Comparison of ODE methods for laminar reacting gas flow simulations. (English) Zbl 1159.76030
Summary: We present two-dimensional transient simulations of transport phenomena and multispecies, multireaction chemistry in chemical vapor deposition. The transient simulations are run until steady state, such that the steady state can be validated against the steady-state solutions from literature. We compare various time integration methods in terms of efficiency and robustness. Besides stability, which is important due to the stiffness of the problem, preservation of non-negativity is crucial. It appears that this latter condition on a time integration method is much more restrictive toward the time step size than stability.
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76V05 | Reaction effects in flows |
| 76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |
References:
| [1] | Kleijn, J Cryst Growth 303 pp 362– (2007) |
| [2] | Alam, J Appl Phys 94 pp 3403– (2003) |
| [3] | van Veldhuizen, Int J Multiscale Comput Eng 5 pp 1– (2007) |
| [4] | Computational modeling of transport phenomena and detailed chemistry in chemical vapor deposition–a benchmark solution, Thin Solid Films, Vol. 365, Elsevier, 2000, pp. 294–306. |
| [5] | , , and , Multiple scale integrated modeling of deposition processes, Thin Solid Films, Vol. 365, Elsevier, 2000, pp. 368–375. |
| [6] | and , Thermal modelling of RTP and RTCVD processes, Thin Solid Films, Vol. 365, Elsevier, 2000, pp. 307–321. |
| [7] | Transport phenomena in chemical vapor deposition reactors, PhD Thesis, Delft University of Technology, Delft, 1991. |
| [8] | and , Numerical solution of time-dependent advection–diffusion–reaction Equations, Springer series in computational mathematics, Vol. 33, Springer, Berlin, 2003. |
| [9] | Bolley, RAIRO Anal Numer 12 pp 237– (1973) |
| [10] | Gottlieb, SIAM Rev 43 pp 89– (2001) |
| [11] | Hundsdorfer, SIAM J Numer Anal 41 pp 605– (2003) |
| [12] | Principles of computational fluid dynamics, Springer series in computational mathematics, Vol. 29, Springer, Berlin, 2001. |
| [13] | and , Solving ordinary differential equations II: stiff and differential-algebraic problems, 2nd Ed., Springer series in computational mathematics, Vol. 14, Springer, Berlin, 1996. · Zbl 0859.65067 |
| [14] | , and , A note on the numerical simulation of Kleijn’s benchmark problem, Technical report at the Delft University of Technology, Report 06-15, Delft University of Technology, Delft, 2006. |
| [15] | Verwer, SIAM J Sci Comp 20 pp 1456– (1999) |
| [16] | , and , Solving ordinary differential equations I: nonstiff problems, Springer series in computational mathematics, Vol. 8, Springer, Berlin, 1987. |
| [17] | Verwer, J Comp Phys 201 pp 61– (2004) |
| [18] | Solving nonlinear equations with Newton’s method, fundamentals of algorithms, SIAM, Philadelphia, 2003. · Zbl 1031.65069 · doi:10.1137/1.9780898718898 |
| [19] | and , Numerical method for unconstrained optimization and nonlinear equations, series in automatic computing, Prentice-Hall, Englewood Cliffs, NJ, 1983. |
| [20] | , , , , , , , , , and , LAPACK users’ guide, 2nd Ed., SIAM, Philadelphia, 1995. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
