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Section B

Modified alternating direction-implicit iteration method for linear systems from the incompressible Navier–Stokes equations

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Pages 3762-3779 | Received 26 Nov 2010, Accepted 04 Sep 2011, Published online: 19 Oct 2011

References

  • Axelsson , O. 1994 . “ Iterative Solution Methods ” . Cambridge : Cambridge University Press .
  • Axelsson , O. , Bai , Z.-Z. and Qiu , S.-X. 2004 . A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part . Numer. Algorithms , 35 : 351 – 372 .
  • Bai , Z.-Z. 1999 . A class of modified block SSOR preconditioners for symmetric positive definite systems of linear equations . Adv. Comput. Math , 10 : 169 – 186 .
  • Bai , Z.-Z. 2001 . Modified block SSOR preconditioners for symmetric positive definite linear systems . Ann. Oper. Res , 103 : 263 – 282 .
  • Bai , Z.-Z. and Chi , X.-B. 2003 . Asymptotically optimal successive overrelaxation methods for systems of linear equations . J. Comput. Math , 21 : 603 – 612 .
  • Bai , Z.-Z. and Huang , T.-Z. 1998 . On the convergence of the relaxation methods for positive definite linear systems . J. Comput. Math , 16 : 527 – 538 .
  • Bai , Z.-Z. and Wang , D.-R. 1993 . Generalized matrix multisplitting relaxation methods and their convergence . Numer. Math. J. Chinese Univ. (English Ser.) , 2 : 87 – 100 .
  • Bai , Z.-Z. , Golub , G. H. and Ng , M. K. 2003 . Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems . SIAM J. Matrix Anal. Appl , 24 : 603 – 626 .
  • Bai , Z.-Z. , Golub , G. H. , Lu , L.-Z. and Yin , J.-F. 2005 . Block triangular and skew-Hermitian splitting methods for positive-definite linear systems . SIAM J. Sci. Comput , 26 : 844 – 863 .
  • Bai , Z.-Z. , Golub , G. H. and Ng , M. K. 2008 . On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems . Linear Algebra Appl , 428 : 413 – 440 .
  • Beam , R. M. and Warming , R. F. 1976 . An implicit finite-difference algorithm for hyperbolic systems in conservation-law form . J. Comput. Phys , 22 : 87 – 110 .
  • Chorin , A. J. 1967 . A numerical method for solving incompressible viscous flow problems . J. Comput. Phys , 2 : 12 – 26 .
  • Chorin , A. J. 1968 . Numerical solution of the Navier–Stokes equations . Math. Comput , 22 : 742 – 762 .
  • Gresho , P. M. 1991 . Incompressible fluid dynamics: Some fundamental formulation issues . Ann. Rev. Fluid Mech , 23 : 413 – 453 .
  • MacCormack , R. W. and Candler , G. V. 1989 . The solution of the Navier–Stokes equations using Gauss–Seidel line relaxation . Comput. Fluids , 17 : 135 – 150 .
  • Orlandi , P. 1999 . Fluid Flow Phenomena: A Numerical Toolkit , Amsterdam : Kluwer Academic Publishers .
  • Peaceman , D. W. and Rachford Jr , H. H. 1955 . The numerical solution of elliptic and parabolic differential equations . SIAM J. Soc. Indust. Appl. Math , 3 : 28 – 41 .
  • Pearcy , C. 1962 . On convergence of alternating direction procedures . Numer. Math , 4 : 172 – 176 .
  • Pulliam , T. H. and Chaussee , D. S. 1981 . A diagonal form of an implicit approximate-factorization algorithm . J. Comput. Phys , 39 : 347 – 363 .
  • Ran , Y.-H. and Yuan , L. 2010 . On modified block SSOR iteration methods for linear systems from steady incompressible viscous flow problems . Appl. Math. Comput , 217 : 3050 – 3068 .
  • Shah , A. and Yuan , L. 2009 . Flux-difference splitting-based upwind compact schemes for the incompressible Navier–Stokes equations . Intern. J. Numer. Methods Fluids , 61 : 552 – 568 .
  • Shah , A. , Guo , H. and Yuan , L. 2009 . A third-order upwind compact scheme on curvilinear meshes for the incompressible Navier–Stokes equations . Commun. Comput. Phys , 5 : 712 – 729 .
  • Shah , A. , Yuan , L. and Khan , A. 2010 . Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier–Stokes equations . Appl. Math. Comput , 215 : 3201 – 3213 .
  • Yoon , S. and Jameson , A. 1988 . Lower-upper symmetric-Gauss–Seidel method for the Euler and Navier–Stokes equations . AIAA J , 26 : 1025 – 1026 .

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