A variational method for multiphase volume-preserving interface motions

• Autores: Karel Svadlenka, Elliott Ginder, Seiro Omata
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 257, Nº 1, 2014, págs. 157-179
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.08.027
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• Resumen

  • We develop a numerical method for realizing mean curvature motion of interfaces separating multiple phases, whose volumes are preserved throughout time. The foundation of the method is a thresholding algorithm of the Bence�Merriman�Osher type. The original algorithm is reformulated in a vector setting, which allows for a natural inclusion of constraints, even in the multiphase case. Moreover, a new method for overcoming the inaccuracy of thresholding methods on non-adaptive grids is designed, since this inaccuracy becomes especially prominent in volume-preserving motions. Formal analysis of the method and numerical tests are presented.