A general algorithm for compressible and incompressible flows. Part III: The semi-implicit form

International Journal for Numerical Methods in Fluids

Volumn 27, Issue 1-4, 1998, Pages 13-32

  Codina, R ^a   Vazquez M ^a   Zienkiewicz, O C ^b  

^a INTERNATIONAL CENTER FOR NUMERICAL METHODS IN ENGINEERING CIMNE   (Spain)

^b SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Characteristic schemes; Pressure stabilization; Splitting

Indexed keywords

CHARACTERISTIC SCHEMES; COMPATIBILITY CONDITIONS; CONTINUITY EQUATIONS; EQUATION OF STATE; FRACTIONAL STEP FINITE ELEMENT METHOD; INCOMPRESSIBLE LIMIT; PRESSURE DISSIPATION; SPLITTING;

BOUNDARY CONDITIONS; COMPRESSIBLE FLOW; EQUATIONS OF STATE; ALGORITHMS; DENSITY (SPECIFIC GRAVITY); INTERPOLATION; PRESSURE; TEMPERATURE;

INCOMPRESSIBLE FLOW; FINITE ELEMENT METHOD;

CONTINUITY EQUATION; INCOMPRESSIBLE FLOW; PRESSURE DISSIPATION; SEMI IMPLICIT METHOD;

ALGORITHM; BOUNDARY CONDITIONS; COMPRESSIBLE FLOW; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW;

ALGORITHM; BOUNDARY CONDITIONS; COMPRESSIBLE FLOW; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW;

EID: 0031901317     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0363(199801)27:1/4<13::AID-FLD647>3.0.CO;2-8     Document Type: Article

References (20)

1. A. J. Chorin, 'Numerical solution of the Navier-Stokes equations', Math. Comput., 22, 745-762 (1968).
2. R. Temam, 'Sur I'approximation de la soluiton des equations de Navier-Stokes par la methode des pas fractionaires (I)', Arch. Rat. Mech. Anal., 32, 135-153 (1969).
3. O. C. Zienkiewicz and R. Codina, 'A general algorithm for compressible and incompressible flow. Part I: The split, characteristic based scheme', Int. j. numer. methods fluids, 20, 869-885 (1995).
4. O. C. Zienkiewicz, K. Morgan, B. V. K. Satya Sai, R. Condina and M. Vazquex, 'A generall algorithm for compressible and incompressible flow. Part II: Tests on the explicit form', Int. j. numer. methods fluids, 20, 887-913 (1995).
5. O. C. Zienkiewicz and J. Wu, 'A general explicit or semi-explicit algorithm for compressible or incompressible flows', Int. j. numer. methods eng., 35, 457-479 (1992).
6. O. C. Zienkiewicz, B. V. K. Satya Sai, K. Morgan and R. Codina, 'Split, characteristic based semi-implict algorithm for laminar/turbulent incompressible flows', Int. j. numer. methods fluids, 23, 787-809 (1996).
7. R. Codina and J. Blasco, 'A finite element formulation for the Stokes problem allowing equal velocity-pressure interpolation', Comput. Methods Appl. Mech. Eng., 143, 373-391 (1997).
8. M. O. Bristeau, R. Glowinsky, L. Dutto and J. Periaux, 'Compressible viscous flow calculations using compatible finite element approximations', Int. j. numer. methods fluids, 11, 719-749 (1990)
9. A. Soulaimani and M. Fortin, 'Finite element soluiton of compressible viscous flows using conservative variables', Comput. Methods Appl. Mech. Eng., 118, 319-350 (1994).
10. O. C. Zienkiewicz, J. Szmelter and J. Peraire, 'Compressible and incompressible flow; an algorithm for all seasons', Comput. Methods Appl. Mech. Eng., 78, 105-121 (1990).
11. O. Pironneau and J. Rappaz, 'Numerical analysis for compressible viscous isentropic stationary flows', Impact Comput. Sci. Eng., 1, 109-137 (1989).
12. F. Shakib, T. J. R. Hughes and Z. Johan, 'A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations', Comput. Methods Appl. Mech. Eng., 89, 141-219 (1991).
13. G. Hauke and T. J. R. Hughes, 'A unifed approach to compressible and incompressible flows', Comput. Methods Appl. Mech. Eng., 113, 389-395 (1994).
14. T. C. Papanastasiou, N. Malamataris and K. Ellwood, 'A new outflow boundary condition', Int. j. numer. methods fluids, 14, 587-608 (1992).
15. R. Codina, 'A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation', Comput. Methods Appl. Mech. Eng., 110, 325-342 (1993).
16. G. E. Schneider, G. D. Raithby and M. M. Yovanovich, 'Finite element analysis of incompressible fluid flow incorporatiing equal order pressure and velocity interpolation', in C. Taylor, K. Morgan and C. A. Brebbia (eds), Numerical Methods in Laminar and Turbulent Flow, Pentech, Plyhmouth, 1978.
17. M. Kawahara and K. Ohmiya, 'Finite element analysis of density flow using the velocity correction method', Int. j. numer. methods fluids, 5, 981-993 (1985).
18. M. Vazquez, R. Codina and O. C. Zienkiewicz, 'A fractional step method for the soluiton of Navier-Stokes equations', CIMNE Rep. 103, 1996.
19. U. Ghia, K. N. Ghia and C. T. Shin, 'High-Re soluitons for incompressible flow using the Navier-Stokes equations and a multi-grid method', J. Comput. Phys., 48, 387-441 (1982).
20. L. Demkowicz, J. T. Oden and W. Rachowicz, 'A new finite element method for solving compressible Navier-Stokes equations based on an operator splitting method and h-p adaptivity', Comput. Methods Appl. Mech. Eng., 84, 275-326 (1990).