Advertisement

Fast Solution for Large-Scale 2-D Convection-Diffusion, Reacting Flows

  • Hoang Duc Minh
  • Hans Georg Bock
  • Steffen Tischer
  • Olaf Deutschmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5072)

Abstract

2-D convection-diffusion, reacting flows in a single channel of catalytic monoliths are investigated. The fluid dynamics are modelled by a steady state, boundary-layer equations, which is a large system of parabolic partial differential equations (PDEs) with nonlinear boundary conditions arising from the coupling between the gas-phase and surface processes. The chemical processes are modelled using detailed chemistry. The PDEs are semi-discretized by a method of lines leading to a large-scale, structured differential algebraic equations (DAEs). The DAEs are solved using a tailored BDF code. We exploit the structure of the Jacobian and freeze the diffusion coefficients during approximation of Jacobian by the finite difference. By applying our approach, the computation times have been reduced by a factor of 4 to 10 and more depending on the particular problem.

Keywords

Newton Iteration Sandia National Laboratory Differential Algebraic Equation Nonlinear Boundary Condition Fast Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kee, R.J., Miller, J.A.: A computational model for chemically reacting flow in boundary layers, shear layers, and ducts. Technical Report SAND81-8241, Sandia National Laboratories, Albuquerque, NM (1981)Google Scholar
  2. 2.
    Coltrin, M.E., Kee, R.J., Miller, J.A.: A mathematical model of the coupled fluid mechanics and chemical kinetics in a chemical vapor deposition reactor. Journal of The Electrochemical Society 131(2), 425–434 (1984)CrossRefGoogle Scholar
  3. 3.
    Coltrin, M.E., Kee, R.J., Miller, J.A.: A mathematical model of silicon chemical vapor deposition. Journal of The Electrochemical Society 133(6), 1206–1213 (1986)CrossRefGoogle Scholar
  4. 4.
    Coltrin, M.E., Moffat, H.K., Kee, R.J., Rupley, F.M.: CRESLAF (verison 4.0): A Fortran program for modelling laminar, chemically reacting, boundary-layer flow in the cylindrical or planar channels. Technical Report SAND93–0478, Sandia National Laboratories (April 1993)Google Scholar
  5. 5.
    Minh, H.D.: Numerical Methods for Simulation and Optimization of Chemically Reacting Flows in Catalytic Monoliths. PhD thesis, Faculty of Mathematics and Computer Science, University of Heidelberg (December 2005)Google Scholar
  6. 6.
    Warnatz, J.: Influence of transport models and boundary conditions on flame structure. In: Peters, N., Warnatz, J. (eds.) Numerical Methods in Flame Propagation, Fridr. Vieweg and Sohn, Wiesbaden (1982)Google Scholar
  7. 7.
    Kee, R.J., Warnatz, J., Miller, J.A.: A Fortran computer code package for the evaluation of gas phase viscosities, heat conductivities, and diffusion coefficients. Technical Report SAND83-8209, Sandia National Laboratories (1983)Google Scholar
  8. 8.
    Warnatz, J., Dibble, R., Maas, U.: Combustion, Physical and Chemcial Fundamentals, Modeling and Simulation, Experiments, Pullutant Formation. Springer, New York (1996)Google Scholar
  9. 9.
    Deutschmann, O., Tischer, S., Kleditzsch, S., Janardhanan, V.M., Correa, C., Chatterjee, D., Mladenov, N., Minh, H.D.: DETCHEM - User’s manual (2007), www.detchem.com
  10. 10.
    Schiesser, W.E.: The Numerical Method of Lines, Integration of Partial Differential Equations. Academmic Press, San Diego (1991)zbMATHGoogle Scholar
  11. 11.
    Bauer, I., Bock, H.G., Schlöder, J.P.: DAESOL – a BDF-code for the numerical solution of differential algebraic equations. Technical report, SFB 359, IWR, University of Heidelberg (1999)Google Scholar
  12. 12.
    Bauer, I., Finocchi, F., Duschl, W., Gail, H., Schlöder, J.: Simulation of chemical reactions and dust destruction in protoplanetary accretion disks. Astronomy & Astrophys 317, 273–289 (1997)Google Scholar
  13. 13.
    Bischof, C., Carle, A., Hovland, P., Khademi, P., Mauer, A.: ADIFOR 2.0 User’s Guide (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hoang Duc Minh
    • 1
  • Hans Georg Bock
    • 2
  • Steffen Tischer
    • 1
  • Olaf Deutschmann
    • 1
  1. 1.Institute for Chemical Technology and Polymer ChemistryUniversity of Karlsruhe (TH)KarlsruheGermany
  2. 2.Interdisciplinary Center for Scientific Computing (IWR)University of HeidelbergGermany

Personalised recommendations