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Zbl 0659.65132
Osher, Stanley; Sethian, James A.
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. (English)
[J] J. Comput. Phys. 79, No.1, 12-49 (1988). ISSN 0021-9991

New methodologies are formulated for following fronts propagating with curvature-dependent speed, which models, among other things, crystal growth and flame propagation. The algoritms are based on an approximation of the Hamilton-Jacobi formulations for such problems. The paper is carefully written with numerical exemplification (including detailed graphics) which shows that the numerical schemes accurately capture the formation of sharp gradients and cusps in the moving fronts.
[R.S.Anderssen]

MSC 2000:: *65Z05 Applications to physics
65M99 Numerical methods for IVP of PDE
35L65 Conservation laws
80A25 Combustion, interior ballistics
82D25 Crystals

Keywords: hyperbolic conservation laws; numerical example; following fronts propagating; curvature-dependent speed; crystal growth; flame propagation; Hamilton-Jacobi formulations; moving fronts

Cited in: Zbl 1216.94007 Zbl 1168.65392 Zbl 1169.74543 Zbl 1196.65218 Zbl 1177.76295 Zbl 1096.65020 Zbl 1091.76054 Zbl 1077.35070 Zbl 1069.65070 Zbl 1069.65016 Zbl 1076.74045 Zbl 1081.53029 Zbl 0995.65100 Zbl 0994.65090 Zbl 0964.76069 Zbl 0866.76059 Zbl 0849.65075 Zbl 0855.76092 Zbl 0805.65090 Zbl 0804.35021 Zbl 0802.65098 Zbl 0783.35034 Zbl 0736.65066 Zbl 0726.53029

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