Sub-Grid Accuracy in Multi-Phase Flow Modeling

Dr. Jean-Christophe Nave

Massachusetts Institute of Technology, Department of Mathematics

The focus of this talk is the numerical solution of the two-phase incompressible Navier-Stokes equations. These equations have discontinuous coefficients and their solutions exhibit jumps in the pressure field and in gradients of the velocity field. Traditional methods aim at smearing discontinuities. However, when considering numerical approximations on a grid of finite resolution, the smearing approach leads to inaccurate solutions. I will give an overview of the issues encountered, and provide some solutions to systematically tackle these problems. Specifically, I will first present a novel gradient-augmented level set scheme to evolve the interface and second, a general approach to enforce sub-grid jump conditions to a high order of accuracy. The presented approach leads to several desirable computational features: high order, optimally local stencils, minimal modification of existing linear solvers, and sub-grid accuracy. Throughout this talk, we will motivate and illustrate the present approach using examples such as falling liquid films, partial coalescence, bouncing droplets on a soap film, and walking droplets on a parametrically excited bath.

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