2010/09/14 by Daniel Ševčovič, Sevcovic, Daniel, Shigetoshi Yazaki +1 · 1 citation
Computer Science · Engineering · Mathematics · #35K65 #53C80 #65N40 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1009.2588
openalex publication_date 2010/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study evolution of a closed embedded plane curve with the normal velocity depending on the curvature, the orientation and the position of the curve. We propose a new method of tangential redistribution of points by curvature adjusted control in the tangential motion of evolving curves. The tangential velocity distributes grid points along the curve not only uniform but also lead to a suitable concentration and/or dispersion depending on the curvature. Our study is based on solutions to the governing system of nonlinear parabolic equations for the position vector, tangent angle and curvature of a curve. We furthermore present a semi-implicit numerical discretization scheme based on the flowing finite volume method. Several numerical examples illustrating capability of the new tangential redistribution method are also presented in this paper.