An Interface-Fitted Finite Element Level Set Method with Application to Solidification and Solvation
Year: 2011
Communications in Computational Physics, Vol. 10 (2011), Iss. 1 : pp. 32–56
Abstract
A new finite element level set method is developed to simulate the interface motion. The normal velocity of the moving interface can depend on both the local geometry, such as the curvature, and the external force such as that due to the flux from both sides of the interface of a material whose concentration is governed by a diffusion equation. The key idea of the method is to use an interface-fitted finite element mesh. Such an approximation of the interface allows an accurate calculation of the solution to the diffusion equation. The interface-fitted mesh is constructed from a base mesh, a uniform finite element mesh, at each time step to explicitly locate the interface and separate regions defined by the interface. Several new level set techniques are developed in the framework of finite element methods. These include a simple finite element method for approximating the curvature, a new method for the extension of normal velocity, and a finite element least-squares method for the reinitialization of level set functions. Application of the method to the classical solidification problem captures the dendrites. The method is also applied to the molecular solvation to determine optimal solute-solvent interfaces of solvation systems.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.230510.240910a
Communications in Computational Physics, Vol. 10 (2011), Iss. 1 : pp. 32–56
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
-
Prediction of grain-size transition during solidification of hypoeutectic Al-Si alloys by an improved three-dimensional sharp-interface model
Ren, Zhe | Pu, Zhenpeng | Liu, Dong-RongComputational Materials Science, Vol. 203 (2022), Iss. P.111131
https://doi.org/10.1016/j.commatsci.2021.111131 [Citations: 7] -
A Moving Mesh Method for Kinetic/Hydrodynamic Coupling
Hu, Zhicheng | Wang, HeyuAdvances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 06 P.685
https://doi.org/10.4208/aamm.12-12S01 [Citations: 2] -
Aplicación del método level set para modelar el proceso de combustión premezclada en un motor Otto de dos tiempos
Lamas Galdo, M.I. | Rodríguez Vidal, C.G. | Rodríguez García, J.D.Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol. 29 (2013), Iss. 4 P.234
https://doi.org/10.1016/j.rimni.2012.06.003 [Citations: 0] -
3D level set methods for evolving fronts on tetrahedral meshes with adaptive mesh refinement
Morgan, Nathaniel R. | Waltz, Jacob I.Journal of Computational Physics, Vol. 336 (2017), Iss. P.492
https://doi.org/10.1016/j.jcp.2017.02.030 [Citations: 19] -
A hybrid level set–front tracking finite element approach for fluid–structure interaction and two-phase flow applications
Basting, Steffen | Weismann, MartinJournal of Computational Physics, Vol. 255 (2013), Iss. P.228
https://doi.org/10.1016/j.jcp.2013.08.018 [Citations: 18] -
A comprehensive review of modeling water solidification for droplet freezing applications
Akhtar, Saad | Xu, Minghan | Mohit, Mohammaderfan | Sasmito, Agus P.Renewable and Sustainable Energy Reviews, Vol. 188 (2023), Iss. P.113768
https://doi.org/10.1016/j.rser.2023.113768 [Citations: 8] -
Simulation of Incompressible Free Surface Flow Using the Volume Preserving Level Set Method
Yu, Ching-Hao | Sheu, Tony Wen-HannCommunications in Computational Physics, Vol. 18 (2015), Iss. 4 P.931
https://doi.org/10.4208/cicp.081214.240515s [Citations: 5] -
An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension
Zheng, Xiaoming | Lowengrub, JohnAdvances in Computational Mathematics, Vol. 42 (2016), Iss. 5 P.1225
https://doi.org/10.1007/s10444-016-9460-5 [Citations: 8] -
A conformal decomposition finite element method for arbitrary discontinuities on moving interfaces
Kramer, Richard M. J. | Noble, David R.International Journal for Numerical Methods in Engineering, Vol. 100 (2014), Iss. 2 P.87
https://doi.org/10.1002/nme.4717 [Citations: 20]