Finite elements for CFD - How does the theory compare?

International Journal for Numerical Methods in Fluids

Volumn 31, Issue 1, 1999, Pages 345-358

  Baker, A J ^a   Chaffin, D J ^a   Iannelli, J S ^a   Roy, S ^b  

^a UNIVERSITY OF TENNESSEE   (United States)

^b Case Corporation   (United States)

Author keywords

Accuracy; CFD; Convergence; Finite elements; Galerkin boundary value

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; CONVECTION; FINITE ELEMENT METHOD;

COMPUTATIONAL FLUID DYNAMICS; CONVECTIVE SYSTEM; FINITE ELEMENT METHOD;

EID: 0032694699     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0363(19990915)31:1<345::AID-FLD974>3.0.CO;2-L     Document Type: Article

References (26)

1. A.J. Baker and J.W. Kim, 'A Taylor weak statement algorithm for hyperbolic conservation laws', Int. J. Numer. Methods Fluids, 7, 489-520 (1987).
2. P.D. Lax, 'Weak solutions of nonlinear hyperbolic equations and their numerical computation', Comm. Pure Appl. Math., 7, 159-193 (1954).
3. H.O. Kreiss and J. Lorenz, Initial-Boundary Value Problems and the Navier-Stokes Equations, Academic Press, New York, 1989.
4. J.P. Boris and D.L. Book, 'Flux-corrected transport, I. SHASTA, a fluid transport algorithm that works', J. Comput. Phys., 11, 38-69 (1973).
5. S.T. Salezak, 'Fully multidimensional flux corrected algorithms for fluids', J. Comput. Phys., 31, 355-362 (1979).
6. B. van Leer, 'Flux vector splitting for the Euler equations', Proceedings of the 8th International Conference on Numerical Methods in Fluid Dynamics, Springer, Berlin, 1983.
7. H.T. Huynh, 'Accurate monotone cubic interpolation', SIAM J. Numer. Anal., 30, 57-100 (1993).
8. I. Babuska, B.Q. Guo and E.P. Stephan, 'On the exponential convergence of the hp version for boundary element Galerkin methods on polygons', Math. Methods Appl. Sci., 12, 413-427 (1990).
9. L. Demkowicz, A. Karafiat and J.T. Oden, 'Solution of elastic scattering problems in linear acoustics using hp boundary element method', Comput. Methods Appl. Mech. Eng., 101, 251-282 (1992).
10. S. Jensen, 'p version of mixed finite element methods for Stokes-like problems', Comput. Methods Appl. Mech. Eng., 101, 27-41 (1992).
11. C. Johnson and P. Hansbo, 'Adaptive finite element methods in computational mechanics', Comput. Methods Appl. Mech. Engrg., 101, 143-181 (1992).
12. J.T. Oden, 'Optimal hp finite element methods', TICOM Report 92-09, University of Texas, Austin, TX, 1992.
13. O.C. Zienkiewicz, D.W. Kelly, J. Gago and I. Babuska, 'Hierarchical finite element approaches, error estimates and adaptive refinement', in J. Whiteman (ed.), The Mathematics of Finite Elements and Applications IV, 1982, pp. 311-346.
14. O.C. Zienkiewicz and J.Z. Zhu, 'The super convergent patch recovery (SPR) and adaptive finite element refinement', Comput. Methods Appl. Mech. Eng., 101, 207-224 (1992).
15. J.T. Oden, 'Optimal hp finite element methods', Comput. Methods Appl. Mech. Engrg., 112, 309-331 (1994).
16. T.J.R Hughes, 'Multi-scale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods', Comput. Methods Appl. Mech. Eng., 127, 387-401 (1995).
17. A.J. Baker, Finite Element Computational Fluid Dynamics, Taylor & Francis, Washington, DC.
18. D.J. Chaffin and A.J. Baker, 'On Taylor weak statement finite element methods for computational fluid dynamics', Int. J. Numer. Methods Fluids, 21, 273-294 (1995).
19. P. Lax and B. Wendroff, 'Systems of conservation laws', Comm. Pure Appl. Math., 8, 217-237 (1960).
20. J. Donea, 'A Taylor-Galerkin method for convective transport problems', Int. J. Numer. Methods Eng., 20, 101-119 (1984).
21. S. Roy, 'On improved methods for monotone CFD solution accuracy', Ph.D. Dissertation, The University of Tennessee, 1994.
22. S. Roy and A.J. Baker, 'A nonlinear subgrid embedded finite element basis for accurate monotone steady CFD solutions', Int. J. Numer. Heat Transf., 31, 135-176 (1997).
23. M.S. Liou and B. van Leer, 'Choice of implicit and explicit operators for the upwind differencing method', Tech. AIAA 88-0624, 26th Aerospace Sciences Meeting, 1988.
24. D.J. Chaffin, 'A Taylor weak statement finite element method for computational fluid dynamics', Ph.D. Dissertation, University of Tennessee, 1997.
25. R.F. Warming and B.J. Hyett, The modified equation approach to the stability and accuracy analysis of finite difference methods', J. Comp. Phys., 14, 159-179 (1974).
26. J. Iannelli, AIAA 96-0763, 34th Aerospace Sciences Meeting, 1996.