Background
Aerostructural interactions are extremely important in the design and safe operation of aircraft engines. Unsteady fluid flows through the engine can give rise to unwanted vibration in the engine through phenomena such as forced response and flutter. In turn, these can give rise to fatigue crack nucleation and propagation, resulting in increased maintenance costs and potential safety issues. Computational Fluid Dynamics (CFD) provides a means of modelling the fluid flows and the AU3D computer code has been developed at Imperial College over a number of years, principally by Prof. Mehdi Vahdati and his colleagues. Whilst such simulations have proved extremely valuable in understanding phemomena observed under test and in service, current methods suffer from a number of limitations:
 Simulations are timeconsuming to set up and run. Meshing of the fluid domain needs to be carried out and this mesh needs to be adapted as the engine structure moves. With large displacements this is not always possible.
 Current simulations are not fully coupled between the fluid and solid solvers. Resonant frequencies and mode shapes are determined in the solid solver without considering the effect of the fluid. These then serve as the boundary conditions for the fluids analysis. Hence, coupling only considers the effect of the solid on the fluid and not viceversa. A fullycoupled method would consider both effects.
 Modelling currently requires the fluid domain to be meshed in the traditional manner. More recent approaches such as the LatticeBoltzmann method do not require a mesh, but are not yet welldeveloped for high Reynolds numbers and compressible flow. If they can reach sufficient maturity they might offer distinct advantages over traditional methods.
Programme of work
The work undertaken was in two main areas: The use of meshless methods for high Reynolds number compressible flows was investigated and developed. Essentially this was a low Technology Readiness Level (TRL) activity. In the second area, a coupling interface was developed so that the AU3D code could interface with Imperial College’s nonlinear solids solver (FORSE).

Lattice Boltzmann Method
Research Student Sam Mitchell worked with RollsRoyce engineer Dr Bharat Lad to extend the use of LatticeBoltzmann methods to higher Reynolds numbers. The public domain code, OpenLB, was employed and its functionality was extended to high Reynolds numbers and thin aerofoils. This required new collision operators, solid wall boundary conditions and grid refinement. The new developments were validated on academic benchmarks and an application to the analysis of a thin double circular arc aerofoil was successful.
2. Higher Order Methods
Research student Vinko Jezerkic worked to implement a higher order method within the existing AU3D code. As currently used, AU3D is a 2nd order finite volume code, which has been extensively validated and which has dedicated aeroelastic analysis capabilities. It possesses an efficient edge based data structure, where the mesh nodes are centres of a volumetric cell. Accurate and stable implicit second order time integration is employed and parallel calculations are used with domain decomposition. Vinko reformulated the data structure to allow a higher order discretisation yet preserving the edge based approach. A hybrid method was used with a continuous Galerkin formulation inside a volume and discontinuous Galerkin between volumes. Efficient time integration is maintained using only mesh skeleton nodes.
3. Improved Meshing Approaches
A higher TRL method than those described above is to streamline the generation of fluid meshes. Rather than regenerating a complex mesh each time one is required, a Cartesian mesh is used and a cutcell approach is used where the mesh meets the boundary with a solid. A proof of concept has been developed with quasi 2D elements, and below you can see a comparison of solutions achieved with a body fitted mesh and a cartesian one with cuts. The standard mesh suffers from some loss of quality close to regions with large curvature, while the Cartesian cut cell maintains good behaviour.
4. FullyCoupled Solution Method
As described in the background section, there is a need to fully couple the fluid and solid solvers. Dr Fadi ElHaddad worked on this part of the Work Package, together with Drs Loic Salles and Ludovic Renson. The preexisting library, preCICE was used to provide the coupling and adapters were written to interface preCICE with AU3D and with FORSE. The advantage of this approach is that different codes can be used in future with a new adapter to preCICE being the only new software required.
 “COVID was as unwelcome in the CORNERSTONE project as it was everywhere else. It slowed progress in a number of ways but has not deflected us from the main objectives and neither has it undermined the value of the work.
 “Working from home unexpectedly caused some initial issues and resulted in some delays, but as the work package focussed on computational work, the closure of the laboratories and physical spaces had less of an effect on this work package as opposed to others.
 “.Two CORNERSTONE conferences proceeded notwithstanding (one fully virtual and one hybrid physicalvirtual) but the ability to visit between the universities was severely hampered. The consortium is extremely grateful to EPSRC for the accommodation of an extension in the end date of the award to April 2023. Without this accommodation, the negative effects would have been significant.”