An adjoint method for control of liquid-gas flows using a sharp interface model

Lam Vu, Alexandru Fikl, Daniel J. Bodony, Olivier Desjardins

Research output: Contribution to journalArticlepeer-review


We present a computational, continuous adjoint framework for the control of liquid-gas flows using a sharp interface model. The two-phase Navier–Stokes equations are solved using a mass-conserving geometric Volume-of-Fluid method, while the adjoint equations consider a level set-based representation of the interface. To facilitate the accurate transport of a surface adjoint variable, a geometric surface transport method is formulated and applied. We verify our method by comparing adjoint-calculated gradients against analytical gradients or finite difference approximations. The method is then applied to a variety of benchmark two-phase flow problems, including the multi-dimensional inflow control of droplet position and optimal control of the initial velocity profile in a temporally evolving liquid-gas mixing layer.

Original languageEnglish (US)
Article number112057
JournalJournal of Computational Physics
StatePublished - Jul 1 2023
Externally publishedYes


  • Adjoint method
  • Control theory
  • Liquid-gas flows
  • Volume-of-fluid method

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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