Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
01 Nov 1988-Journal of Computational Physics (Academic Press Professional, Inc.)-Vol. 79, Iss: 1, pp 12-49
TL;DR: The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.
About: This article is published in Journal of Computational Physics.The article was published on 1988-11-01. It has received 13020 citations till now. The article focuses on the topics: Equations of motion & Curvature.
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TL;DR: The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorem, and continuous dependence may now be proved by very efficient and striking arguments as discussed by the authors.
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TL;DR: Two methods of sharpening contact discontinuities-the subcell resolution idea of Harten and the artificial compression idea of Yang, which those authors originally used in the cell average framework-are applied to the current ENO schemes using numerical fluxes and TVD Runge-Kutta time discretizations.
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TL;DR: An hierarchy of uniformly high-order accurate schemes is presented which generalizes Godunov's scheme and its second- order accurate MUSCL extension to an arbitrary order of accuracy.
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