An equal-order velocity-pressure algorithm for incompressible thermal flows, part 1: Formulation

Numerical Heat Transfer, Part B: Fundamentals

Volumn 32, Issue 1, 1997, Pages 1-15

  Nonino, C ^a   Comini, G ^a  

^a UNIVERSITY OF UDINE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; HEAT TRANSFER; PRESSURE MEASUREMENT; VELOCITY MEASUREMENT;

MOMENTUM EQUATIONS; VELOCITY PRESSURE COUPLING;

LAMINAR FLOW;

EID: 0031176452     PISSN: 10407790     EISSN: 15210626     Source Type: Journal    
DOI: 10.1080/10407799708914996     Document Type: Article

References (27)

1. C. Taylor and T. G. Hughes, Finite Element Programming of the Navier-Stokes Equations, Pineridge Press, Swansea, UK, 1981.
2. C. Cuvelier, A. Segal, and A. A. van Steenhoven, Finite Element Methods and Navier-Stokes Equations, D. Reidel, Dordrecht, Holland, 1986.
3. V. Haroutunian, M. S. Engelman, and I. Hasbani, Segregated Finite Element Algorithms for the Numerical Solution of Large-Scale Incompressible Flow Problems, Int. J. Numer. Meth. Fluids, vol. 17, pp. 323-348, 1993.
4. G. Comini, W. J. Minkowycz, and W. Shyy, General Algorithms for the Finite Element Solution of Incompressible Flow Problems Using Primitive Variables, in W. J, Minkowycz and E. M. Sparrow (eds.), Advances in Numerical Heat Transfer, vol. I, pp. 137-170, Taylor & Francis, Washington, DC, 1997.
5. 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. 1787-1806, 1972.
6. S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC 1980.
7. P. Gresho, R. Lee, and R. Sani, On the Time-Dependent Solution of the Incompressible Navier-Stokes Equations in Two and Three Dimensions, in C. Taylor and K. Morgan (eds.), Recent Advances in Numerical Methods in Fluids, vol. 1, pp. 27-79, Pineridge Press, Swansea, UK, 1980.
8. P. T. Williams and A. J. Baker, Incompressible Computational Fluid Dynamics and the Continuity Constraint Method for the Three-Dimensional Navier-Stokes Equations, Numer. Heat Transfer, Part B, vol. 29, pp. 137-273, 1966.
9. P. M. Gresho, On the Theory of Semi-Implicit Projection Methods for Viscous Incompressible Flow and Its Implementation via a Finite Element Method that also Introduces a Nearly Consistent Mass Matrix. Part 1: Theory, Int. J. Numer, Meth. Fluids, vol. 11, pp. 587-620, 1990.
10. P. M. Gresho and S. T. Chan, On the Theory of Semi-Implicit Projection Methods for Viscous Incompressible Flow and Its Implementation via a Finite Element Method that also Introduces a Nearly Consistent Mass Matrix. Part 2: Implementation, Int. J. Numer. Meth. Fluids, vol. 11, pp. 621-659, 1990.
11. P. M. Gresho, S. T. Chan, M. A. Christon, and C. Hindmarsh, A Little More on Stabilized for Transient Viscous Incompressible Flow, Int. J. Numer. Meth. Fluids, vol. 21, pp. 837-856, 1995.
12. G. E. Schneider, G. D. Raithby, and M. M. Yovanovich, Finite-Element Solution Procedures for Solving the Incompressible Navier-Stokes Equations Using Equal Order Variable Interpolation, Numer. Heat Transfer, vol. 1, pp. 433-451, 1978.
13. G. Comini and S. Del Giudice, Finite-Element Solution of the Incompressible Navier-Stokes Equations, Numer. Heat Transfer, vol. 5, pp. 463-478, 1982.
14. M. Kawahara and K. Ohmiya, Finite Element Analysis of Density Flow Using the Velocity Correction Method, Int. J. Numer. Meth. Fluids, vol. 5, pp. 981-993, 1985.
15. G. Comini and S. Del Giudice, Parabolic Systems: Finite-Element Method, in W. J. Minkowycz, E. M. Sparrow, G. E. Schneider, and R. H. Pletcher (eds.), Handbook of Numerical Heat Transfer, pp. 155-181, John Wiley, New York, 1988.
16. J. L. Sohn, Y. Kim, and T. J. Chung, Finite Element Solvers for Incompressible Fluid Flows and Heat Transfer, in T. J. Chung and G. R. Karr (eds.), Finite Element Analysis in Fluids, Proc. Seventh Int. Conf. on Finite Element Methods in Flow Problems, pp. 880-885, UAH Press, Huntsville, AL, 1989.
17. C. Nonino and G. Croce, An Equal-Order Velocity-Pressure Algorithm for Incompressible Thermal Flows, Part 2: Validation, Numer. Heat Transfer, vol. 32, pp. 17-35, 1997.
18. A. Chorin, Numerical Solution of the Navier-Stokes Equations, Math. Comput., vol. 22, pp. 745-762, 1968.
19. J. K. Dukowicz, Approximate Factorization as a High Order Splitting for the Implicit Incompressible Flow Equations, J. Comput. Phys., vol. 102, pp. 336-347, 1992.
20. R. I. Issa, Solution of the Implicitly Discretized Fluid Flow Equations by Operator-Splitting, J. Comput. Phys., vol. 62, pp. 40-65, 1985.
21. G. Comini, S. Del Giudice and C. Nonino, Finite Element Analysis in Heat Transfer: Basic Formulation and Linear Problems, Taylor & Francis, Washington, DC, 1994.
22. W. Shyy, Effects of Open Boundary Condition on Incompressible Navier-Stokes Flow Computation, Numer. Heat Transfer, vol. 12, pp. 257-278, 1987.
23. E. Blosch, W. Shyy, and R. Smith, The Role of Mass Conservation in Pressure-Based Algorithms, Numer. Heat Transfer, Part B, vol. 24, pp. 415-429, 1993.
24. R. L. Sani and P. M. Gresho, Resume and Remarks on the Open Boundary Condition Minisymposium, Int. J. Numer. Meth. Fluids, vol. 18, pp. 983-1008, 1994.
25. K. N. Ghia and U. Ghia, Elliptic Systems: Finite-Difference Method III, in W. J. Minkowycz, E. M. Sparrow, G. E. Schneider, and R. H. Pletcher (eds.), Handbook of Numerical Heal Transfer, pp. 215-240, John Wiley, New York, 1988.
26. J. Banaszek, A Conservative Property in Finite-Element Approximation of Convective-Diffusive Transport Phenomena, Arch. Thermodynam.,\o\. 14, pp. 93-116, 1993.
27. J. Banaszek, On Improvement of Computational Efficiency in FEM Calculations of Incompressible Fluid Flow and Heat Transfer, Comput. Assisted Mech. Eng. ScL, vol. 2, pp. 87-104, 1995