A COMPARATIVE ASSESSMENT WITHIN A MULTIGRID ENVIRONMENT OF SEGREGATED PRESSURE-BASED ALGORITHMS FOR FLUID FLOW AT ALL SPEEDS

References

• Poussin , F. V. 1968 . An Accelerated Relaxation Algorithm for Iterative Solution of Elliptic Equations . SIAM J. Numer. Anal. , vol. 5 : pp. 340 – 351 .
   Web of Science ®Google Scholar
• Brandt , A. 1977 . Multi-Level Adaptive Solutions for Boundary Value Problems . Math. Comput. , vol. 31 : pp. 333 – 390 .
   Web of Science ®Google Scholar
• Brandt , A. 1982 . Guide to Multigrid Development , Berlin : Springer-Verlag .
   Google Scholar
• Hackbusch , W. 1985 . Multi-Grid Methods and Applications , Berlin : Springer-Verlag .
   Google Scholar
• Trottenberg , U. , Oosterlee , C. and Schuller , A. 2001 . Multigrid , Cornwall, , England : Academic Press .
   Google Scholar
• Brandt , A. and Dinar , N. 1979 . “ Multigrid Solutions to Flow Problems ” . In Numerical Methods for Partial Differential Equations, Part S , 43 – 147 . New York : Academic Press .
   Google Scholar
• Thompson , C. P. and Lezeau , P. 1998 . Application of the Full Approximation Storage Method to the Numerical Simulation of Two-Dimensional Steady Incompressible Viscous Multiphase Flows . Int. J. Numer. Meth. Fluids , vol. 28 ( no. 8 ) : pp. 1217 – 1239 .
   Web of Science ®Google Scholar
• Thompson , M. C. and Ferziger , J. H. 1989 . An Adaptive Multigrid Technique for the Incompressible Navier-Stokes Equations . J. Comput. Phys. , vol. 82 : pp. 94 – 121 .
   Web of Science ®Google Scholar
• Rubini , P. , Becker , H. E. , Grandmaison , E. , Pollard , A. , Sobisak , A. and Thurgood , C. 1992 . Multigrid Acceleration of Three Dimensional Turbulent Variable Density Flows . Numer. Heat Transfer B , vol. 22 : pp. 163 – 177 .
   Web of Science ®Google Scholar
• Zeng , S. and Wesseling , P. 1994 . Multigrid Solution of the Incompressible Navier-Stokes in Generalized Coordinates . SIAM J. Numer. Anal. , vol. 31 : pp. 1764 – 1784 .
   Web of Science ®Google Scholar
• Peric , M. , Rüger , M. and Scheuerer , G. 1989 . “ A Finite Volume Multigrid Method for Calculating Turbulent Flows ” . In Proc. 7th Symp. on Turbulent Shear Flows , 7.3.1 – 7.3.6 . Stanford, CA : Stanford University .
   Google Scholar
• Paisley , M. F. 1999 . Multigrid Solution of the Incompressible Navier-Stokes Equations for Three-Dimensional Recirculating Flow: Coupled and Decoupled Smoothers Compared . Int. J. Numer. Meth. Fluids , vol. 30 : pp. 441 – 459 .
   Web of Science ®Google Scholar
• Kiao , S. J. and Mashayek , F. 2001 . A Multigrid Approach for Steady State Laminar Viscous Flows . Int. J. Numer. Meth. Fluids , vol. 37 : pp. 107 – 123 .
   Web of Science ®Google Scholar
• Patankar , S. V. and Spalding , D. B. 1972 . A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows . Int. J. Mass Transfer , vol. 15 : pp. 1787 – 1806 .
   Web of Science ®Google Scholar
• Sivaloganathan , S. and Shaw , G. J. 1988 . An Efficient Non-linear Multigrid Procedure for the Incompressible Navier-Stokes Equations . Int. J. Numer. Meth. Fluids , vol. 8 : pp. 417 – 440 .
   Google Scholar
• Shyy , W. and Sun , C. S. 1993 . Development of a Pressure-Correction/Staggered Grids Based Multigrid Solver for Incompressible Recirculating Flow . Comput. Fluids , vol. 22 : pp. 51 – 76 .
   Web of Science ®Google Scholar
• Becker , C. , Ferziger , J. H. , Períc , M. and Scheurer , G. 1988 . Finite Volume Multigrid Solutions of the Two-Dimensional Incompressible Navier-Stokes Equations . Notes Numer. Fluid Mech. , vol. 23 : pp. 37 – 47 .
   Google Scholar
• Smith , K. M. , Cope , W. K. and Vanka , S. P. 1993 . Multigrid Procedure for Three Dimensional Flows on Non-orthogonal Collocated Grids . Int. J. Numer. Meth. Fluids , vol. 17 : pp. 887 – 904 .
   Web of Science ®Google Scholar
• Lien , F. S. and Lechziner , M. A. 1994 . Multigrid Acceleration for Recirculating Laminar and Turbulent Flow Computed on a Non-orthogonal, Collocated Finite Volume Scheme . Comput. Meth. Appl. Mech. Eng. , vol. 118 : pp. 351 – 371 .
   Web of Science ®Google Scholar
• Gjesdal , T. and Lossius , M. E. H. 1997 . Comparison of Pressure Correction Smoothers for Multigrid Solution of Incompressible Flow . Int. J. Numer. Meth. Fluids , vol. 25 : pp. 393 – 405 .
   Web of Science ®Google Scholar
• Maliska , C. R. and Raithby , G. D. 1983 . “ Calculating 3-D Fluid Flows Using Non-orthogonal Grid ” . In Proc. Third Int. Conf. on Numerical Methods in Laminar and Turbulent Flows 656 – 666 . Seattle, WA
   Google Scholar
• Moukalled , F. and Darwish , M. 2000 . A Unified Formulation of the Segregated Class of Algorithms for Fluid Flow at All Speeds . Numer. Heat Transfer B , vol. 37 ( no. 1 ) : pp. 103 – 139 .
   Web of Science ®Google Scholar
• Moukalled , F. and Darwish , M. 2001 . A High-Resolution Pressure-Based Algorithm for Fluid Flow at All Speeds . J. Comput. Phys. , vol. 168 ( no. 1 ) : pp. 101 – 133 .
   Web of Science ®Google Scholar
• Mavriplis , D. J. and Jameson , A. 1988 . Multigrid Solution of the Two-Dimensional Euler Equations on Unstructured Triangular Meshes . AIAA J. , vol. 26 ( no. 7 ) : pp. 824 – 831 .
   Google Scholar
• Connel , S. D. and Holmes , D. G. 1994 . A 3D Unstructured Adaptive Multigrid Scheme for the Euler Equations . AIAA J. , vol. 32 ( no. 8 ) : pp. 1626 – 1632 .
   Google Scholar
• Chorin , A. J. 1967 . A Numerical Method for Solving Incompressible Viscous Flow Problems . J. Comput. Phys. , vol. 2 : pp. 12 – 26 .
   Google Scholar
• Rizzi , A. and Eriksson , L. E. 1985 . Computation of Inviscid Incompressible Flow with Rotation . J. Fluid Mech. , vol. 153 ( no. 3 ) : pp. 275 – 312 .
   Google Scholar
• Choi , D. and Merkle , C. L. 1985 . Application of Time-Iterative Schemes to Incompressible Flow . AIAA J. , vol. 23 : pp. 1518 – 1524 .
   Google Scholar
• Karki , K. C. 1986 . A Calculation Procedure for Viscous Flows at All Speeds in Complex Geometries , Twin Cities, MN : University of Minnesota . Ph.D. thesis
   Google Scholar
• Rhie , C. M. 1986 . A Pressure Based Navier-Stokes Solver Using the Multigrid Method AIAA Paper 86–0207
   Google Scholar
• Shyy , W. and Braaten , M. E. 1988 . Adaptive Grid Computation for Inviscid Compressible Flows Using a Pressure Correction Method AIAA paper 88–3566-CP
   Google Scholar
• Lien , F. S. and Leschziner , M. A. 1993 . A Pressure-Velocity Solution Strategy for Compressible Flow and Its Application to Shock/Boundary-Layer Interaction Using Second-Moment Turbulence Closure . J. Fluids Eng. , vol. 115 : pp. 717 – 725 .
   Web of Science ®Google Scholar
• Politis , E. S. and Giannakoglou , K. C. 1997 . A Pressure-Based Algorithm for High-Speed Turbomachinery Flows . Int. J. Numer. Meth. Fluids , vol. 25 : pp. 63 – 80 .
   Web of Science ®Google Scholar
• Van Doormaal , J. P. and Raithby , G. D. 1984 . Enhancement of the SIMPLE Method for Predicting Incompressible Fluid Flows . Numer. Heat Transfer , vol. 7 : pp. 147 – 163 .
   Google Scholar
• Issa , R. I. 1982 . “ Solution of the Implicit Discretized Fluid Flow Equations by Operator Splitting ” . In Mech. Eng. Rep. , London, UK : Imperial College . FS/82/15
   Google Scholar
• Van Doormaal , J. P. and Raithby , G. D. An Evaluation of the Segregated Approach for Predicting Incompressible Fluid Flows . ASME paper 85-HT-9 . 4-7 August , Denver, CO : National Heat Transfer Conference .
   Google Scholar
• Spalding , D. B. 1980 . “ Mathematical Modelling of Fluid Mechanics, Heat Transfer and Mass Transfer Processes ” . In Mech. Eng. Dept. Rep. , London, UK : Imperial College of Science, Technology and Medecine . HTS/80/1
   Google Scholar
• Darwish , M. S. and Moukalled , F. 1994 . Normalized Variable and Space Formulation Methodology for High Resolution Schemes . Numer. Heat Transfer B , vol. 26 : pp. 79 – 96 .
   Web of Science ®Google Scholar
• Patankar , S. V. 1981 . Numerical Heat Transfer and Fluid Flow , New York : Hemisphere .
   Google Scholar
• Rhie , C. M. and Chow , W. L. 1983 . Numerical Study of the Turbulent Flow Past and Airfoil with Trailing Edge Separation . AIAA J. , vol. 21 : pp. 1525 – 1532 .
   Google Scholar
• Peric , M. 1985 . A Finite Volume Method for the Prediction of Three Dimensional Fluid Flow in Complex Ducts , London, UK : Imperial College . Ph.D. thesis
   Google Scholar
• Sivaloganathan , S. and Shaw , G. J. 1988 . On the Smoothing Properties of the SIMPLE Pressure Correction Algorithm . Int. J. Numer. Meth. Fluids , vol. 8 : pp. 441 – 461 .
   Web of Science ®Google Scholar
• Favini , B. , Broglia , R. and Di Mascio , A. 1996 . Multigrid Acceleration of Second-Order ENO Schemes from Low Subsonic to High Supersonic Flows . Int. J. Numer. Meth. Fluids , vol. 23 : pp. 589 – 606 .
   Web of Science ®Google Scholar
• Demirdzic , I. , Lilek , Z. and Peric , M. 1993 . A Collocated Finite Volume Method for Predicting Flows at all Speeds . Int. J. Numer. Meth. Fluids , vol. 16 : pp. 1029 – 1050 .
   Web of Science ®Google Scholar
• Hwang , C. J. and Wu , S. J. 1993 . Adaptive Finite Volume Upwind Approach on Mixed Quadrilateral-Triangular Meshes . AIAA J. , vol. 31 : pp. 61 – 67 .
   Google Scholar
• Yang , J. Y. , Perng , Y. C. and Yen , R. H. 2001 . Implicit Weighted Essentially non-Oscillatory Schemes for the Navier-Stokes Equations . AIAA J. , vol. 39 : pp. 2082 – 2090 .
   Google Scholar
• Batina , J. T. 1991 . Implicit Flux-Split Euler Schemes for Unsteady Aerodynamic Analysis Involving Unstructured Dynamic Meshes . AIAA J. , vol. 29 : pp. 1836 – 1843 .
   Google Scholar
• Yaldin , Y. and Caughy , D. 1991 . Block Multigrid Implicit Solution of the Euler Equations of Compressible Fluid Flow . AIAA J. , 29 : 712 – 719 .
   Google Scholar