On the convergence and local splitting error of different splitting schemes

Progress in Computational Fluid Dynamics

Volumn 5, Issue 8, 2005, Pages 495-504

  Faragó, István ^a   Havasi, Ágnes ^a  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

Author keywords

Application to CFD; Convergence; Local splitting error; Semigroup; Shallow water model; Strang splitting

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; ITERATIVE METHODS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; THEOREM PROVING; VECTORS;

LOCAL SPLITTING ERROR; SHALLOW WATER MODEL; STRANG SPLITTING;

COMPUTATIONAL FLUID DYNAMICS;

COMPUTATIONAL FLUID DYNAMICS; MATHEMATICAL METHOD; SHALLOW-WATER EQUATION;

EID: 27344439649     PISSN: 14684349     EISSN: None     Source Type: Journal    
DOI: 10.1504/PCFD.2005.007684     Document Type: Article

References (22)

1. Zlatev, Z. (1995) Computer Treatment of Large Air Pollution Models, Kluwer Academic Publishers, Dordrecht, Boston, London.
2. Bermúdez, B., Nicolás, A. and Sánchez, F.J. (1996) 'On operator splitting methods with upwinding for the unsteady Navier-Stokes equations', East-West Journal on Numer. Math., December, Vol. 4, No. 4, pp.237-309.
3. Bermúdez, B., Nicolás, A. and Sánchez, F.J. (1996) 'On operator splitting for the Navier-Stokes equations at high Reynolds numbers', ECOAMS 96, John Wiley and Sons, New York, pp.85-89.
4. Bermúdez, B., Nicolás, A. and Sánchez, F.J. (1997) 'Operator splitting for the Navier-Stokes equations', Comp. Mechanics, Vol. 20, pp.475-477.
5. Holden, H., Karlsen, K.H. and Risebrot, N.H. (1999) 'Operator splitting methods for generalized Korteweg-de Vries equations', J. Comp. Phys., Vol. 153, pp.203-222.
6. Pudjaprasetya, S.R., Van Groesen, E. and Soewono, E. (1999) 'The splitting of solitary waves running over a shallow water', Wave Motion, Vol. 29, No. 4, pp.375-389.
7. Bleck, R. and Smith, L.T. (1999) 'A wind-driven isopycnic coordinate model of the north and equatorial Atlantic Ocean 1. Model development and supporting experiments', J. Geophys. Res. C, Vol. 95, p.3273.
8. Dukowicz, J.K. and Smith, R.D. (1994) 'Implicit free-surface method for the Bryan-Cox-Semtner ocean model', J. Geophys. Res C., Vol. 99, p.7991.
9. Killworth, P.D., Stainforth, D., Webb, D.J. and Paterson, S.M. (1991) 'The development of a free-surface Bryan-Cox-Semtner ocean model', J. Phys. Oceanogr., Vol. 21, p.1333.
10. Lanser, D., Blom, J.G. and Verwer, J.G. (2001) 'Time integration of the shallow water equations in spherical geometry', J. Comput. Phys., Vol. 1, pp.86-98.
11. Strang, G. (1963) 'Accurate partial difference methods I: linear Cauchy problems', Archive for Rational Mechanics and Analysis, Vol. 12, pp.392-402.
12. Hundsdorfer, W. (1992) 'Unconditional convergence of some Crank-Nicolson LOD methods for initial-boundary value problems', Math. Comput., Vol. 58, No. 197, pp.35-53.
13. Csomós, P., Faragó, I. and Havasi, Á. (2003) 'Weighted sequential splittings and their analysis', Computer and Mathematics with Applications, to appear.
14. Bochev, M.A., Faragó, I. and Havasi, Á (2004) 'Testing weighted splittings on a one-column transport-chemistry model', International Journal of Environment and Pollution, Vol. 22, Nos. 1/2.
15. Barbu, V. (1976) Nonlinear Semigroups and Differential Equations in Banach Spaces, Nordhoff Int. Publ., Leyden.
16. Belleni-Morante, A. and McBride, A.C. (1998) Applied Nonlinear Semigroups, J. Wiley & Sons, New York.
17. Engel, K.J. and Nagel, R. (2000) One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, Springer.
18. Lax, P. (2002) Functional Analysis, Wiley Interscience Publ., New York.
19. Lanser, D. and Verwer, J.G. (1999) 'Analysis of operator splitting for advection-diffusion-reaction problems in air pollution modelling', J. Comput. Appl. Math., Vol. 111, Nos. 1-2, pp.201-216.
20. Varadarajan, V.S. (1974) Lie Groups, Lie Algebras and Their Representations,, Prentice-Hall Inc., Englewood Cliffs, New Jersey.
21. Verwer, J.G., Hundsdorfer, W.H. and Blom, J.G. (1998) 'Numerical time integration for air pollution models', Report MAS-R9825, CWI (Centre for Mathematics and Computer Science), Amsterdam, The Netherlands.
22. Strang, G. (1968) 'On the construction and comparison of difference schemes', SIAM J. Numer. Anal., Vol. 5, No. 3, pp.506-517.