A Front-Tracking Method for Motion by Mean Curvature with Surfactant
Ming-Chih Lai 1*, Che-Wei Hsu 1, Huaxiong Huang 21 Department of Applied Mathematics, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu 300, Taiwan.
2 Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3.
Received 15 November 2008; Accepted (in revised version) 15 February 2009
In this paper, we present a finite difference method to track a network of curves whose motion is determined by mean curvature. To study the effect of inhomogeneous surface tension on the evolution of the network of curves, we include surfactant which can diffuse along the curves. The governing equations consist of one parabolic equation for the curve motion coupled with a convection-diffusion equation for the surfactant concentration along each curve. Our numerical method is based on a direct discretization of the governing equations which conserves the total surfactant mass in the curve network. Numerical experiments are carried out to examine the effects of inhomogeneous surface tension on the motion of the network, including the von Neumann law for cell growth in two space dimensions.AMS subject classifications: 65M06
Key words: Front-tracking method, motion by mean curvature, triple-junction, surface tension, surfactant.
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