modeled through the lattice Boltzmann method, while the solid domain is idealized by corotational beam finite elements undergoing large displacements. Structure dynamics is predicted by using the time discontinuous Galerkin method and the fluid–structure interface conditions are handled by the Immersed Boundary method. An explicit coupling strategy to combine the adopted numerical methods is proposed and its effectiveness is tested by computing the error in terms of the energy that is artificially introduced at the fluid–solid interface.

[1]  R. Benzi,et al.  The lattice Boltzmann equation: theory and applications , 1992 .

[2]  C. Peskin.  The immersed boundary method , 2002, Acta Numerica.

[3]  Francesco Ubertini,et al.  An efficient time discontinuous Galerkin procedure for non-linear structural dynamics , 2006 .

[4]  Stefano Ubertini,et al.  A partitioned approach for two-dimensional fluid–structure interaction problems by a coupled lattice Boltzmann-finite element method with immersed boundary , 2014 .

[5]  Alfonso Caiazzo,et al.  Analysis of lattice Boltzmann nodes initialisation in moving boundary problems , 2008 .

[6]  Alessandro De Rosis,et al.  Fluid-structure interaction by a coupled lattice Boltzmann-finite element approach , 2013 .

[7]  Sauro Succi,et al.  Lattice Boltzmann Methods for Multiphase Flow Simulations across Scales , 2011 .

[8]  Olivier Delestre,et al.  SWASHES: a compilation of shallow water analytic solutions for hydraulic and environmental studies , 2011, 1110.0288.

[9]  Wei Shyy,et al.  Force evaluation in the lattice Boltzmann method involving curved geometry. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[11]  A. Shu,et al.  Large eddy simulation of turbulent shallow water flows using multi‐relaxation‐time lattice Boltzmann model , 2012 .

[12]  Alessandro De Rosis,et al.  Analysis of blood flow in deformable vessels via a lattice Boltzmann approach , 2014 .

[13]  Raffaele Casciaro,et al.  Asymptotic post-buckling FEM analysis using corotational formulation , 2009 .

[14]  M Cerrolaza,et al.  Analysis of 3D transient blood flow passing through an artificial aortic valve by Lattice-Boltzmann methods. , 1998, Journal of biomechanics.

[15]  Sauro Succi,et al.  Lattice Boltzmann Analysis of Fluid-Structure Interaction with Moving Boundaries , 2013 .

[16]  D. W. Scharpf,et al.  Finite element method — the natural approach , 1979 .

[17]  Takaji Inamuro,et al.  Lattice Boltzmann methods for moving boundary flows , 2012 .

[18]  Chen-Hao Wang,et al.  A lattice Boltzmann approach for the non-Newtonian effect in the blood flow , 2011, Comput. Math. Appl..

[19]  Haifei Liu,et al.  Lattice Boltzmann simulations of the transient shallow water flows , 2010 .

[20]  O. Filippova,et al.  Lattice-Boltzmann simulation of gas-particle flow in filters , 1997 .

[21]  J. Wu,et al.  Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications , 2009 .

[22]  J. Boon.  The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , 2003 .

[23]  E. Rank,et al.  Fixed‐grid fluid–structure interaction in two dimensions based on a partitioned Lattice Boltzmann and p‐FEM approach , 2009 .

[24]  Francesco Ubertini,et al.  Time discontinuous Galerkin methods with energy decaying correction for non‐linear elastodynamics , 2010 .

[25]  B. Chopard,et al.  Lattice Boltzmann Simulations of Blood Flow: Non-Newtonian Rheology and Clotting Processes , 2005 .

[26]  Stefano Ubertini,et al.  A coupled lattice Boltzmann-finite element approach for two-dimensional fluid-structure interaction , 2013 .

[27]  J. Eggels,et al.  Direct and large-eddy simulation of turbulent fluid flow using the lattice-Boltzmann scheme , 1996 .

[28]  Q. Zou,et al.  On pressure and velocity boundary conditions for the lattice Boltzmann BGK model , 1995, comp-gas/9611001.

[29]  Carlos A. Felippa,et al.  A unified formulation of small-strain corotational finite elements: I. Theory , 2005 .

[30]  Frank T.-C. Tsai,et al.  GPU accelerated lattice Boltzmann model for shallow water flow and mass transport , 2011 .