Many practical applications imply the solution of free boundary value problems. If the free boundary is complex and can change its topology, it will be hard to solve such problems numerically. In recent years a new method has been developed, which can handle boundaries with complex geometries. This new method is called the level set method. However, the level set method also has some drawbacks, which are mainly concerning conservation of mass or numerical instabilities of the boundaries. Our aim is to analyze some aspects of the level set method on the basis of two‐phase flow in a Hele‐Shaw cell. We investigate instabilities of two‐phase flow between two parallel plates. A solution of the linearized problem is obtained analytically in order to check whether the numerical schemes compute reasonable results. The developed numerical scheme is based on finite difference approximations and the level set method. The equations of two‐phase Hele‐Shaw flow are written in a modified formulation using the one‐dimensional Dirac delta‐function. Since the level set function is not smooth enough after re‐initialization, special attention during the computation of curvature is needed. We propose a method that can solve the problems for two‐phase Hele‐Shaw flow with changing topology. The numerical solution shows good agreement with the analytical solution of the linearized problem. We describe the method below and analyze the results.
Moog, M., Keck, R., & Zemitis, A. (1998). Some numerical aspects of the level set method. Mathematical Modelling and Analysis, 3(1), 140-151. https://doi.org/10.3846/13926292.1998.9637097
Authors who publish with this journal agree to the following terms
that this article contains no violation of any existing copyright or other third party right or any material of a libelous, confidential, or otherwise unlawful nature, and that I will indemnify and keep indemnified the Editor and THE PUBLISHER against all claims and expenses (including legal costs and expenses) arising from any breach of this warranty and the other warranties on my behalf in this agreement;
that I have obtained permission for and acknowledged the source of any illustrations, diagrams or other material included in the article of which I am not the copyright owner.
on behalf of any co-authors, I agree to this work being published in the above named journal, Open Access, and licenced under a Creative Commons Licence, 4.0 https://creativecommons.org/licenses/by/4.0/legalcode. This licence allows for the fullest distribution and re-use of the work for the benefit of scholarly information.
For authors that are not copyright owners in the work (for example government employees), please contact VILNIUS TECHto make alternative agreements.
