High-order methods on mixed-element unstructured meshes for aeronautical applications

Higher resolution and reliability are the desiderata for Computational Fluid Dynamics and main drivers for the development, implementation and validation of highorder accurate methods. Complex fluid dynamic phenomena such as shock-wave boundary-layer interactions, turbulent separated flows and fluid problems involving multiple scales are adequately resolved with high-order schemes. The spatial representation of the flow field by an unstructured mesh provides flexibility, automation, fast and effortless grid generation and exceptional load balance on multiple processor computers. This plethora of advantages is mirrored by the unprecedented popularity of unstructured-based schemes. The objective of this PhD project is the implementation of two high-order schemes for the compressible Navier-Stokes equations in the context of the finite volume “kexact” framework: the MUSCL-TVD and WENO. The schemes are formulated in two and three space dimensions for mixed-element unstructured meshes; in addition, the Spalart-Allmaras turbulence model is implemented into the developed numerical framework. A wide range of applications are considered spanning from low-speed flows (M = 0.08) to supersonic conditions (M = 5.0); inviscid and viscous simulations in a broad spectrum of Reynolds numbers ranging from Re = 500 up to Re = 37×106. The applications include: the Taylor-Green vortex, the ONERA-M6 wing, flat plate, the NACA-0012 and the MD 30P-30N aerofoils, and a shock-wave boundary-layer interaction. For the examined cases, WENO schemes demonstrate superior accuracy, numerical dissipation and non-oscillatory behaviour over the MUSCL-TVD. High-order schemes inherit low numerical dissipation properties while turbulence models induce dissipation, this disequilibrium has adverse effects on the stability, convergence and accuracy of the simulation; therefore, turbulence model re-calibration would be required in order to accommodate high-order discretisation methods.