A SECOND-ORDER UPWIND LEAST-SQUARES SCHEME FOR INCOMPRESSIBLE FLOWS ON UNSTRUCTURED HYBRID GRIDS

REFERENCES

• J. H. Ferziger and M. Peric , Computational Method for Fluid Dynamics , Springer , New York , 1996 .
   Google Scholar
• A. Jameson and D. Mavriplis , Finite Volume Solution of the Two–Dimensional Euler Equations on a Regular Triangular Mesh , AIAA J. , vol. 24 , pp. 611 – 618 , 1986 .
   Google Scholar
• M. H. Lallemand , H. Steve , and A. Dervieux , Unstructured Multigriding by Volume Agglomeration Current Status, Comput . Fluids , vol. 21 , pp. 397 – 433 , 1992 .
   Google Scholar
• J. S. Mathur and N. P. Weatherill , The Simulation of Inviscid, Compressible Flows Using an Upwind Kinetic Method on Unstructured Grids , Int. J. Numer. Meth. Fluids , vol. 15 , pp. 59 – 82 , 1992 .
   Google Scholar
• P. Tamamidis , A New Upwind Scheme on Triangular Meshes Using the Finite Volume Method , Comput. Meth. Appl. Mech. Eng. , vol. 144 , pp. 15 – 31 , 1995 .
   Google Scholar
• W. K. Anderson and D. L. Bonhaus , An Implicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids , Comput. Fluids , vol. 23 , pp. 1 – 21 , 1994 .
   Web of Science ®Google Scholar
• C. J. Hwang and S. J. Wu , Adaptive Finite Volume Upwind Approach on Mixed Quadrilateral–Triangular Meshes , AIAA J. , vol. 31 , pp. 61 – 67 , 1993 .
   Google Scholar
• T. J. Barth , Aspects of Unstructured Grids and Finite–Volume Solvers for the Euler and Navier–Stokes Equations, Lecture Notes , Von Karmann Inst., Lecture Ser. , 1994–05,1994 .
   Google Scholar
• I. Demirdzic and S. Muzaferija , Numerical Method for Coupled Fluid Flow, Heat Transfer and Stress Analysis Using Unstructured Moving Meshes with Cells of Arbitrary Topology , Comput. Meth. Appl. Mech. Eng. , vol. 125 , pp. 235 – 255 , 1995 .
   Web of Science ®Google Scholar
• M. Thomadakis and M. Leschziner , A Pressure–Correction Method for the Solution of Incompressible Viscous Flows on Unstructured Grids , Int. J. Numer. Meth. Fluids , vol. 22 , no. 7 , pp. 581 – 601 , 1996 .
   Web of Science ®Google Scholar
• Y. F. Egorov , A. O. Galgukov , L. A. Kadinskii , Y. N. Makarov , and A. I. Zhmakin , Modeling of Flow and Growth Processes in Epitaxial Reactors Using Unstructured Grids , in J. A. Desideri , C. Hirsch , P. Le Tallec , M. Randolp , and J. Periaux (eds.), Computational Fluid Dynamics ’96 , pp. 704 – 710 , John Wiley , New York , 1996 .
   Google Scholar
• H. J. Saabas and B. R. Baliga , A Co–Located Equal–Order Control–Volume Finite–Element Method for Multi–Dimensional, Incompressible, Fluid Flow—Part I Formulation , Numer. Heat Transfer, B , vol. 26 , pp. 381 – 407 , 1995 .
   Google Scholar
• M. H. Kobayashi and J. C. F. Pereira , A Comparison of Second Order Convection Discretization Schemes for Incompressible Fluid Flow , Comm. Numer. Meth. Eng. , vol. 12 , pp. 395 – 411 , 1996 .
   Google Scholar
• M. H. Kobayashi and J. C. F. Pereira , Comparison of Several Convection Discretization Schemes for All Mach Number Arbitrary 2D Flows , in C. Taylor , J. H. Chin , and G. Homsy (eds.), Numerical Methods in Laminar and Turbulent Flows , vol. VII , pp. 863 – 873 , Pineridge Press , Swansea , U.K. , 1991 .
   Google Scholar
• M. D. Bristeau , R. Glowinski , J. Periaux , P. Perrier , O. Pironneau , and G. Poirier , Transonic Flow Simulation by Finite Element and Least Squares , in Finite Elements in Fluids , vol. 4 , John Wiley , Chichester , 1980 .
   Google Scholar
• R. Glowinski and J. Periaux , Least Squares and Domain Decomposition Methods Applied to Numerical Solution of Non–linear Problems in Fluid Dynamics , Von Karmann Inst. Lecture Ser. , 1983 – 04 , Rhode St . Genese , Belgium , 1983 .
   Google Scholar
• P. J. Coelho and J. C. F. Pereira , Calculation of a Confined Axisymmetric Laminar Diffusion Flame Using a Local Grid Refinement Technique , Combustion Sci. Technoi , vol. 92 , pp. 243 – 264 , 1993 .
   Web of Science ®Google Scholar
• B. van Leer , Towards the Ultimate Conservative Difference Scheme V. A Second–Order Sequel to Godunov's Method , J. Comput. Phys. , vol. 32 , pp. 101 – 136 , 1979 .
   Web of Science ®Google Scholar
• R. Fletcher , Conjugate Gradient Methods for Indefinite Systems , Lecture Notes in Math. , vol. 506 , pp. 73 – 89 , 1976 .
   Google Scholar
• H. A. van der Vorst , BI–CGSTAB A Fast and Smoothly Converging Variant of BI–CG for the Solution of Nonsymmetric Linear Systems , SIAM J. Stat. 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. Stat. Comput. , vol. 10 , pp. 36 – 52 , 1989 .
   Web of Science ®Google Scholar
• D. Howard , W. M. Connolley , and J. S. Rollet , Unsymmetric Conjugate Gradient Methods and Sparse Direct Methods in Finite Element Flow Simulation , Int. J. Numer. Meth. Fluids , vol. 10 , pp. 925 – 945 , 1990 .
   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. Stat. Comput. , vol. 3 , pp. 856 – 869 , 1986 .
   Google Scholar
• V. Venkatakrishnan , Preconditioned Conjugate Gradient Methods for the Compressible Navier–Stokes Equations , AlAA J. , vol. 29 , no. 7 , pp. 1092 – 2000 , 1991 .
   Google Scholar
• H. P. Langtangen , Conjugate Gradient Methods as in Preconditioning of Nonsymmetric Matrix Systems with Arbitrary Sparsity Patterns , Int. J. Numer. Meth. Fluids , vol. 9 , pp. 213 – 233 , 1989 .
   Web of Science ®Google Scholar
• Address correspondence to Prof. J. C. Pereira, Technical University of Lisbon, Instituto Superior Tecnico, Mechanical Engineering Department, Av. Rovisco Pais, 1096 Lisbon Codex, Portugal, E-mail: [email protected]
   Google Scholar