Abstract
Abstract
Highlights
In this article we develop and apply an adjoint-based approach for controlling incompressible two-phase flows with sharp interfaces governed by the Stokes equations
We have presented a derivation of the adjoint equations and adjoint-based gradient for two multiphase flow problems with a sharp interface
The main difficulty in handling sharp interfaces lies in the fact that the problem variables are not shape differentiable over the whole domain and must be considered separately over each fluid domain
Summary
In this article we develop and apply an adjoint-based approach for controlling incompressible two-phase flows with sharp interfaces governed by the Stokes equations. In the case of incompressible two-phase flows with a sharp interface, a commonly used formulation is the so-called one-fluid model (see Prosperetti & Tryggvason 2009) In this model, the velocity and pressure are considered as variables over the whole domain, e.g. p αp+ + (1 − α)p−, where α is an indicator function. The current work can provide a starting point for the adjoint-based optimization of higher Reynolds number multiphase flows governed by the incompressible Navier–Stokes equations. The current method requires the more complex shape calculus to handle the sharp discontinuities explicitly, but the resulting gradients are not quickly varying and the optimization is shown to be well behaved.
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