Structure-preserving or mimetic discretisations are a class of advanced discretisation techniques derived by employing concepts from differential geometry. Such techniques can attain specific conservation properties at the discrete level such as conservation of mass, kinetic energy, etc when applied to conservation laws. However, like traditional techniques, they are not entirely robust in specific multiscale cases such as under-resolved simulations which are often encountered in industrial applications. This ties into the concept of Large Eddy Simulations (LES) of which an enticing approach is the Variational Multiscale (VMS) method. Both Mimetic methods and VMS approaches have been extensively studied independently, however, their combination offers the potential of achieving a favorable robust solver capable of handling complicated industrial problems. Moreover, the extension of the Hybridised variant of the Mimetic methods towards advection-dominated problems is an interesting avenue yet to be explored. Therefore, this thesis focuses on the extension of the Hybridised Mimetic method and its combination with the VMS theory. The said combination is tested on simple linear equations, namely the advection-diffusion equation in both steady and unsteady cases. Additionally, the Hybridised Mimetic method is studied in more complex test cases such as the Burgers' equation and the incompressible Euler/Navier-Stokes equations.

Sustainability has become an increasingly important issue, and several different governments around the world have been working towards more environmentally friendly approaches throughout different industries. This has led to measures such as the European Green Deal, which aims to make Europe climate neutral by 2050. For the aircraft industry, however, this goal creates a so-called circular causality problem. This is because there may be limited investment in increasing production of alternative energy sources due to the limited availability of aircraft that use them. On the other hand airlines may hesitate due to the limited availability of fuel to buy such aircraft. In order to solve this problem, the carbon neutral ready aircraft has been proposed. The carbon neutral ready aircraft is designed such that it initially is powered by fossil fuels and can then be converted to be powered by a carbon neutral energy source. The carbon neutral energy source that is chosen for this aircraft design is synthetic kerosene. The carbon neutral aircraft has a high wing configuration with a high aspect ratio wing. To cope with the large span of the aircraft it was decided to give the aircraft the ability of the wing tips to be folded up. Furthermore, the wing has support struts which connect the wing to the lower part of the fuselage. The propulsion system of the aircraft has two novel features: two wing mounted ultra high bypass ratio turbofan engines and an electrically powered ducted fan, which ingests the boundary layer at the aft of the fuselage. An additional five-gear configuration was chosen for the landing gear to provide the aircraft with stable ground operations while not creating a need for a fairing which interferes with the boundary layer being ingested by the aft ducted fan. Carrying out the design of this aircraft shows that the aircraft is financially feasible and performs as well as the baseline A320 aircraft in terms of payload and range, while allowing sustainability goals such as the European Grean Deal to be met. The aircraft has a 17 % emission reduction compared to the A320neo, while still employing fossil fuel based kerosene. Furthermore, at least 90% by mass of the primary structure of the aircraft is recyclable. From the recommendations however, it is clear that a lot still needs to be done before the carbon neutral aircraft can enter into service in 2030.