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Volumn 59, Issue 6, 2011, Pages 442-472

Improved formulations of the discretized pressure equation and boundary treatments in co-located equal-order control-volume finite-element methods for incompressible fluid flow

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY TREATMENT; CO-LOCATED; CONTROL VOLUMES; CONTROL-VOLUME FINITE-ELEMENT METHODS; DIAGONALLY DOMINANT; INCOMPRESSIBLE FLUID FLOW; ITERATIVE SOLUTIONS; PRESSURE EQUATIONS; TEST PROBLEM; TWO-DIMENSIONAL PROBLEM;

EID: 79958847663     PISSN: 10407790     EISSN: 15210626     Source Type: Journal    
DOI: 10.1080/10407790.2011.578020     Document Type: Article
Times cited : (16)

References (48)
  • 1
    • 0002226863 scopus 로고    scopus 로고
    • Control-volume finite element methods for fluid flow and heat transfer
    • W. J. Minkowycz and E. M. Sparrow eds., chap. 3, Taylor & Francis, New York
    • 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.
    • (1997) Advances in Numerical Heat Transfer , vol.1
    • Baliga, B.R.1
  • 2
    • 34447645942 scopus 로고    scopus 로고
    • Control-volume-based finite-difference and finite-element methods
    • W. J. Minkowycz, E. M. Sparrow, and J. Y. Murthy eds., 2nd ed., chap. 6, Wiley, New York
    • 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.
    • (2006) Handbook of Numerical Heat Transfer
    • Baliga, B.R.1    Atabaki, N.2
  • 3
    • 34447642193 scopus 로고    scopus 로고
    • Pressure-based finite-volume methods in computational fluid dynamics
    • DOI 10.1115/1.2716419
    • 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. (Pubitemid 47090839)
    • (2007) Journal of Heat Transfer , vol.129 , Issue.4 , pp. 407-424
    • Acharya, S.1    Baliga, B.R.2    Karki, K.3    Murthy, J.Y.4    Prakash, C.5    Vanka, S.P.6
  • 5
    • 0019071052 scopus 로고
    • A new finite element formulation for convection-diffusion problems
    • 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. (Pubitemid 11490923)
    • (1980) Numerical Heat Transfer , vol.3 , Issue.4 , pp. 393-409
    • Baliga, B.R.1    Patankar, S.V.2
  • 6
    • 0020524356 scopus 로고
    • A control-volume finite element method for two-dimensional fluid flow and heat transfer
    • 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. (Pubitemid 14504888)
    • (1983) Numerical heat transfer , vol.6 , Issue.3 , pp. 245-261
    • Baliga, B.R.1    Patankar, S.V.2
  • 7
    • 0021818941 scopus 로고
    • A control-volume-based finite-element method for solving the navier-stokes equations using equal-order velocity-pressure interpolation
    • 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. (Pubitemid 15541314)
    • (1985) Numerical heat transfer , vol.8 , Issue.3 , pp. 259-280
    • Prakash, C.1    Patankar, S.V.2
  • 8
    • 0022439809 scopus 로고
    • A skewed, positive influence coefficient upwinding procedure for control-volume-based-finite-element convection-diffusion computation
    • 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. (Pubitemid 16462155)
    • (1986) Numerical heat transfer , vol.9 , Issue.1 , pp. 1-26
    • Schneider, G.E.1    Raw, M.J.2
  • 9
    • 0028173924 scopus 로고
    • Co-located equal-order control-volume finite element method for two-dimensional axisymmetric incompressible fluid flow
    • 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. (Pubitemid 276941)
    • (1994) International Journal for Numerical Methods in Engineering , vol.18 , Issue.1 , pp. 1-26
    • Masson, C.1    Saabas, H.J.2    Baliga, B.R.3
  • 10
    • 0032583617 scopus 로고    scopus 로고
    • Simulation of gas-solid particle flows over a wide range of concentration
    • DOI 10.1002/(SICI)1097-0363(19981230)28:10<1441::AID-FLD771>3.0. CO;2-U
    • 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. (Pubitemid 29081653)
    • (1998) International Journal for Numerical Methods in Fluids , vol.28 , Issue.10 , pp. 1441-1479
    • Masson, C.1    Rabi Baliga, B.2
  • 11
    • 0028756967 scopus 로고
    • A co-located equal-order control-volume finite element method for multidimensional, incompressible fluid flow, part i: Formulation
    • 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.
    • (1994) Numer. Heat Transfer B , vol.26 , pp. 381-407
    • Saabas, H.J.1    Baliga, B.R.2
  • 12
    • 0028992572 scopus 로고
    • A control-volume-based finite element method for three-dimensional incompressible turbulent fluid flow, heat transfer and related phenomena
    • 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.
    • (1995) Int. J. Numer. Meth. Fluids , vol.21 , pp. 591-613
    • Costa, V.A.1    Oliveira, F.L.A.2    Figueiredo, A.R.3
  • 13
    • 33745574994 scopus 로고    scopus 로고
    • A stable second-order mass-weighted upwind scheme for unstructured meshes
    • DOI 10.1002/fld.1146
    • L. D. Tran, C. Masson, and A. Smäili, A Stable Second-Order Mass-Weighted Upwind Scheme for Unstructured Meshes, Int. J. Numer. Meth Fluids, vol. 51, pp. 749-771, 2006. (Pubitemid 43978385)
    • (2006) International Journal for Numerical Methods in Fluids , vol.51 , Issue.7 , pp. 749-771
    • Tran, L.D.1    Masson, C.2    Smaili, A.3
  • 16
    • 49949139816 scopus 로고
    • Numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh
    • A. M. Winslow, Numerical Solution of the Quasilinear Poisson Equation in a Nonuniform Triangle Mesh, J. Comput. Phys., vol. 2, pp. 149-172, 1967.
    • (1967) J. Comput. Phys. , vol.2 , pp. 149-172
    • Winslow, A.M.1
  • 17
    • 0006024755 scopus 로고
    • Numerical integration of fluid flow over triangular grids
    • D. Williamson, Numerical Integration of Fluid Flow over Triangular Grids, Monthly Weather Rev., vol. 97, pp. 885-895, 1969.
    • (1969) Monthly Weather Rev. , vol.97 , pp. 885-895
    • Williamson, D.1
  • 18
    • 0025505045 scopus 로고
    • Discretization of incompressible vorticity-velocity equations on triangular meshes
    • 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.
    • (1990) Int. J. Numer. Meth. Fluids , vol.11 , pp. 823-833
    • Choudhury, S.1    Nicolaides, R.A.2
  • 19
    • 0027611226 scopus 로고
    • A collocated finite volume method for predicting flows at all speeds
    • 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.
    • (1993) Int. J. Numer. Meth. Fluids , vol.16 , pp. 1029-1050
    • Demirdzic, I.1    Lilek, Z.2    Perić, M.3
  • 20
    • 0031099550 scopus 로고    scopus 로고
    • A pressure-based method for unstructured meshes
    • S. R. Mathur and J. Y. Murthy, A Pressure-Based Method for Unstructured Meshes, Numer. Heat Transfer A, vol. 31, pp. 195-216, 1997.
    • (1997) Numer. Heat Transfer A , vol.31 , pp. 195-216
    • Mathur, S.R.1    Murthy, J.Y.2
  • 21
    • 18644376901 scopus 로고    scopus 로고
    • Unstructured finite volume methods for multi-mode heat transfer
    • W. J. Minkowycz and E. M. Sparrow eds., Taylor and Francis, New York
    • 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.
    • (2000) Advances in Numerical Heat Transfer , vol.2 , pp. 37-67
    • Mathur, S.R.1    Murthy, J.Y.2
  • 22
    • 0001686840 scopus 로고
    • Adaptive mesh generation for viscous flows using delaunay triangulation
    • D. Mavriplis, Adaptive Mesh Generation for Viscous Flows Using Delaunay Triangulation, J. Comp. Phys., vol. 90, pp. 271-291, 1990.
    • (1990) J. Comp. Phys. , vol.90 , pp. 271-291
    • Mavriplis, D.1
  • 23
    • 0034319303 scopus 로고    scopus 로고
    • Viscous flow analysis using a parallel unstructured multigrid solver
    • D. Mavriplis, Viscous Flow Analysis Using a Parallel Unstructured Multigrid Solver, AIAA J., vol. 38, pp. 2067-2076, 2000. (Pubitemid 32021950)
    • (2000) AIAA journal , vol.38 , Issue.11 , pp. 2067-2076
    • Mavriplis, D.J.1
  • 25
    • 34447628018 scopus 로고    scopus 로고
    • Survey of numerical methods
    • J. W. Minkowycz, E. M. Sparrow, and J. Y. Murthy eds., 2nd ed., chap. 1, Wiley, New York
    • 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.
    • (2006) Handbook of Numerical Heat Transfer
    • Murthy, J.Y.1    Minkowycz, W.J.2    Sparrow, E.M.3    Mathur, S.R.4
  • 26
    • 33749190078 scopus 로고
    • Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface
    • 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.
    • (1965) Phys. Fluids , vol.8 , pp. 2182-2189
    • Harlow, F.H.1    Welch, J.E.2
  • 27
    • 33044504607 scopus 로고
    • A calculation procedure for heat, mass, and momentum transfer in three-dimensional parabolic flows
    • 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.
    • (1972) Int. J. Heat Mass Transfer , vol.15 , pp. 1767-1806
    • Patankar, S.V.1    Spalding, D.B.2
  • 28
    • 0015566427 scopus 로고
    • A numerical solution of the navier-stokes equations using the finite element technique
    • 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.
    • (1973) Comput. Fluids , vol.1 , pp. 73-100
    • Taylor, C.1    Hood, P.2
  • 29
    • 0020844260 scopus 로고
    • Numerical study of the turbulent flow past an airfoil with trailing edge separation
    • 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. (Pubitemid 14483724)
    • (1983) AIAA journal , vol.21 , Issue.11 , pp. 1525-1532
    • Rhie, C.M.1    Chow, W.L.2
  • 30
    • 0023843712 scopus 로고
    • Comparison of finite-volume numerical methods with staggered and colocated grids
    • DOI 10.1016/0045-7930(88)90024-2
    • 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. (Pubitemid 18663460)
    • (1988) Computers and Fluids , vol.16 , Issue.4 , pp. 389-403
    • Peric, M.1    Kessler, R.2    Scheuerer, G.3
  • 31
    • 0021641950 scopus 로고
    • Method for computing three dimensional flows using non-orthogonal boundary-fitted co-ordinates
    • 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. (Pubitemid 14605280)
    • (1984) International Journal for Numerical Methods in Fluids , vol.4 , Issue.6 , pp. 519-537
    • Maliska, C.R.1    Raithby, G.D.2
  • 32
    • 0022476432 scopus 로고
    • Prediction of heat and fluid flow in complex geometries using general orthogonal coordinates
    • 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. (Pubitemid 16492637)
    • (1986) Numerical heat transfer , vol.9 , Issue.2 , pp. 125-142
    • Raithby, G.D.1    Galpin, P.F.2    Van Doormaal, J.P.3
  • 33
    • 0024857521 scopus 로고
    • Improvements to incompressible flow calculation on a non-staggered curvilinear grid
    • 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.
    • (1989) Numer. Heat Transfer B , vol.15 , pp. 131-152
    • Moukalled, F.1    Acharya, S.2
  • 34
    • 0002424557 scopus 로고
    • On the adoption of velocity variable and grid system for fluid flow computation in curvilinear coordinates
    • 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.
    • (1991) J. Comput. Phys. , vol.92 , pp. 82-105
    • Shyy, W.1    Vu, T.C.2
  • 35
    • 0027874082 scopus 로고
    • Numerical method for the computation of flow and scalar transport using non-orthogonal boundary-fitted coordinates
    • 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.
    • (1993) Numer. Heat Transfer B , vol.24 , pp. 391-414
    • Kelkar, K.1    Choudhury, D.2
  • 38
    • 0015368687 scopus 로고
    • A novel finite-difference formulation for differential expressions involving both first and second derivatives
    • 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.
    • (1972) Int. J. Numer. Meth. Eng. , vol.4 , pp. 551-559
    • Spalding, D.B.1
  • 39
    • 0017009617 scopus 로고
    • Skew upstream differencing schemes for problems involving fluid flow
    • G. D. Raithby, Skew Upstream Differencing Schemes for Problems Involving Fluid Flow, Comput. Meth. Appl. Mech. Eng., vol. 9, pp. 153-164, 1976.
    • (1976) Comput. Meth. Appl. Mech. Eng. , vol.9 , pp. 153-164
    • Raithby, G.D.1
  • 40
    • 79958803103 scopus 로고    scopus 로고
    • On first-and second-order mass-weighted schemes for control-volume finite element methods
    • Canmore, Alberta, Canada, June 18-22
    • 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.
    • (2007) Proc. 5th Inter. Conf. on Computational Heat and Mass Transfer , pp. 378-384
    • Costa, V.A.F.1    Oliveira, L.A.2    Baliga, B.R.3
  • 42
    • 3142698698 scopus 로고    scopus 로고
    • A simple mesh generator in matlab
    • P. O. Persson and G. Strang, A Simple Mesh Generator in MATLAB, SIAM Rev., vol. 46, pp. 329-345, 2004.
    • (2004) SIAM Rev. , vol.46 , pp. 329-345
    • Persson, P.O.1    Strang, G.2
  • 43
    • 0000954713 scopus 로고
    • Multigrid calculation of steady, viscous flow in triangular cavity
    • R. Joytsna and S. P. Vanka, Multigrid Calculation of Steady, Viscous Flow in Triangular Cavity, J. Comput. Phys., vol. 122, pp. 107-117, 1995.
    • (1995) J. Comput. Phys. , vol.122 , pp. 107-117
    • Joytsna, R.1    Vanka, S.P.2
  • 44
    • 0032779894 scopus 로고    scopus 로고
    • A finite element analysis of steady viscous flow in triangular cavities
    • 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.
    • (1999) Proc. Inst. Mech. Eng., Part C , vol.213 , pp. 263-276
    • Gaskell, P.H.1    Thompson, H.M.2    Savage, M.D.3
  • 45
    • 0000170864 scopus 로고
    • The approximate arithmetical solution by finite differences of physical problems involving differential equations with application to a masonry dam
    • 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.
    • (1910) Trans. Roy. Soc. London, Ser. A , vol.210 , pp. 307-357
    • Richardson, L.F.1
  • 46
    • 84987505901 scopus 로고
    • A test problem for outflow boundary conditions-flow over a backward facing step
    • 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.
    • (1990) Int. J. Numer. Meth. Fluids , vol.11 , pp. 953-967
    • Gartling, D.K.1
  • 47
    • 0031234401 scopus 로고    scopus 로고
    • The entrance effect of laminar flow over a backward-facing step geometry
    • 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.
    • (1997) Int. J. Numer. Meth. Fluids , vol.25 , pp. 633-644
    • Barton, I.E.1
  • 48
    • 43049173439 scopus 로고    scopus 로고
    • Numerical solutions of 2-D steady incompressible flow over a backward-facing step, Part I: High Reynolds number solutions
    • DOI 10.1016/j.compfluid.2007.09.003, PII S0045793007001545
    • 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. (Pubitemid 351636023)
    • (2008) Computers and Fluids , vol.37 , Issue.6 , pp. 633-655
    • Erturk, E.1


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