Adjoint CFD Technology

Adjoint Optimisation Software Technology for Computational Fluid Dynamics.

ENGYS developers have implemented a continuous adjoint flow solver as part of HELYX. The methodology has been successfully employed to perform general topology and shape optimisation of real industrial applications, as described in more detail in the following original work:


  • E. de Villiers, C. Othmer, “Multi-objective Adjoint Optimization of Intake Port Geometry”, SAE World Congress 2012, Detroit, USA, SAE2012-01-0905
  • E. de Villiers, “Multi-Objective Adjoint Optimization of Flows in Duct and Pipe Networks”, Flow Problem Analysis in Oil & Gas Industry, Rotterdam, The Netherlands, 2011

The adjoint solver flow solution provides surface or volume sensitivities with respect to one or multiple objective cost functions, such as minimising drag, minimising pressure drop, maximising flow uniformity, etc. These sensitivities can be coupled with a standard optimisation algorithm to drive a surface-morphing tool or to penalise (remove) fluid cells from the domain. By modifying the shape or topology of the initial design or available fluid domain based on the sensitivities, an optimal solution can be achieved in a few solver iterations.

Explore our CFD Adjoint Services section for further information on current features and availability.

Related Links


De Villiers, E. "Adjoint Optimisation for Vehicle External Aerodynamics". JSAE 2015.


Othmer, C. "The Adjoint Method Hits the Road: Applications in Car Aerodynamics". Stanford University 2014.


Othmer, C. "Adjoint Methods for Cars Aerodynamics". Journal of Mathematics in Industry 2014.