On Numerical Issues in Time Accurate Laminar Reacting Gas Flow Solvers
methods enables us to reduce the required CPU time by an order of magnitude to
300 CPU seconds.
Acknowledgements The work of S. van Veldhuizen was financially supported by the Delft Center
for Computational Science and Engineering.
References
1. C. Bolley and M. Crouzeix. Conservation de la positivit´e lors de la discr´etisation des
probl`emes d’´evolution paraboliques. RAIRO Anal. Numer., 12:237–245, 1973.
2. K. Brenan, S. Campbell, and L. R. Petzold. Numerical solution of initial value problems in
differential-algebraic equations. SIAM, Philadelphia, 1989. Second Edition.
3. P. N. Brown, G. D. Byrne, and A. C. Hindmarsch. VODE, a variable coefficient ODE solver.
SIAM J. Stat. Comput., 10:1038–1051, 1989.
4. M. E. Coltrin, R. J. Kee, and G. H. Evans. A mathematical model of the fluid mechanics and
gas-phase chemistry in a rotating Chemical Vapor Deposition reactor. J. Electrochem. Soc,
136:819–829, 1989.
5. M. E. Coltrin, R. J. Kee, G. H. Evans, E. Meeks, F. M. Rupley, and J. F. Grcar. Spin (ver-
sion 3.83): A FORTRAN program for modeling one-dimensional rotatingdisk/stagnation-flow
Chemical Vapour Deposition reactors. Technical Report SAND91-80, Sandia National Labo-
ratories, Albuquerque, NM/Livermore, CA, USA, 1993.
6. S. C. Eisenstat and H. F. Walker. Choosing the forcing terms in an inexact Newton method.
SIAM J. Sci. Comput., 17:16–32, 1996.
7. C. W. Gear. Numerical Initial value problems in ordinary differential equations. Prentice Hall,
Englewood Cliffs, 1971.
8. M. Graziadei and J. H. M. ten Thije Boonkkamp. Local defect correction for laminar flame
simulation. In A. Di Bucchianico, R.M.M. Mattheij, and M.A. Peletier, editors, Progress in
industrial mathematics at ECMI 2004, volume 8 of Math. Ind., pages 242–246, Berlin, 2006.
Springer.
9. E. Hairer, S. P. Nørsett, and G. Wanner. Solving ordinary differential equations I: nonstiff
problems. Number 8 in Springer Series in Computational Mathematics. Springer, 1987.
10. E. Hairer and G. Wanner. Solving ordinary differential equations II: stiff and differential-
algebraic problems. Number 14 in Springer Series in Computational Mathematics. Springer,
Berlin, 1996.
11. M. L. Hitchman and K. F. Jensen. Chemical Vapor Deposition- Principles and Applications.
Academic Press, London, 1993.
12. W. Hundsdorfer and J. G. Verwer. Numerical Solution of Time-Dependent Advection-
Diffusion-Reaction Equations. Number 33 in Springer Series in Computational Mathematics.
Springer, Berlin, 2003.
13. K. F. Jensen. Modeling of chemical vapor deposition reactors. In Modeling of Chemical Vapor
Deposition reactors for semiconduction fabrication. Berkeley, 1988. Course notes.
14. C. R. Kleijn. Transport phenomena in Chemical Vapor Deposition reactors. PhD thesis, Delft
University of Technology, Delft, 1991.
15. C. R. Kleijn. Computational modeling of transport phenomena and detailed chemistry in
Chemical Vapor Deposition- A benchmark solution. Thin Solid Films, 365:294–306, 2000.
16. C. R. Kleijn, R. Dorsman, K. J. Kuijlaars, M. Okkerse, and H. van Santen. Multi-scale mod-
eling of chemical vapor deposition processes for thin film technology. J. Cryst. Growth,
303:362–380, 2007.
17. J. M. Ortega and W. C. Rheinboldt. Iterative solution of nonlinear equations in several vari-
ables. Number 30 in Classics in Applied Mathematics. SIAM, Philadelphia, 2000. Reprint of
the 1970 original.
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