HELYX® Adjoint

Continuous adjoint CFD solver for topology and shape optimisation of complex engineering designs.

HELYX-Adjoint is a continuous adjoint CFD solver for topology and shape optimisation developed by ENGYS based on the extensive theoretical work of Dr. Carsten Othmer of Volkswagen AG, Corporate Research. The technology has been extensively proven and validated through productive use in real-life design applications, including: vehicle external aerodynamics, in-cylinder flows, HVAC ducts, turbomachinery components, battery cooling channels, among others.


The solver can deliver in a single flow solution both surface and volume sensitivities with respect to any combination of 15 pre-defined design objectives and target constraints, such as: minimisation of power losses, maximisation of flow uniformity, minimisation of drag force, maximisation of turbomachinery efficiency, maximisation of flow rate, equalisation of flow split across multiple outlets, etc.


For topology optimisation, the volume sensitivities calculated from the mean flow are employed to penalise "bad" regions of the existing volume domain to achieve an optimal design. The geometry interface is automatically shrunk using an advanced level set approach with immersed wall boundaries to provide a smooth optimised surface suitable for CAD manipulation or 3D printing/prototyping. 


For shape optimisation, the surface sensitivities with respect to a specific combination of objective functions are used to construct a design map which can then be employed to morph the original geometry as needed to improve performance and reach a more optimal solution.


Some other unique features of HELYX-Adjoint include:


  • Single solver execution
  • Similar hardware and memory requirements to standard flow simulations
  • Fully supported in the graphical user interface
  • Multi-objective
  • 2nd order adjoint convection for improved accuracy
  • Sensitivities calculated from RANS and DES/LES primal calculations   

The continuous adjoint add-on solver module developed by ENGYS is released under the GNU General Public License and it is available in different versions for both HELYX and ELEMENTS, depending on your specific application. For further information about this extension module please contact us today or speak to one of our local sales representatives.

Related Links


De Villiers, E. et.al. "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.



Related Videos


Adjoint surface sensitivities with respect to drag on a passenger vehicle (DRIVAER car model courtesy of TUM).



Adjoint topology optimisation of HVAC duct with respect to power losses (courtesy of Volkswagen).



Multi-objective adjoint topology optimisation with resspect to power losses and flow uniformity.