Mixing and Mixtures in Geo- and Biophysical Flows: A Focus on Mathematical Theory and Numerical Methods

Convergence of a boundary integral method for 3D interfacial flow with surface tension

David Ambrose

Drexel University


A non-stiff boundary integral method for computing 2D interfacial flows with surface tension was developed by Hou, Lowengrub, and Shelley (HLS). Important elements of the HLS method are the choice of geometric dependent variables, the choice of a favorable parameterization, and the identification of leading-order terms to treat implicitly in the time-stepping. Furthermore, Hou and Ceniceros have proven convergence of such methods. We make a generalization of some aspects of these works to 3D: For a 3D interfacial flow with surface tension with fluid velocities given by Darcy's Law, we develop a non-stiff boundary integral method, and we prove that a version of this method converges.