Applications: Adjoint Optimisation Course

This training is suitable for CFD engineers seeking a reliable tool for shape optimisation. It covers theoretical and applied concepts related to the use of the adjoint method in aerodynamic and hydrodynamic shape optimization using OpenFOAM.

Both the computation of the so-called sensitivity maps and the full optimisation process will be covered, including shape and mesh morphing. The theoretical background is accompanied by hands-on training focusing on the set-up of the OpenFOAM adjoint solver, discussing its capabilities and following the steps required to perform a shape optimisation loop.

The first part of the course introduces the continuous adjoint method applied to fluid mechanics with a focus om the key features that make it a valuable tool for industrial problems.

The course is organised with collaboration of leading experts in the development of continuous adjoint methods in aerodynamics, with a rich portfolio of applications in internal and external aerodynamics, e.g. cars, aircraft, turbo machinery, from the group of Prof. K.C. Giannakoglou, National Technical University of Athens (NTUA).

The training provides examples of process and best practice, useful to existing OpenFOAM users wishing to broaden their application knowledge of OpenFOAM towards adjoint-based optimisation.

Topics Covered

  • The continuous adjoint in the Official release of OpenFOAM
  • Introduction to the continuous adjoint method. Examples relating to 1D flow of incompressible fluids
  • Interpretation of the adjoint fields
  • Development of the continuous adjoint method in multi-dimensional flows
  • Handling of various objective and constraint functions
  • Adjoint methods for turbulent flows
    • The adjoint to the Reynolds-Averaged Navier-Stokes equations
    • Adjoint to the Spalart-Allmaras turbulence model
  • Continuous adjoint methods and grid sensitivities
  • Use of sensitivity maps
  • Workflow for automated shape optimization loops
  • Example applications for internal and external flows

Course details


Participants undertake exercises in simulating cases and programming in OpenFOAM using ESI’s Cloud-based HPC computing platform, accessed via a secure ssh connection between desktop PCs (provided) or participants laptops, applicable to all operating systems. All work from the training will be stored on the cloud and participants may download all the work and exercises on their USB flash drives at the end of the training.


For online courses, users will receive a printable pdf with a manual containing the course presentation and additional materials.
Classroom attendees will receive a high-quality, A5-sized (80-100 page) wire-bound manual containing the course presentation and additional materials.
Please note: registration and payment for classroom courses must be completed at least 10 days in advance of the training date to allow sufficient time for material delivery.


The language used in all OpenFOAM courses is English. Translations or delivery in French, German, Italian, Spanish, Chinese, Japanese and Korean languages are available on request.

Course times

The course is 2 days in duration and usually runs from 09.00 to 17.30 (local time for classroom training, CET for virtual training) each day.

Target audience

This Adjoint-based Optimisation course is suitable for existing users of OpenFOAM seeking to broaden their application knowledge, background knowledge and CFD best practice knowledge for CFD-based shape optimisation and the use of sensitivity maps.


Prior knowledge of OpenFOAM and Linux command line via the Foundation course or similar is necessary. Users should be able to:

  • Create a new case in OpenFOAM for simple incompressible flow
  • Set the boundary conditions and main numerical parameters
  • Run the simulation in parallel regime
  • Post-process the case in ParaView