High-order accurate solution of the incompressible Navier-Stokes equations on massively parallel computers

[1]  E. Meiburg,et al.  DIRECT NUMERICAL SIMULATION OF A MODEL ESTUARY , 2009, Proceeding of Sixth International Symposium on Turbulence and Shear Flow Phenomena.

[2]  Javier Jiménez,et al.  A high-resolution code for turbulent boundary layers , 2009, J. Comput. Phys..

[3]  S. L. Borne,et al.  Block computation and representation of a sparse nullspace basis of a rectangular matrix , 2008 .

[4]  Sabine Le Borne,et al.  Hierarchical matrix preconditioners for the Oseen equations , 2008 .

[5]  J. Xu,et al.  Benchmarks on tera-scalable models for DNS of turbulent channel flow , 2007, Parallel Comput..

[6]  Javier Jiménez,et al.  Scaling of the velocity fluctuations in turbulent channels up to Reτ=2003 , 2006 .

[7]  K. Chen,et al.  Matrix preconditioning techniques and applications , 2005 .

[8]  Takashi Nodera,et al.  Breakdown-Free ML(k)BiCGStab Algorithm for Non-Hermitian Linear Systems , 2005, ICCSA.

[9]  Per Lötstedt,et al.  High order accurate solution of the incompressible Navier-Stokes equations , 2005 .

[10]  Jonathan J. Hu,et al.  Parallel multigrid smoothing: polynomial versus Gauss--Seidel , 2003 .

[11]  V. E. Henson,et al.  BoomerAMG: a parallel algebraic multigrid solver and preconditioner , 2002 .

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

[13]  Paul N. Swarztrauber,et al.  A comparison of optimal FFTs on torus and hypercube multicomputers , 2001, Parallel Comput..

[14]  Alex Povitsky,et al.  Parallelization of Pipelined Algorithms for Sets of Linear Banded Systems , 1999, J. Parallel Distributed Comput..

[15]  Howard C. Elman,et al.  Preconditioning for the Steady-State Navier-Stokes Equations with Low Viscosity , 1999, SIAM J. Sci. Comput..

[16]  Yuguo Li Wavenumber-Extended High-Order Upwind-Biased Finite-Difference Schemes for Convective Scalar Transport , 1997 .

[17]  S. Turek a Comparative Study of Time-Stepping Techniques for the Incompressible Navier-Stokes Equations: from Fully Implicit Non-Linear Schemes to Semi-Implicit Projection Methods , 1996 .

[18]  Robert E. Tarjan,et al.  Analysis of Multigrid Algorithms on Massively Parallel Computers: Architectural Implications , 1996, J. Parallel Distributed Comput..

[19]  Timothy J. Williams,et al.  Algorithm for Solving Tridiagonal Matrix Problems in Parallel , 1995, Parallel Comput..

[20]  Jinhee Jeong,et al.  On the identification of a vortex , 1995, Journal of Fluid Mechanics.

[21]  R. LeVeque,et al.  A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources , 2006 .

[22]  P. Moin,et al.  Effects of the Computational Time Step on Numerical Solutions of Turbulent Flow , 1994 .

[23]  Thomas Eidson,et al.  Implementation of a fully balanced periodic tridiagonal solver on a parallel distributed memory architecture , 1994, Concurr. Pract. Exp..

[24]  S. Lele Compact finite difference schemes with spectral-like resolution , 1992 .

[25]  Dan S. Henningson,et al.  An efficient spectral integration method for the solution of the Navier-Stokes equations , 1992 .

[26]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[27]  S. Orszag,et al.  High-order splitting methods for the incompressible Navier-Stokes equations , 1991 .

[28]  R. Moser,et al.  Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions , 1991 .

[29]  S. Armfield Finite difference solutions of the Navier-Stokes equations on staggered and non-staggered grids , 1991 .

[30]  G. Blaisdell,et al.  Numerical simulation of compressible homogeneous turbulence , 1991 .

[31]  G. Wittum Multi-grid methods for stokes and navier-stokes equations , 1989 .

[32]  Parviz Moin,et al.  On the numerical solution of time-dependent viscous incompressible fluid flows involving solid boundaries , 1980 .

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

[34]  L. Kleiser,et al.  Simulation of Gravity-Driven Flows Using an Iterative High-Order Accurate Navier–Stokes Solver , 2010 .

[35]  John N. Shadid,et al.  A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations , 2008, J. Comput. Phys..

[36]  P. Schlatter Large-eddy simulation of transition and turbulence in wall-bounded shear flow , 2005 .

[37]  Fuzhen Zhang The Schur complement and its applications , 2005 .

[38]  T. Fujimoto,et al.  TWO CHARACTERIZATIONS OF INVERSE-POSITIVE MATRICES: THE HAWKINS-SIMON CONDITION AND THE LE CHATELIER-BRAUN PRINCIPLE ∗ , 2004 .

[39]  P. Wesseling Principles of Computational Fluid Dynamics , 2000 .

[40]  P. Moin,et al.  DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research , 1998 .

[41]  Anne Greenbaum,et al.  Iterative methods for solving linear systems , 1997, Frontiers in applied mathematics.

[42]  Wolfgang Joppich,et al.  A Comparison of Parallel Multigrid and a Fast Fourier Transform Algorithm for the Solution of the Helmholtz Equation in Numerical Weather Prediction , 1997, Parallel Comput..

[43]  Leonhard Kleiser,et al.  Numerical simulation of transition in wall-bounded shear flows , 1991 .

[44]  Wolfgang Hackbusch,et al.  Multi-grid methods and applications , 1985, Springer series in computational mathematics.