On a Wavenumber Optimized Streamline Upwinding Method for Solving Steady Incompressible Navier-Stokes Equations

REFERENCES

• A. Brooks and T. J. R. Hughes , Streamline Upwind/Petrov-Galerkin Formulation for Convection Dominated Flow with Particular Emphasis on the Incompressible Navier-Stokes Equations , Comput. Meth. Appl. Mech. Eng. , vol. 32 , pp. 199 – 259 , 1982 .
   Web of Science ®Google Scholar
• R. W. Freund , Transpose-Free Quasi-Minimal Residual Methods for Non-Hermitian Linear Systems , in G. H. Golub , A. Greenbaum , and M. Luskin (eds.), Recent Advances in Iterative Methods , IMA Vol. Math. Appl. , vol. 60 , pp. 69 – 94 , 1994 .
   Google Scholar
• V. Simoncini and D. B. Szyld , Recent Computational Developments in Krylov Subspace Method for Linear Systems , Numer. Linear Algebr. , vol. 14 , pp. 1 – 59 , 2007 .
   Web of Science ®Google Scholar
• T. J. R. Hughes , I. Levit , and J. M. Winget , An Element-by-Element Solution Algorithm for Problems of Structural and Solid Mechanics , Comput. Meth. Appl. Mech. Eng. , vol. 36 , pp. 241 – 254 , 1983 .
   Web of Science ®Google Scholar
• R. Codina , E. Oñate , and M. Cervera , The Intrinsic Time for the Streamline Upwind/Petrov-Galerkin Formulation Using the Quadratic Elements , Comput. Meth. Appl. Mech. Eng. , vol. 94 , pp. 239 – 262 , 1992 .
   Web of Science ®Google Scholar
• C. K. W. Tam and J. C. Webb , Dispersion-Relation-Preserving Finite Difference Schemes for Computational Acoustics, J. Comput. Phys. , vol. 107, pp. 262–281, 1993.
   Web of Science ®Google Scholar
• Y. Saad and M. H. Schultz , GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems , SIAM J. Sci. Comput. , vol. 7 , pp. 856 – 869 , 1986 .
   Web of Science ®Google Scholar
• H. A. Van der Vorst , Bi-CGSTAB: A Fast and Smoothly Converging Variants of Bi-CG for the Solution of Non-Symmetric Linear Systems , SIAM J. Sci. Comput. , vol. 13 , pp. 631 – 644 , 1992 .
   Web of Science ®Google Scholar
• P. Sonneveld , CGS: A Fast Lanczos-Type Solver for Nonsymmetric Linear Systems , SIAM J. Sci. Comput. , vol. 10 , pp. 36 – 52 , 1989 .
   Web of Science ®Google Scholar
• R. W. Freund and M. Hochbruck , On the Use of Two QMR Algorithms for Solving Singular Systems and Applications in Markov Chain Modeling , Numer. Linear Algebr. , vol. 1 , pp. 403 – 420 , 1994 .
   Web of Science ®Google Scholar
• R. W. Freund and N. M. Nachtigal , OMR: A Quasi-Minimal Residual Methods for Non-Hermitian Linear Systems , Numer. Math. , vol. 60 , pp. 315 – 339 , 1991 .
   Web of Science ®Google Scholar
• C. Brezinski , M. D. Zaglia , and H. Sadok , Breakdowns in the Implementation of the Lanczos Method for Solving Linear Systems , Comput. Math. Appl. , vol. 33 , pp. 31 – 44 , 1997 .
   Web of Science ®Google Scholar
• M. H. Gutknecht , Variants of BICGSTAB for Matrices with Complex Specturm , SIAM J. Sci. Comput. , vol. 14 , pp. 1020 – 1033 , 1993 .
   Web of Science ®Google Scholar
• G. L. G. Sleijpen and D. R. Fokkema , BICGSTAB (l) for Linear Equations Involving Unsymmetric Matrices with Complex Spectrum , Electron. Trans. Numer. Anal. , vol. 1 , pp. 11 – 32 , 1993 .
   Google Scholar
• M. R. Hestenes and E. Stiefel , Methods of Conjugate Gradients for Solving Linear Systems , J. Res. Natl. Inst. Stan. , vol. 49 , pp. 409 – 436 , 1952 .
   Web of Science ®Google Scholar
• P. Concus , G. H. Golub , and D. P. O'Leary , A Generalized Conjugate Gradient Method for the Numerical Solutions of the Elliptic Partial Differential Equations , in J. R. Bunch and D. J. Rose (eds.), Sparse Matrix Computations , Academic Press , New York , 1976 .
   Google Scholar
• M. A. Ajiz and A. Jennings , A Robust Incomplete Cholesky Conjugate Gradient Algorithm , Int. J. Numer. Meth. Eng. , vol. 20 , pp. 949 – 966 , 1984 .
   Web of Science ®Google Scholar
• Y. Saad , Practical Use of Polynomial Preconditioning for the Conjugate Gradient Method , SIAM J. Sci. Comput. , vol. 6 , pp. 865 – 881 , 1985 .
   Web of Science ®Google Scholar
• V. E. Bulgakov and G. Kuhn , High-Performance Multi-Level Iterative Aggregation Solver for Large Finite-Element Structure Analysis Problems , Int. J. Numer. Meth. Eng. , vol. 38 , pp. 3529 – 3544 , 1995 .
   Web of Science ®Google Scholar
• J. M. Winget and T. J. R. Hughes , Solution Algorithm for Non-Linear Transient Heat Conduction Analysis Employing Element-by-Element Iterative Strategies , Comput. Meth. Appl. Mech. Eng. , vol. 52 , pp. 811 – 815 , 1985 .
   Web of Science ®Google Scholar
• B. Nour-Omid and B. N. Parlett , Element Preconditioning Using Splitting Technique , SIAM J. Sci. Stat. Comput. , vol. 6 , pp. 761 – 770 , 1985 .
   Web of Science ®Google Scholar
• F. H. Lee , K. K. Phoon , K. C. Lim , and S. H. Chan , Performance of Jacobi Precondtioning in Krylov Subspace Solutiom of Finite Element Equations , Int. J. Numer. Anal. Meth. , vol. 26 , pp. 341 – 372 , 2002 .
   Web of Science ®Google Scholar
• R. W. Freund , G. H. Golub , and N. M. Nacgtigal , Recent Advances in Lanczos-Based Iterative Methods for Nonsymmetic Linear Systems , in M. Y. Hussaini , A. Kumar , and M. D. Salas , (eds.), Algorithm Trends in Computational Fluid Dynamics , Springer-Verlag Press , Berlin , 1993 .
   Google Scholar
• C. C. Fang and T. W. H. Sheu , Two Element-by-Element Iterative Solutions for Shallow Water Equations , SIAM J. Sci. Comput. , vol. 22 , pp. 2075 – 2092 , 2001 .
   Web of Science ®Google Scholar
• H. Ding , C. Shu , K. S. Yeo , and D. Xu , Numerical Computaion of Three-Dimensional Incompressible Viscous Flows in the Primitive Variable Form by Local Multiquadratic Differential Quadrature Method , Comput. Meth. Appl. Mech. Eng. , vol. 195 , pp. 516 – 533 , 2006 .
   Web of Science ®Google Scholar
• Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/unhb.
   Google Scholar