Partitioned Simulation of Fluid-Structure Interaction on Cartesian Grids

This contribution describes recent developments and enhancements of the coupling tool preCICE and the flow solver Peano used for our partitioned simualtions of fluid-structure interaction scenarios. Peano brings together hardware efficiency and numerical efficiency exploiting advantages of tree-structured adaptive Cartesian computational grids that, in particular, allow for a very memory-efficient implementation of parallel adaptive multilevel solvers – an efficiency which is crucial facing the large computational requirements of multi-physics applications and the recent trend in computer architectures towards multi- and many-core systems. preCICE is the successor of our coupling tool FSIsce and offers a solver-independent implementation of coupling strategies and data mapping functionalities for general multi-physics problems. The underlying client-server-like concept maintains the full flexibilty of the partitioned approach with respect to exchangeability of solvers. The data mapping relies on fast spacepartitioning tree algorithms for the detection of geometric neighbourhood relations between components of non-matching grids.

[1]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[2]  Peter Deuflhard,et al.  Numerische Mathematik II , 1994 .

[3]  Hans-Joachim Bungartz,et al.  Numerical Simulation of Particle Transport in a Drift Ratchet , 2008, SIAM J. Sci. Comput..

[4]  D R Bowler,et al.  Automatic data distribution and load balancing with space-filling curves: implementation in CONQUEST , 2008, Journal of physics. Condensed matter : an Institute of Physics journal.

[5]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[6]  Michael Griebel,et al.  Parallel multigrid in an adaptive PDE solver based on hashing and space-filling curves , 1999, Parallel Comput..

[7]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .

[8]  Hari Sundar,et al.  Dendro: parallel algorithms for multigrid and AMR methods on 2:1 balanced octrees , 2008, HiPC 2008.

[9]  R. Rannacher,et al.  Benchmark Computations of Laminar Flow Around a Cylinder , 1996 .

[10]  Hans-Joachim Bungartz,et al.  EFFICIENT INTERFACE TREATMENT FOR FLUID-STRUCTURE INTERACTION ON CARTESIAN GRIDS , 2005 .

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

[12]  J. Tinsley Oden,et al.  Problem decomposition for adaptive hp finite element methods , 1995 .

[13]  Hans-Joachim Bungartz,et al.  Fluid-Structure Interaction on Cartesian Grids: Flow Simulation and Coupling Environment , 2006 .

[14]  Yohsuke Imai,et al.  A higher-order implicit IDO scheme and its CFD application to local mesh refinement method , 2006 .

[15]  E. Hairer,et al.  Stiff and differential-algebraic problems , 1991 .

[16]  Hans-Joachim Bungartz,et al.  A precompiler to reduce the memory footprint of multiscale PDE solvers in C++ , 2010, Future Gener. Comput. Syst..

[17]  Hari Sundar,et al.  Bottom-Up Construction and 2: 1 Balance Refinement of Linear Octrees in Parallel , 2008, SIAM J. Sci. Comput..

[18]  Miriam Mehl,et al.  A cache‐oblivious self‐adaptive full multigrid method , 2006, Numer. Linear Algebra Appl..

[19]  Hester Bijl,et al.  Review of coupling methods for non-matching meshes , 2007 .

[20]  Hans-Joachim Bungartz,et al.  A Parallel Adaptive Cartesian PDE Solver Using Space-Filling Curves , 2006, Euro-Par.

[21]  Yohsuke Imai,et al.  Accuracy study of the IDO scheme by Fourier analysis , 2006, J. Comput. Phys..

[22]  Andreas Dedner,et al.  A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE , 2008, Computing.

[23]  Tobias Neckel.  The PDE Framework Peano: An Environment for Efficient Flow Simulations , 2009 .

[24]  Steven G. Parker,et al.  A component-based parallel infrastructure for the simulation of fluid–structure interaction , 2006, Engineering with Computers.

[25]  Takayuki Aoki,et al.  Interpolated differential operator (IDO) scheme for solving partial differential equations , 1997 .

[26]  Hans-Joachim Bungartz,et al.  DaStGen-A Data Structure Generator for Parallel C++ HPC Software , 2008, ICCS.

[27]  Tobias Weinzierl,et al.  A Framework for Parallel PDE Solvers on Multiscale Adaptive Cartesian Grids , 2009 .

[28]  Pablo D. Mininni,et al.  High-order low-storage explicit Runge-Kutta schemes for equations with quadratic nonlinearities , 2008, 0808.1883.

[29]  William F. Mitchell,et al.  A refinement-tree based partitioning method for dynamic load balancing with adaptively refined grids , 2007, J. Parallel Distributed Comput..

[30]  Josef Stoer,et al.  Numerische Mathematik 2 , 1990 .

[31]  E. Hairer,et al.  Solving Ordinary Differential Equations II , 2010 .

[32]  Jay Walter Larson,et al.  The Model Coupling Toolkit: A New Fortran90 Toolkit for Building Multiphysics Parallel Coupled Models , 2005, Int. J. High Perform. Comput. Appl..

[33]  Jan Vierendeels,et al.  Implicit Coupling of Partitioned Fluid-Structure Interaction Solvers using Reduced-Order Models , 2005 .

[34]  David R. O'Hallaron,et al.  Scalable Parallel Octree Meshing for TeraScale Applications , 2005, ACM/IEEE SC 2005 Conference (SC'05).

[35]  W. Wall,et al.  Fluid–structure interaction approaches on fixed grids based on two different domain decomposition ideas , 2008 .

[36]  P. F. Filtschakow.  Die Integration gewöhnlicher Differentialgleichungen , 1975 .

[37]  J. Szmelter.  Incompressible flow and the finite element method , 2001 .

[38]  D. Braess.  Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics , 1995 .

[39]  Boris Vexler,et al.  Adaptive Space-Time Finite Element Methods for Parabolic Optimization Problems , 2007, SIAM J. Control. Optim..

[40]  Andreas Dedner,et al.  A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework , 2008, Computing.

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

[42]  E. K. Blum,et al.  A modification of the Runge-Kutta fourth-order method , 1962 .

[43]  S. Turek,et al.  Proposal for Numerical Benchmarking of Fluid-Structure Interaction between an Elastic Object and Laminar Incompressible Flow , 2006 .

[44]  Michael Bader,et al.  Cache oblivious matrix multiplication using an element ordering based on the Peano curve , 2006 .

[45]  Gerhard Zumbusch,et al.  Parallel Multilevel Methods , 2003 .

[46]  Rolf Rannacher,et al.  Goal-oriented error control of the iterative solution of finite element equations , 2009, J. Num. Math..

[47]  Yohsuke Imai,et al.  Stable coupling between vector and scalar variables for the IDO scheme on collocated grids , 2006, J. Comput. Phys..

[48]  H. Sagan.  Space-filling curves , 1994 .

[49]  Miriam Mehl,et al.  On the Parallelization of a Cache-Optimal Iterative Solver for PDEs Based on Hierarchical Data Structures and Space-Filling Curves , 2004, PVM/MPI.

[50]  Bruce M. Irons,et al.  A version of the Aitken accelerator for computer iteration , 1969 .

[51]  Hans-Joachim Bungartz,et al.  The PDE framework Peano applied to fluid dynamics: an efficient implementation of a parallel multiscale fluid dynamics solver on octree-like adaptive Cartesian grids , 2010 .

[52]  Kenji Takizawa,et al.  Conservative form of interpolated differential operator scheme for compressible and incompressible fluid dynamics , 2008, J. Comput. Phys..

[53]  Ekkehard Ramm,et al.  Accelerated iterative substructuring schemes for instationary fluid-structure interaction , 2001 .

[54]  Hans-Joachim Bungartz,et al.  CARTESIAN DISCRETISATIONS FOR FLUID-STRUCTURE INTERACTION { CONSISTENT FORCES , 2006 .