The Characteristic-Based-Split (CBS) algorithm, stability and boundary conditions

Archives of Mechanics

Volumn 52, Issue 4-5, 2000, Pages 857-887

  Zienkiewicz, O C ^a   Nithiarasu, P ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001323928     PISSN: 03732029     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (33)

1. O. C. ZIENKIEWICZ and R. CODINA, Search for a general fluid mechanics algorithm, Frontiers of Computational Fluid Dynamics, D. A. CAUGHEY and M. M. HAFEZ [Eds.], J. Wiley & Sons, 101-113, 1995.
2. O. C. ZIENKIEWICZ and R. CODINA, A general algorithm for compressible and incompressible flow, Part I. The split characteristic based scheme, Int. J. Num. Meth. Fluids, 20, 869-885, 1995.
3. O. C. ZIENKIEWICZ, B. V. K. SATYA SAI, K. MORGAN, R. CODINA and M. VÁZQUEZ, A general algorithm for compressible and incompressible flow, Part II. Tests on the explicit form, Int. J. Num. Meth. Fluids, 20, 887-913, 1995.
4. R. CODINA, M. VÁZQUEZ and O. C. ZIENKIEWICZ, General algorithm for compressible and incompressible flows, Part III. A semi-implicit form, Int. J. Num. Meth. Fluids, 27, 13-32, 1998.
5. R. CODINA, M. VÁZQUEZ and O. C. ZIENKIEWICZ, A fractional step method for the solution of compressible Navier-Stokes equations, Frontiers of computational fluid dynamics, M. HAFEZ and K. OSHIMA [Eds.], 1, 331-347, World Scientific Pub. co.Ltd, 1998.
6. B. V. K. SATYA SAI, O. C. ZIENKIEWICZ, M. T. MANZARI, P. R. M. LYRA and K. MORGAN, General purpose Vs Special Algorithms for high speed flows with shocks, Int. J. Num. Meth. Fluids, 27, 57-80, 1998.
7. O. C. ZIENKIEWICZ, P. NITHIARASU, R. CODINA, M. VÁZQUEZ and P. ORTIZ, An Efficient and Accurate Algorithm for Fluid Mechanics Problems. The Characteristic Based Split (CBS) Algorithm, Int. J. Num. Meth. Fluids, 31, 1, 359-392, 1999.
8. N. MASSAROATTI, P. NITHIARASU and O. C. ZIENKIEWICZ, Characteristic- Based-Split (CBS) Algorithm for Incompressible Flow Problems with Heat Transfer, International Journal of Numerical Methods for Heat and Fluid Flow, 8, 8, 969-990, 1998.
9. P. NITHIARASU, and O. C. ZIENKIEWICZ, On Stabilization of the CBS Algorithm. Internal and External Time Steps, Int. J. Num. Meth. Engng., 48, 875-880, 2000.
10. O. C. ZIENKIEWICZ, J. SZMELTER and J. PERAIRE, Compressible and incompressible flow: An algorithm for all seasons, Comp. Meth. Appl. Mech. Engng., 78, 105-121, 1990.
11. O. C. ZIENKIEWICZ, Explicit or semi-explicit general algorithm for compressible and incompressible flows with equal finite element interpolation, Report 90/5, Chalmers University of Technology, 1990.
12. O. C. ZIENKIEWICZ and J. WU, A general explicit of semi-explicit algorithm for compressible and incompressible flows, Int. J. Num. Meth. Engng., 35, 457-479, 1992.
13. P. D. LAX and B. WENDROFF, Systems of conservation laws, Comm. Pure. Appl. Math., 13, 217-237, 1960.
14. J. DONEA, A Taylor-Galerkin method for convective transport problems, Int. J. Num. Meth. Engng., 20, 101-119, 1984.
15. O. C. ZIENKIEWICZ, R. LÖHNER, K. MORGAN and J. PERAIRE, High speed compressible flow and other advection dominated problems of fluid mechanics, Finite elements in fluids, 6, Ch. 2, 41-88, R. H. GALLAGHER, G. F. CAREY, J. T. ODEN and O. C. ZIENKIEWICZ [Eds.], J. Wiley & Sons, 1985.
16. R. LÖHNER, K. MORGAN and O. C. ZIENKIEWICZ, The solution of non-linear hyperbolic equation system by the finite element method, Int. J. Num. Meth. Fluids, 4, 1043-1063, 1984.
17. H. LAVAL and L. QUARTAPELLE, A fractional step Taylor-Galerkin method for unsteady incompressible flows, Int. J. Num. Meth. Fluids, 11, 501-513, 1990.
18. C. B. JIANG, M. KAWAHARA and K. KASHIYAMA, A Taylor-Galerkin based finite element method for turbulent flows, Fluid Dynamic Research, 9, 165-178, 1992.
19. L. DEMKOWICZ, J. T. ODEN, W. RACHOWICZ and O. HARDY, An h-p Taylor-Galerkin finite element method for compressible Euler equations, Comp. Meth. Appl. Mech. Engng., 88, 363-396, 1991.
20. A. J. CHORIN, Numerical solution of Navier Stokes equations, Math. Comp., 22, 745-762, 1968.
21. R. A. ADEY and C. A. BREBBIA, Finite element solution of effluent dispersion, Numerical Methods in Fluid Mechanics, C. A. BREBBIA and J. J. CONNOR [Eds.], 325-354, Pentech Press, 1974.
22. O. PRIONNEAU, On the transport diffusion algorithm to the Navier-Stokes equation, Num. Math., 38, 309-332, 1982.
23. th ed., Butterworth, London 2000.
24. E. OÑATE, Derivation of stabilized equations for numerical solution of advective-diffusive transport and fluid flow problems, Comp. Meth. App. Mech. Engng., 151, 233-265, 1998.
25. E. OÑATE and M. MANZÁN, A general procedure for deriving stabilized space time finite element methods for advective diffusive equations, Int. J. Num. Meth. Fluids, 31, 203-221, 1999.
26. R. CODINA, Stability analysis of forward Euler scheme for the convection diffusion equation using the SUPG formulation in space, Int. J. Num. Meth. Engng., 36, 1445-1464, 1993.
27. T. H. PULLIAM and J. T. BARTON, Euler computations of AGARD working group 07 aerofoil test cases, AIAA 23rd Aerospace Sciences Meeting, Jan 14-17, Reno, Nevada 1985.
28. P. NITHIARASU, O. C. ZIENKIEWICZ, B. V. K. S. SAI, K. MORGAN, R. CODINA, M. VÁZQUEZ, Shock capturing viscosities for the general fluid mechanics algorithm, Int. J. Num. Meth. Fluids, 28, 1325-1353, 1998.
29. J. E. CARTER, Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner, NASA TR-R-385, 1972.
30. U. GHIA, K. N. GHIA and C. T. SHIN, High-Re solution for incompressible flow using the Navier-Stokes equations and multigrid method, J. Comp. Phys., 48, 387-411, 1982.
31. P. NITHIARASU and O. C. ZIENKIEWICZ, Adaptive mesh generation for fluid mechanics problems, Int. J. Num. Meth. Engng., 47, 629-662, 2000.
32. J. PERAIRE, M. VAHDATI, K. MORGAN and O. C. ZIENKIEWICZ, Adaptive remeshing for compressible flow computations, J. Comp. Phys., 72, 449-466, 1987.
33. G. de VAHL DAVIS, Natural convection of air in a square cavity: a bench mark numerical solution, Int. J. Num. Meth. Fluids, 3, 249-264, 1983.