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Adaptive mesh refinement techniques for the immersed interface method applied to flow problems
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DOI：10.1016/j.compstruc.2013.03.013.png)
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Abstract
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In this paper, we develop an adaptive mesh refinement strategy of the Immersed Interface Method for flow problems with a moving interface. The work is built on the AMR method developed for two-dimensional elliptic interface problems in the paper [12] (CiCP, 12(2012), 515-527). The interface is captured by the zero level set of a Lipschitz continuous function phi(x,y,t). Our adaptive mesh refinement is built within a small band of vertical bar phi(x,y,t)vertical bar <= delta with finer Cartesian meshes. The AMR-IIM is validated for Stokes and Navier-Stokes equations with exact solutions, moving interfaces driven by the surface tension, and classical bubble deformation problems. A new simple area preserving strategy is also proposed in this paper for the level set method. (C) 2013 Elsevier Ltd. All rights reserved.
Keywords:
Adaptive mesh refinement method
Immersed interface method
Stokes and Navier-Stokes equations
Surface tension
Bubble deformation
Level set method
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