Summary
We present the numerical simulation of stationary, laminar diffusion flames with detailed chemical reaction mechanism on distributed memory parallel computers. The problem consists in solving the conservation equations of total mass, momentum, energy and species masses for a compressible fluid. For the numerical solution we suggest a hybrid algorithm which is a combination of data and domain decomposition techniques. This approach has been tested on a variety of parallel computers ranging from moderately to massively parallel and has proven uniformly high parallel efficiencies. Results for Parsytec GC/PP, a Cray T3D and an IBM-SP2 computer are presented. Calculations for a model bunsen burner with axisymmetric configuration are presented and discussed.
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References
D. A. ANDERSON, J. C. TANNEHILL, R. H. PLETCHER, Computational Fluid Mechanics and Heat Transfer, New York, Hemisphere Publishing Corporation (1984).
G. BADER, E. GEHRKE, On the performance of transputer networks for solving linear systems of equations, Parallel Computing, Vol. 17 (1991) 1397–1407.
G. BADER, E. GEHRKE, Solution of Flame Sheet Models on Transputer Systems, in Flow Simulation with High-Performance Computers I, DFG Priority Research Programme Results 1989–1992, E. H. Hirschel (Hrsg.), Notes on Numerical Fluid Mechanics, Vol. 38, Vieweg (1993) 31–40.
M. W. CHASE JR., C. A. DAVIES, J. R. DOWNEY JR., D. J. FRURIP, R. A. MCDONALD AND A. N. SYVERUND, Jannaf thermochemical tables, third edition, J. Phys. Chem. Ref. data Suppl. 1, 14 (1985) 1–1856.
A. R. CURTIS, M. J. POWELL, J. K. REID, On the Estimation of Sparse Jacobian Matrices, J. Inst. Math. Appl. 13 (1974) 117–119.
A. ERN, C. C. DOUGLAS, M. D. SMOOKE, Detailed chemistry Modelling of laminar Diffusion Flames on parallel Computers, Yale University, (1994)
P. DEUFLHARD, A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with applications to multiple shooting, Numer. Math., 22 (1974) 289–315.
E. GEHRKE, Parallele Methoden zur numerischen Simulation reaktiver Strömungen am Beispiel laminarer Diffusionsflammen, PhD thesis, Institute of applied mathematics, University of Heidelberg (1994).
E. GEHRKE, G. BADER, Parallel Methods for the Numerical Simulation of Stationary Diffusion Flames, in Proceedings of the 2nd Summer Conference Numerical Modelling in Continuum Mechanics, Academy of Sciences of the Czech Republic, Vol. 40, Prague, (1995).
W. G. GROPP, D. E. KEYES, Domain Decomposition with local Mesh Refinement, Techn. Report 91-19, NASA Langley Research Center (1991).
W. GROPP, E. LUSK AND A. SKJELLUM, Using MPI: Portable Parallel Programming with the Message Passing, MIT Press (1994).
R. J. KEE, J. A. MILLER, T. H. JEFFERSON, CHEMKIN: A General-Purpose, Transportable Fortran Chemical Kinetics Code Package, Sandia National Laboratories Report, SAND 80-8003.
D. E. KEYES, M. D. SMOOKE, Flame Sheet Starting Estimates for Counterflow Diffusion Flame Problems, J. of Comp. Physics, vol. 73 (1986) 267–288.
D. E. KEYES, M. D. SMOOKE, A Parallelized Elliptic Solver for Reacting Flows, in Parallel Computations and Their Impact on Mechanics. A. K. Noor (Ed.), Numerical Society of Mechanical Engineers (1989) 375–402.
M. MEINKE, E. ORTNER, Implementation of Explicit Navier-Stokes Solvers on Massively Parallel Systems, in Flow Simulation with High-Performance Computers I, DFG Priority Research Programme Results 1989–1992, E. H. Hirschel (Hrsg.), Notes on Numerical Fluid Mechanics, Vol. 38, Vieweg (1993) 138–151.
Y. SAAD, M. H. SCHULTZ, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. 7 (1986) 856–869.
M. SMOOKE, R. MITCHELL AND D. KEYES, Numerical Solution of Two-Dimensional Axisymmetric Laminar Diffusion Flames, Combust. Sci. and Tech., 67 (1989) 85–122.
H. A. VAN DER VORST, BI-CGSTAB: A FAST and Smoothly Converging Variant of BI-CG for the Solution of Nonsymmetric Linear Systems, SIAM J. Sci. Stat. Comput. 13 (1992) 631–644.
F. A. WILLIAMS, Combustion Theory, Addison-Wesley Publishing Company Inc, second edition (1988).
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© 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Bader, G., Gehrke, E. (1996). Simulation of Detailed Chemistry Stationary Diffusion Flames on Parallel Computers. In: Hirschel, E.H. (eds) Flow Simulation with High-Performance Computers II. Notes on Numerical Fluid Mechanics (NNFM), vol 48. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-89849-4_11
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DOI: https://doi.org/10.1007/978-3-322-89849-4_11
Publisher Name: Vieweg+Teubner Verlag
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