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

Authors:
B. H. Bradshaw-Hajek;S. J. Miklavcic;D. A. Ward
Affiliations:
School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095, Australia;School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095, Australia and Department of Science and Technology, University of Linköping, S-601 74, Norrköp ...;School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095, Australia
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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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.