A composite Level Set and Extended-Domain-Eigenfunction Method for simulating 2D Stokes flow involving a free surface

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Abstract

In this paper, the Extended-Domain-Eigenfunction-Method (EDEM) is combined with the Level Set Method in a composite numerical scheme for simulating a moving boundary problem. The liquid velocity is obtained by formulating the problem in terms of the EDEM methodology and solved using a least square approach. The propagation of the free surface is effected by a narrow band Level Set Method. The two methods both pass information to each other via a bridging process, which allows the position of the interface to be updated. The numerical scheme is applied to a series of problems involving a gas bubble submerged in a viscous liquid moving subject to both an externally generated flow and the influence of surface tension. © 2012 Elsevier B.V. All rights reserved.

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Bradshaw-Hajek, B. H., Miklavcic, S. J., & Ward, D. A. (2013). A composite Level Set and Extended-Domain-Eigenfunction Method for simulating 2D Stokes flow involving a free surface. Journal of Computational and Applied Mathematics, 237(1), 389–402. https://doi.org/10.1016/j.cam.2012.06.009

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