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Keywords:
Mean curvature flow; level set equation; numerical solution; semi-implicit scheme; discrete duality finite volume method (DDFV)
Mean curvature flow; level set equation; numerical solution; semi-implicit scheme; discrete duality finite volume method (DDFV)
Summary:
In this work we describe two schemes for solving level set equation in 3D with a method based on finite volumes. These schemes use the so-called dual volumes as in [Coudiére, Y., Hubert, F.: A 3D discrete duality finite volume method for nonlinear elliptic equations Algoritmy 2009 (2009), 51–60.], [Hermeline, F.: A finite volume method for approximating 3D diffusion operators on general meshes Journal of Computational Physics 228, 16 (2009), 5763–5786.], where they are used for the nonlinear elliptic equations. We describe these schemes theoretically and also compare results of the numerical experiments based on exact solution using proposed schemes.
References:
[1] Andreianov, B., Bendahmare, M., Karlsen, K. H.: A Gradient Reconstruction Formula for Finite Volume Schemes and Discrete Duality. In: Finite Volume For Complex Applications, Problems And Perspectives. 5th International Conference, Wiley, London, 2008, 161–168. MR 2451403
[2] Andreianov, B., Boyer, F., Hubert, F.: Discrete duality finite volume schemes for Leray–Lions type elliptic problems on general 2D meshes. Numerical Methods PDE 23, 1 (2007), 145–195. DOI 10.1002/num.20170 | MR 2275464 | Zbl 1111.65101
[3] Coudiére, Y., Hubert, F.: A 3D discrete duality finite volume method for nonlinear elliptic equations. Algoritmy 2009 (2009), 51–60. Zbl 1171.65441
[4] Evans, L. C., Spruck, J.: Motion of the level sets by mean curvature I. J. Differential Geometry 3 (1991), 635–681. MR 1100206
[5] Eymard, R., Gallouë, T., Herbin, R.: Finite volume methods. Handbook of Numerical Analysis (Ph., Ciarlet, J. L., Lions, eds.), 3 (2000), 713–1018. MR 1804748
[6] Handlovičová, A., Kotorová, D.: Stability of the semi-implicit discrete duality finite volume scheme for the curvature driven level set equation in 2D. Tatra Mountains Mathematical Publications, accepted.
[7] Hermeline, F.: A finite volume method for approximating 3D diffusion operators on general meshes. Journal of Computational Physics 228, 16 (2009), 5763–5786. DOI 10.1016/j.jcp.2009.05.002 | MR 2542915 | Zbl 1168.76340
[8] Kotorová, D.: Discrete duality finite volume scheme for the curvature-driven level set equation. Acta Polytechnica Hungarica 8, 3 (2011), 7–12.
[9] Kotorová, D.: Discrete duality finite volume scheme for the curvature driven level set equation in 3D. In: Advances in architectural, civil and environmental engineering [electronic source]: 22nd Annual PhD Student Conference, Nakl. STU, Bratislava, 2012, 33–39.
[10] Kotorová, D.: 3D numerical schemes for the level set equation based on discrete duality finite volumes. to appear.
[11] Sethian, J. A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Material Science. Cambridge University Press, New York, 1999. MR 1700751
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