Axisymmetric boundary integral formulation for a two‐fluid system |
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| Authors: | M Garzon L J Gray J A Sethian |
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| Institution: | 1. Department of Applied Mathematics, University of Oviedo, , Oviedo, Spain;2. Mathematics Department, Lawrence Berkeley National Laboratory, University of California Berkeley, , Berkeley, CA, USA;3. Computer Science and Mathematics Division, Oak Ridge National Laboratory, , Oak Ridge, TN, 37831 USA;4. Department of Mathematics, University of California Berkeley, , Berkeley, CA, USA |
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| Abstract: | A 3D axisymmetric Galerkin boundary integral formulation for potential flow is employed to model two fluids of different densities, one fluid enclosed inside the other. The interface variables are the velocity potential and the normal velocity, and they can be solved for separately, the second linear system being symmetric. The algorithm is validated by comparing with the analytic solutions for a static interior spherical drop over a range of values for the relative densities  of exterior and interior fluids and various boundary conditions. For time‐dependent simulations utilizing a level set method for the interface tracking, the accuracy has been checked by comparing against the known oscillation frequency of the sphere. Pinch‐off profiles corresponding to an initial two‐lobe geometry drop and D = 6 are also presented. Published in 2011 by John Wiley & Sons, Ltd. |
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| Keywords: | axisymmetric Laplace two fluids boundary integral equation Galerkin approximation |
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