Topology optimisation of transient turbulent compressible flow

Journal article

Purpose: We present the first topology optimisation formulation for transient turbulent compressible flow modelled with the unsteady Favre-averaged Navier–Stokes equations.

Design/Methodology/Approach: The topology to be designed is incorporated in each of the momentum balance, the energy balance, and the turbulence closure. The forward and adjoint equations are implemented with different discretisations: the forward model with a finite volume method, and the adjoint model with a discontinuous Galerkin finite element scheme, since the former is very robust and the latter can be adjoined automatically. Once discretised, the topology optimisation problem is solved with an integer linear programming algorithm. We demonstrate the capability of our approach in the design of a U-bend, a pipe joint, and a double pipe joint.

Findings: The formulation is developed and demonstrated through numerical examples, showcasing the developed approach.

Originality/Value: No previous topology optimisation formulation was available for transient turbulent compressible flow modelled with the unsteady Favre-averaged Navier–Stokes equations.

Authors: Farrell, P

• Publication status: Accepted
• Peer review status: Peer reviewed
• Publisher: Emerald
• Journal: International Journal of Numerical Methods for Heat and Fluid Flow
• Acceptance date: 2026-05-01
• EISSN: 1758-6585
• ISSN: 0961-5539
• Language: English
• Keywords: fluid topology optimisation; discontinuous Galerkin; transient flow; turbulent flow; compressible flow