Parametric Study of an Improved Gamma Differencing Scheme Based on Normalized-Variable Formulation for Low-Speed Flow With Artificial Compressibility Technique

REFERENCES

• D. T. Elsworth and E. F. Toro , A Numerical Investigation of the Artificial Compressibility Method for the Solution of the Navier-Stokes Equations, College of Aeronautics Report No. 9213 , Cranfield Institute of Technology , UK , 1992 .
   Google Scholar
• S. V. Patankar , Numerical Heat Transfer and Fluid Flow , Hemisphere , Washington , DC , 1980 .
   Google Scholar
• R. I. Issa , Solution of Implicitly Discretized Fluid Flow Equations by Operator-Splitting , J. Comput. Phys. , vol. 62 , pp. 40 – 65 , 1986 . [CSA]
   Web of Science ®Google Scholar
• A. J. Chorin , A Numerical Method for Solving Incompressible Viscous Flow Problems , J. Comput. Phys. , vol. 2 , pp. 12 – 26 , 1967 . [CSA] [CROSSREF]
   Google Scholar
• J. D. Ramshaw and V. A. Mousseau , Accelerated Artificial Compressibility Method for Steady-State Incompressible Flow Calculations , Comput. Fluids , vol. 18 , no. 4 , pp. 361 – 367 , 1990 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• W. K. Anderson , R. D. Rausch , and D. L. Bonhaus , Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids , J. Comput. Phys. , vol. 128 , pp. 391 – 408 , 1996 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• D. Drikakis , O. P. Iliev , and D. P. Vassileva , A Nonlinear Multigrid Method for the Three-Dimensional Incompressible Navier-Stokes Equations , J. Comput. Phys. , vol. 146 , pp. 301 – 321 , 2003 . [CSA] [CROSSREF]
   Google Scholar
• L. He and K. Sato , Numerical Solution of Incompressible Unsteady Flows in Turbomachinery , ASME J. Fluids Eng. , vol. 123 , no. 3 , pp. 680 – 685 , 2001 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• D. T. Elsworth and E. F. Toro , Riemann Solvers for Solving the Incompressible Navier-Stokes Equations Using the Artificial Compressibility Method, College of Aeronautics Report No. 9208, Cranfield Institute of Technology , UK , 1992 .
   Google Scholar
• Y. Zhao and B. L. Zhang , A High-Order Characteristic Upwind FV Method for Incompressible Flow and Heat Transfer Simulation on Unstructured Grids , Comput. Meth. Appl. Mech. Eng. , vol. 190 , pp. 733 – 756 , 2000 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• X. D. Liu and E. Tadmor , Third Order Non-oscillatory Central Scheme for Hyperbolic Conservation Laws , Numer. Math. , vol. 79 , pp. 397 – 425 , 1998 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• P. H. Gaskell and A. K. C. Lau , Curvature-Compensated Convective Transport: SMART, A New Boundedness-Preserving Transport Algorithms , Int. J. Numer. Meth. Fluids , vol. 8 , pp. 617 – 641 , 1988 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• H. Jasak , H. Weller , and A. D. Gosman , High Resolution NVD Differencing Scheme for Arbitrarily Unstructured Meshes, Int. J. Numer. Meth. Fluids , vol. 31, pp. 431–449, 1999. [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• V. Przulj and B. Basara , Bounded Convection Schemes for Unstructured Grids , Proc. AIAA Computational Fluid Dynamics Conf. , Anaheim, CA, AIAA Paper 2001–2593 , 2001 .
   Google Scholar
• J. J. Wei , B. Yu , W. Q. Tao , Y. Kawaguchi , and H. S. Wang , A New High-Order Accurate and Bounded Scheme for Incompressible Flow , Numer. Heat Transfer B , vol. 43 , pp. 19 – 41 , 2003 . [CSA]
   Web of Science ®Google Scholar
• M. Darwish and F. Moukalled , The χ-Schemes: A New Consistent High-Resolution Formulation Based on the Normalized Variable Methodology , Comput. Meth. Appl. Mech. Eng. , vol. 192 , pp. 1711 – 1730 , 2003 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• M. A. Alves , P. J. Oliveira , and F. T. Pinho , A Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection , Int. J. Numer. Meth. Fluids , vol. 41 , pp. 47 – 75 , 2003 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• K. C. Ng , M. Z. Yusoff , and E. Y. K. Ng , Multigrid Solution of Euler Equations Using High-Resolution NVD Differencing Scheme for Unstructured Meshes , Prog. Comput. Fluid Dynam. , in press , 2005 . [CSA]
   Web of Science ®Google Scholar
• A. Jameson , W. Schmidt , and E. Turkel , Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Schemes, AIAA Paper 81-1259 , 1981 . [CSA]
   Google Scholar
• A. Jameson , Transonic Flow Calculations , MAE Report 1651, MAE Department , Princeton University , Princeton , NJ , 1983 .
   Google Scholar
• B. P. Leonard , Simple High-Accuracy Resolution Program for Convective Modeling of Discontinuities , Int. J. Numer. Meth. Eng. , vol. 8 , pp. 1291 – 1318 , 1988 . [CSA]
   Web of Science ®Google Scholar
• H. Jasak , Error Analysis and Estimation for the Finite Volume Method with Applications to Fluid Flow, Ph.D. thesis, Imperial College, University of London , London , UK , 1996 .
   Google Scholar
• B. Song , G. R. Liu , K. Y. Lam , and R. S. Amano , On a Higher-Order Bounded Discretization Scheme , Int. J. Numer. Meth. Fluids , vol. 32 , pp. 881 – 897 , 2000 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• A. M. Binnie and J. R. Green , An Electrical Detector of Condensation in High-Velocity Steam , Proc. Roy. Soc. (Lond.) A , vol. 181 , pp. 134 – 154 , 1943 . [CSA]
   Google Scholar
• M. Z. Yusoff , An Improved Treatment of Two-Dimensional Two-Phase Flows of Steam by a Runge-Kutta Method, Ph.D. thesis, Department of Manufacturing and Mechanical Engineering, University of Birmingham , Birmingham , UK , 1997 .
   Google Scholar
• N. Gregory and C. L. O'Reilly , Low Speed Aerodynamics Characteristics of NACA Airfoil Sections, Including the Effects of Upper Surface Roughness Simulating Hoar Frost, N.P.L., R & M, No. 3726, ARC 31719 , 1970 . [CSA]
   Google Scholar