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A line element algorithm for curve flow problems in the plane

Published online by Cambridge University Press:  17 February 2009

Stephen Roberts
Stephen Roberts
Affiliation:
Mathematics Department, The Faculties, Australian National University.
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Abstract

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In this paper we shall describe a numerical method for the solution of curve flow problems in which the normal velocity of the curve depends locally on the position, normal and curvature of the curve. The method involves approximating the curve by a number of line elements (segments) which are only allowed to move in a direction normal to the element. Hence the normal of each line element remains constant throughout the evolution. In regions of high curvature elements naturally tend to accumulate. The method easily deals with the formation of cusps as found in flame propagation problems and is computationally comparable to a naive marker particle method. As a test of the method we present a number of numerical experiments related to mean curvature flow and flows associated with flame propagation and bushfires.

Type
Research Article
Information
The ANZIAM Journal , Volume 35 , Issue 2 , October 1993 , pp. 244 - 261
Copyright
Copyright © Australian Mathematical Society 1993

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