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Abstract: Simulations of motion by mean curvature in bounded domains, with applicationsto bubble motion and grain growth, rely upon boundary conditions that are onlyapproximately compatible with the equation of motion. Three closed formsolutions for the problem exist, governing translation, rotation and expansionof a single interface 1, providing the only benchmarks for algorithmverification. We derive new identities for the translation solution. Then weestimate the accuracy of a straightforward algorithm to recover the analyticalsolution for different values of the velocity V given along the boundary. Asexpected, for large V the error can reach unacceptable levels especially nearthe boundary. We discuss factors influencing the accuracy and propose a simplemodification of the algorithm which improves the computational accuracy.



Author: Simon Cox, Gennady Mishuris

Source: https://arxiv.org/







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