PRESSURE BOUNDARY CONDITIONS OF INCOMPRESSIBLE FLOWS WITH CONJUGATE HEAT TRANSFER ON NONSTAGGERED GRIDS, PART I: METHODS

REFERENCES

• S. Orszag and M. Israeli , Numerical Simulation of Viscous Incompressible Flows , J. Atmos. Sci. , vol. 24 , pp. 337 – 355 , 1972 .
   Google Scholar
• P. Moin and J. Kim , On the Numerical Solution of Time-Dependent Viscous Incompressible Fluid Flows Involving Solid Boundaries , J. Comput, Phys. , vol. 3 , pp. 381 – 392 , 1980 .
   Google Scholar
• P. M. Gresho and R. L. Sani , On Pressure Boundary Conditions for the Incompressible Navier-Stokes Equations , Int. J. Numer. Methods Fluids , vol. 7 , pp. 1111 – 1145 , 1987 .
   Web of Science ®Google Scholar
• S. Abdallah , Numerical Solutions for the Pressure Poisson Equation with Neumann Boundary Conditions Using a Nonstaggered Grid : I, J. Comput. Phys. , vol. 70 , pp. 182 – 192 , 1987 .
   Web of Science ®Google Scholar
• S. Abdallah , Numerical Solutions for the Incompressible Navier-Stokes Equations in Primitive Variables Using a Nonstaggered Grid II , J. Comput. Phys. , vol. 70 , pp. 193 – 202 , 1987 .
   Web of Science ®Google Scholar
• F. Sotiropoulos and S. Abdallah , The Discrete Continuity Equation in Primitive Variable Solutions of Incompressible Flow , J. Comput. Phys. , vol. 95 , pp. 212 – 227 , 1991 .
   Web of Science ®Google Scholar
• H. H. Francis and J. E. Welch , Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface , Phys. Fluids , vol. 8 , pp. 2182 – 2189 , 1965 .
   Web of Science ®Google Scholar
• S. V. Patankar , Numerical Heat Transfer and Fluid Flow , Hemisphere , Washington , D.C. , 1980 .
   Google Scholar
• J. P. van Doormaal and G. D. Raithby , Enhancements of the SIMPLE Method for Predicting Incompressible Fluid Flows , Numer. Heat Transfer , vol. 7 , pp. 147 – 163 , 1984 .
   Web of Science ®Google Scholar
• Y. Zang , R. L. Street , and J. R. Koseff , A Nonstaggered Grid, Fractional Step Method for Time-Dependent Incompressible Navier-Stokes Equations in Curvilinear Coordi-nates , J. Comput. Phys. , vol. 114 , pp. 18 – 33 , 1994 .
   Web of Science ®Google Scholar
• A. W. Date , Solution of Navier-Stokes Equations on Nonstaggered Grid , Int. J. Heat Mass Transfer , vol. 7 , pp. 1913 – 1922 , 1993 .
   Google Scholar
• H. C. Tien , Finite Analytic Method for Two-Dimensional Flow with Irregular Bound-aries , Ph.D. thesis, Department of Applied Math , University of Iowa , 1993 .
   Google Scholar
• W. L. Lin , Diagonal Cartesian Method for Modeling of Flows over Complex Boundaries , Ph.D. thesis, Department of Mechanical Engineering , Florida State University , 1997 .
   Google Scholar
• E. Paterson and F. Stern , Computation of Unsteady Viscous Flow with Application to the MIT Flapping-Foil Experiment , in Proceedings of the 6th International Conference on Numerical Ship Hydrodynamics , Iowa City , Iowa , |mAugust|m 1993 .
   Google Scholar
• C. M. Rhie and W. L. Chow , Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , AIAA J. , vol. 21 , pp. 1525 – 1532 , 1983 .
   Google Scholar
• H. Aksoy and C. J. Chen , Numerical Solution of Navier-Stokes Equations with Nonstag-gered Grids Using Finite Analytic Method , Numer. Heat Transfer Part B , vol. 21 , pp. 287 – 306 , 1992 .
   Web of Science ®Google Scholar
• K. Gustafson and K. Halasi , Vortex Dynamics of Cavity Flows , J. Comput. Phys. , vol. 64 , pp. 279 – 319 , 1986 .
   Web of Science ®Google Scholar
• P. M. Gresho , Incompressible Fluid Dynamics Some Fundamental Formulation Issues , Annu. Rev. Fluid Mech. , vol. 23 , pp. 413 – 453 , 1991 .
   Web of Science ®Google Scholar
• C. J. Chen , H. Naseri-Neshat , and K. S. Ho , Finite Analytic Numerical Solution of Heat Transfer in Two-Dimensional Cavity Flow , Numer. Heat Transfer , vol. 4 , pp. 179 – 197 , 1981 .
   Google Scholar
• X. J. Zeng and W. Li , The Stability and Convergence of Finite Analytic Method for Unsteady Two-Dimensional Convective Transport Equations , in C. J. Chen , L. D. Chen , and E. M. Holly (eds.), Turbulence Measurements and Flow Modelling , pp. 427 – 433 , Hemisphere , Washington , D.C. , 1987 .
   Google Scholar
• H. C. Chen and V. C. Patel , The Flow Around Wing-Body Junctions , in Proceedings of the 4th Symposium on Numerical and Physical Aspects of Aerodynamics Flows , Long Beach , CA , January 1989 .
   Google Scholar
• K. D. Carlson , W. L. Lin , and C.-J. Chen , Pressure Boundary Conditions of Incompress-ible Flows with Conjugate Heat Transfer on Nonstaggered Grids, Part II Applications , J. Numer. Heat Transfer ( this issue ).
   Google Scholar
• U. Ghia , K. N. Ghia , and C. T. Shin , High-Re Solutions of Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method , J. Comput. Phys. , vol. 48 , pp. 387 – 411 , 1982 .
   Web of Science ®Google Scholar
• R. K. Agarwal , A Third-Order-Accurate Upwind Scheme for Navier-Stokes Solutions at High Reynolds Numbers , AIAA No. 81–0012 , 1981 .
   Google Scholar
• C. S. John and M. N. Yvonne , A Numerical Method for the Incompressible Navier-Stokes Equations in Three-Dimensional Cylindrical Geometry , J. Comput. Phys. , vol. 78 , pp. 64 – 78 , 1988 .
   Google Scholar
• S. Majumdar , Role of Underrelaxation in Momentum Interpolation for Calculation of Flow with Nonstaggered Grids , Numer. Heat Transfer , vol. 13 , pp. 125 – 132 , 1988 .
   Web of Science ®Google Scholar
• Address correspondence to Dr. Ching-Jen Chen, Office of the Dean, College of Engineering,. FAMU/FSU, 2525 Pottsdamer Street, Tallahasse, FL 32310-6046, USA. E-mail: [email protected].
   Google Scholar