| Abstract: |
| We present a boundary integral method for 3D interfacial Darcy flow with surface tension. We make several choices inspired by analytical work on well-posedness, including use of an isothermal parameterization of the free surface. The method uses a small-scale decomposition to remove stiffness, in the spirit of prior work by Hou, Lowengrub, and Shelley. In addition to showing results of the method as implemented, we will show some details of our proof of convergence of a version of the method. This includes joint work with Yang Liu, Nader Masmoudi, Michael Siegel, and Svetlana Tlupova. |
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