Abstract
In many physical problems, a key aspect is the motion of a propagating front separating two components. As fundamental as this may be, the development of a numerical algorithm to track the moving front accurately is difficult. In this report, we describe some previous theoretical and numerical work. We begin with two examples to motivate the problem, followed by some analytical results. These theoretical results are then used as a foundation for two different types of numerical schemes. Finally, we describe the application of one of these schemes to our work in combustion.
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References
K.A. Brakke, The motion of a surface by its mean curvature, Princeton University Press, Princeton, New Jersey (1978).
A.J. Chorin, Curvature and solidification, J. Comp. Phys. (to appear).
A.J. Chorin, Flame advection and propagation algorithms, J. Comp. Phys. 35 (1980), 1–11.
M.L. Frankel and G.I. Sivashinsky, The effect of viscosity on hydrodynamic stability of a plane flame front, Comb. Sci. Tech. 29 (1982), 207–224.
P.R. Garabedian, Partial differential equations. John Wiley and Sons, New York (1961).
E. Hopf, The partial differential equation u t + uu x = μu xx , Comm. Pure Appl. Math. 3 (1950), 201.
G. Huisken, Flow by mean curvature of convex surfaces into spheres, Preprint (1984).
L. Landau, On the theory of slow combustion, ACTA Physiocochimica, URSS 19 (1944), 77–85.
J.S. Langer, Instabilities and patternformation in crystal growth, Rev. Mod. Phys. 52(1980), 1–28.
J.S. Langer and H. Muller-Krumhaar, Mode selection in a dendritelike nonlinear system, Phys. Rev. A 27 (1983), 499–514.
G.H. Markstein, Experimental and theoretical studies offlame front stability, J. Aero. Sci. 18(1951), 199–209.
G.H. Markstein, Non-Steady flame propagation, Pergamon Press, MacMillan Company, New York (1964).
W.W. Mullins and R.F. Sekerka, J. Appl. Phys. 34 (1963), 2885.
F.A. Nichols and W.W. Mullins, Trans. Met. Soc., AIME 223 (1965), 1840.
W. Noh and P. Woodward, A simple line interface calculation, Proceedings, Fifth International Conference on Fluid Dynamics, A.I. van de Vooran and P.J. Zandberger, Eds. Springer-Verlag, New York (1976).
B.R. Pamplin, Crystal Growth. Pergamon Press, New York (1975).
J.A. Sethian, An algorithm for propagatingfronts based on high-order upwind schemes (in progess).
J.A. Sethian, An analysis offlame propagation, PhD. Dissertation, University of California, Berkeley, California, June 1982; CPAM Rep. 79.
J.A. Sethian, Curvature and the evolution of fronts, Communications of Mathematical Physics 101 (1985), 487–499.
J.A. Sethian, Numerical Simulation of Flame Propagation in a Closed Vessel, Notes on Numerical Fluid Mechanics, Editors: Pandolfi, M. and Piva, R., Proceedings of the Fifth GAMM-Conference on Numerical Methods in Fluid Mechanics, Rome, October 5–7, 1983, Friedr, Vieweg & Sohn, Braunschweig/Wiesbaden, 1984, pp. 324–331.
J.A. Sethian, Turbulent combustion in open and closed vessels. J. Comp. Phys. 54 (1984), 425–456.
G.I. Sivashinsky, Nonlinear analysis of hydrodynamic instability in laminar flames, I. Acta Astronautica 4 (1977), 1177–1206.
D. Turnbull, “Phase changes” in solid state physics, 3, ed. Seitz, F. and Turnbull, D., Academic Press, New York (1956).
Y.B. Zeldovich, Structure and stability of steady laminar flame at moderately large Reynolds numbers, Comb. Flame 40 (1981), 225–234.
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© 1987 Springer-Verlag New York Inc.
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Sethian, J.A. (1987). Numerical Methods for Propagating Fronts. In: Concus, P., Finn, R. (eds) Variational Methods for Free Surface Interfaces. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4656-5_18
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DOI: https://doi.org/10.1007/978-1-4612-4656-5_18
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