Journal of Visualization

, Volume 21, Issue 5, pp 819–834 | Cite as

Adjoint-enhanced flow visualization

  • Christopher Koehler
  • Ryan Durscher
  • Philip Beran
  • Nitin Bhagat
Regular Paper


This work presents a novel method of visually capturing the relative importance of different flow regions with respect to a quantity of interest. Existing flow visualization techniques are enhanced to convey flow importance. This is accomplished by filtering their output with additional information obtained from the adjoint counterpart of the physical flow field. The additional adjoint data is of equal resolution to the physical flow field. The adjoint flow data links physical fluid regions to user chosen quantities of interest. Thus, regions that are less relevant to the quantity of interest can be masked or deemphasized to reduce clutter and to highlight the behavior of the more important flow regions. The concept is demonstrated on a series of fluid simulations. The visualizations highlight the temporally changing importance of flow features, regions of influence in complex flows, and occlusion reduction in 3D flows. The method is also demonstrated by checking the impact of perturbations introduced in flow regions that were found to be both important and unimportant based on the adjoint data.

Graphical abstract


Flow visualization Sensitivity analysis Unsteady flow Adjoint Vortex dynamics Clutter reduction 



The early portion of this work was supported by the Air Force Office of Scientific Research under Laboratory Task 09RB01COR (monitored by Dr. Doug Smith).

Supplementary material

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Copyright information

© The Visualization Society of Japan 2018

Authors and Affiliations

  1. 1.Universal Technology CorporationDaytonUSA
  2. 2.US Air Force Research LaboratoryWright-Patterson Air Force BaseDaytonUSA
  3. 3.University of Dayton Research InstituteDaytonUSA

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