Improved Formulations of the Discretized Pressure Equation and Boundary Treatments in Co-Located Equal-Order Control-Volume Finite-Element Methods for Incompressible Fluid Flow

REFERENCES

• B. R. Baliga , Control-Volume Finite Element Methods for Fluid Flow and Heat Transfer , in W. J. Minkowycz and E. M. Sparrow (eds.), Advances in Numerical Heat Transfer , vol. 1 , chap. 3 , Taylor & Francis , New York , 1997 .
   Google Scholar
• B. R. Baliga and N. Atabaki , Control-Volume-Based Finite-Difference and Finite-Element Methods , in W. J. Minkowycz , E. M. Sparrow , and J. Y. Murthy (eds.), Handbook of Numerical Heat Transfer, , 2nd ed. , chap. 6 , Wiley , New York , 2006 .
   Google Scholar
• S. Acharya , B. R. Baliga , K. Karki , J. Y. Murthy , C. Prakash , and S. P. Vanka , Pressure-Based Finite-Volume Methods in Computational Fluid Dynamics , ASME J. Heat Transfer , vol. 129 , pp. 407 – 424 , 2007 .
   Web of Science ®Google Scholar
• S. V. Patankar , Numerical Heat Transfer and Fluid Flow , McGraw-Hill , New York , 1980 .
   Google Scholar
• B. R. Baliga and S. V. Patankar , A New Finite Element Formulation for Convection-Diffusion Problems, Numer. Heat Transfer , vol. 3, pp. 393–409, 1980.
   Google Scholar
• B. R. Baliga and S. V. Patankar , A Control-Volume Finite Element Method for Two-Dimensional Fluid Flow and Heat Transfer , Numer. Heat Transfer , vol. 6 , pp. 245 – 261 , 1983 .
   Google Scholar
• C. Prakash and S. V. Patankar , A Control-Volume-Based Finite-Element Method for Solving the Navier-Stokes Equations Using Equal-Order Velocity-Pressure Interpolation , Numer. Heat Transfer , vol. 8 , pp. 259 – 280 , 1985 .
   Web of Science ®Google Scholar
• G. E. Schneider and M. J. Raw , A Skewed , Positive Influence Coefficient Upwinding Procedure for Control-Volume-Based-Finite-Element Convection-Diffusion Computation , Numer. Heat Transfer , vol. 9 , pp. 1 – 26 , 1986 .
   Web of Science ®Google Scholar
• C. Masson , H. J. Saabas , and B. R. Baliga , Co-located Equal-Order Control-Volume Finite Element Method for Two-dimensional Axisymmetric Incompressible Flow , Int. J. Numer Meth. Fluids , vol. 18 , pp. 1 – 26 , 1994 .
   Web of Science ®Google Scholar
• C. Masson and B. R. Baliga , Simulation of Gas-Solid Particle Flows over a Wide Range of Concentration , Int. J. Numer. Meth. Fluids , vol. 28 , pp. 1441 – 1479 , 1998 .
   Google Scholar
• H. J. Saabas and B. R. Baliga , A Co-located Equal-Order Control-Volume Finite Element Method for Multidimensional, Incompressible Fluid Flow, Part I: Formulation , Numer. Heat Transfer B , vol. 26 , pp. 381 – 407 , 1994 .
   Web of Science ®Google Scholar
• V. A. Costa , F. L. A. Oliveira , and A. R. Figueiredo , A Control-Volume-Based Finite Element Method for Three-Dimensional Incompressible Turbulent Fluid Flow, Heat Transfer and Related Phenomena , Int. J. Numer. Meth. Fluids , vol. 21 , pp. 591 – 613 , 1995 .
   Google Scholar
• L. D. Tran , C. Masson , and A. Smaïli , A Stable Second-Order Mass-Weighted Upwind Scheme for Unstructured Meshes , Int. J. Numer. Meth Fluids , vol. 51 , pp. 749 – 771 , 2006 .
   Web of Science ®Google Scholar
• B. A. Finlayson , The Method of Weighted Residuals and Variational Principles , Academic Press , New York , 1972 .
   Google Scholar
• O. C. Zienkiewicz and R. L. Taylor , The Finite Element Method: Vol. 3, Fluid Dynamics, , 5th ed. , McGraw-Hill , London , 2000 .
   Google Scholar
• A. M. Winslow , Numerical Solution of the Quasilinear Poisson Equation in a Nonuniform Triangle Mesh , J. Comput. Phys. , vol. 2 , pp. 149 – 172 , 1967 .
   Web of Science ®Google Scholar
• D. Williamson , Numerical Integration of Fluid Flow over Triangular Grids , Monthly Weather Rev. , vol. 97 , pp. 885 – 895 , 1969 .
   Web of Science ®Google Scholar
• S. Choudhury and R. A. Nicolaides , Discretization of Incompressible Vorticity-Velocity Equations on Triangular Meshes , Int. J. Numer. Meth. Fluids , vol. 11 , pp. 823 – 833 , 1990 .
   Web of Science ®Google Scholar
• I. Demirdzic , Z. Lilek , and M. Perić , A Collocated Finite Volume Method for Predicting Flows at all Speeds , Int. J. Numer. Meth. Fluids , vol. 16 , pp. 1029 – 1050 , 1993 .
   Web of Science ®Google Scholar
• S. R. Mathur and J. Y. Murthy , A Pressure-Based Method for Unstructured Meshes , Numer. Heat Transfer A , vol. 31 , pp. 195 – 216 , 1997 .
   Google Scholar
• S. R. Mathur and J. Y. Murthy , Unstructured Finite Volume Methods for Multi-Mode Heat Transfer , in W. J. Minkowycz and E. M. Sparrow (eds.), Advances in Numerical Heat Transfer , vol. 2 , pp. 37 – 67 , Taylor and Francis , New York , 2000 .
   Google Scholar
• D. Mavriplis , Adaptive Mesh Generation for Viscous Flows Using Delaunay Triangulation , J. Comp. Phys. , vol. 90 , pp. 271 – 291 , 1990 .
   Web of Science ®Google Scholar
• D. Mavriplis , Viscous Flow Analysis Using a Parallel Unstructured Multigrid Solver , AIAA J. , vol. 38 , pp. 2067 – 2076 , 2000 .
   Google Scholar
• J. H. Ferziger and M. Perić , Computational Methods for Fluid Dynamics, , 3nd ed. , Springer , New York , 2002 .
   Google Scholar
• J. Y. Murthy , W. J. Minkowycz , E. M. Sparrow , and S. R. Mathur , Survey of Numerical Methods, in J. W. Minkowycz , E. M. Sparrow , and J. Y. Murthy (eds.), Handbook of Numerical Heat Transfer, , 2nd ed., chap. 1, Wiley , New York , 2006.
   Google Scholar
• F. H. Harlow 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 and D. B. Spalding , A Calculation Procedure for Heat, Mass, and Momentum Transfer in Three-Dimensional Parabolic Flows , Int. J. Heat Mass Transfer , vol. 15 , pp. 1767 – 1806 , 1972 .
   Web of Science ®Google Scholar
• C. Taylor and P. Hood , A Numerical Solution of the Navier-Stokes Equations Using the Finite Element Technique , Comput. Fluids , vol. 1 , pp. 73 – 100 , 1973 .
   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
• M. Perić , R. Kessler , and G. Scheuerer , Comparison of Finite-Volume Numerical Methods with Staggered and Co-located Grids , Comput. Fluids , vol. 16 , pp. 389 – 403 , 1988 .
   Web of Science ®Google Scholar
• C. R. Maliska and G. D. Raithby , A Method for Computing Three-Dimensional Fluid Flows Using Non-orthogonal Boundary-Fitted Coordinates , Int. J. Numer. Meth. Fluids , vol. 4 , pp. 519 – 537 , 1984 .
   Web of Science ®Google Scholar
• G. D. Raithby , P. F. Galpin , and Van J. P. Doormaal , Prediction of Heat and Fluid Flow in Complex Geometries Using General Orthogonal Coordinates , Numer. Heat Transfer , vol. 9 , pp. 125 – 142 , 1986 .
   Web of Science ®Google Scholar
• F. Moukalled and S. Acharya , Improvements to Incompressible Flow Calculation on a Non-Staggered Curvilinear Grid , Numer. Heat Transfer B , vol. 15 , pp. 131 – 152 , 1989 .
   Google Scholar
• W. Shyy and T. C. Vu , On the Adoption of Velocity Variable and Grid System for Fluid Flow Computation in Curvilinear Coordinates , J. Comput. Phys. , vol. 92 , pp. 82 – 105 , 1991 .
   Web of Science ®Google Scholar
• K. Kelkar and D. Choudhury , Numerical Method for the Computation of Flow and Scalar Transport Using Non-orthogonal Boundary-Fitted Coordinates , Numer. Heat Transfer B , vol. 24 , pp. 391 – 414 , 1993 .
   Web of Science ®Google Scholar
• H. Schlichting , Boundary Layer Theory, , 3nd ed. , McGraw Hill , New York , 1979 .
   Google Scholar
• D. A. Venditti , An h-Adaptive Control-Volume Finite Element Method for Steady, Two-Dimensional Fluid Flow and Heat Transfer, M. Eng. thesis, McGill University, Montreal, Quebec, Canada, 1998.
   Google Scholar
• D. B. Spalding , A Novel Finite-Difference Formulation for Differential Expressions Involving Both First and Second Derivatives , Int. J. Numer. Meth. Eng. , vol. 4 , pp. 551 – 559 , 1972 .
   Google Scholar
• G. D. Raithby , Skew Upstream Differencing Schemes for Problems Involving Fluid Flow , Comput. Meth. Appl. Mech. Eng. , vol. 9 , pp. 153 – 164 , 1976 .
   Google Scholar
• V. A. F. Costa , L. A. Oliveira , and B. R. Baliga , On First- and Second-Order Mass-Weighted Schemes for Control-Volume Finite Element Methods, Proc. 5th Inter. Conf. on Computational Heat and Mass Transfer, pp. 378–384, Canmore, Alberta, Canada, June 18–22, 2007.
   Google Scholar
• D. A. Venditti and B. R. Baliga , An h-Adaptive Strategy for CVFEM Simulations of Viscous Incompressible Flow, Proc. 6th Annual Conf. of the Computational Fluid Dynamics Society of Canada (CFD 98), pp. VIII-65–VIII-70, Quebec City, Canada, June 7–9, 1998.
   Google Scholar
• P. O. Persson and G. Strang , A Simple Mesh Generator in MATLAB , SIAM Rev. , vol. 46 , pp. 329 – 345 , 2004 .
   Web of Science ®Google Scholar
• R. Joytsna and S. P. Vanka , Multigrid Calculation of Steady, Viscous Flow in Triangular Cavity , J. Comput. Phys. , vol. 122 , pp. 107 – 117 , 1995 .
   Google Scholar
• P. H. Gaskell , H. M. Thompson , and M. D. Savage , A Finite Element Analysis of Steady Viscous Flow in Triangular Cavities , Proc. Inst. Mech. Eng., Part C , vol. 213 , pp. 263 – 276 , 1999 .
   Web of Science ®Google Scholar
• L. F. Richardson , The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations with Application to a Masonry Dam, Trans. Roy. Soc. London, Ser. A , vol. 210, pp. 307–357, 1910.
   Google Scholar
• D. K. Gartling , A Test Problem for Outflow Boundary Conditions—Flow over a Backward Facing Step , Int. J. Numer. Meth. Fluids , vol. 11 , pp. 953 – 967 , 1990 .
   Web of Science ®Google Scholar
• I. E. Barton , The Entrance Effect of Laminar Flow over a Backward-Facing Step Geometry , Int. J. Numer. Meth. Fluids , vol. 25 , pp. 633 – 644 , 1997 .
   Web of Science ®Google Scholar
• E. Erturk , Numerical Solutions of 2-D Steady Incompressible Flow over a Backward-Facing Step, Part I: High Reynolds Number Solutions , Comput. Fluids , vol. 37 , pp. 633 – 655 , 2008 .
   Web of Science ®Google Scholar