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 adjoint solver can deliver in a single flow solution both surface and volume sensitivities with respect to any combination of several 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.

Topology Optimisation

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.

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

​Some unique features provided with HELYX-Adjoint include:

Single primal+adjoint solver execution: reduce setup and simulation times.
Similar memory and hardware requirements to standard flow simulations: optimise large models (100+ million cells) without limitations.
Fully supported in HELYX-GUI: for simplified ease-of-use.
Multi-objective optimisation with constraints: optimise any model using multiple objectives and constraints at the same time.
2nd order adjoint convection: for improved numerical accuracy.
Sensitivities calculated from RANS and DES/LES primal calculations: to take advantage of steady-state and transient flow solutions.


Shape Optimisation

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.

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


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.


Want to Buy?

The continuous adjoint add-on solver developed by ENGYS is released under the GNU General Public License and it is available for both HELYX and ELEMENTS, depending on your specific applications. For further information about HELYX-Adjoint features, availability and prices, please contact us today or speak to one of our local sales representatives.

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